Appendix One

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Appendix One

On Ancient Roots of Perspective

n this appendix, I discuss how some of the ancient Greek sciences may Ihave influenced the convention of drawing in antiquity as well as the development that led to the emergence of linear perspective in the Renaissance. The sciences considered are the geometrical theory of optics, methods of making maps of the earth and sky, and scenography. The protagonists are, in chronological order, Plato, Euclid, Vitruvius, Ptolemy, and Proclus.

Optics

The Visual Pyramid and the Angle Axiom s mentioned in the introduction, the discipline now known as perspective Agot its name from optics (page xx). The two subjects are, however, inter- twined by more than mere etymology, most notably by the theory of vision. A basic concept within the latter theory is that of a visual cone whose apex is in the eye point of an observer and contains all the light rays connecting an object and the eye point – the rays being considered as straight lines. When introducing his model for a perspective representation, Alberti, as we have seen, took over this concept, calling it a visual pyramid (page 19). A central part of the theory of vision deals with appearances. For this theory Euclid introduced a fundamental axiom called the angle axiom. Although it has been discussed earlier, I will nevertheless repeat it here: Magnitudes seen within a larger angle appear larger, whereas those seen within a smaller angle appear smaller, and those seen within equal angles appear to be equal. [Translated from EuclidS Optics/1959, 1] The angle axiom implies that the size of the image of a line segment can be determined by measuring the length, seen from the eye point and placed at the location of the picture plane, that covers the line segment. Present-day draughtsmen sometimes apply this result by measuring the length of an image with a pencil. It is quite possible that something similar was done in antiquity, and that the procedure was seen as a consequence of the angle axiom. Perspective was introduced by Alberti as a section in a visual pyramid – corresponding to a central projection upon a plane – and the core problem in

723 724 Appendix One perspective was how to construct such a section. The idea of a section does not occur in Euclid’s optical theory, his aim being to account for visual appearances and not for projections. Irrespective of this, his theory may well have been used for pictorial representations, for instance, as just suggested, to determine the length of the image of a line segment.

The Remoteness Theorem espite the absence of projections in Euclid’s work, the most widely used Dversion of his Optics contains a consideration that, to some degree, resem- bles a projection. This consideration is part of a proof for the following result, which I call the remoteness theorem:1 The more remote parts in planes situated below the eye appear higher. [Translated from ibid., 8] Although Euclid formulated this theorem generally about objects situated in planes below the eye point O (figure 1), he restricted his example to deal with three points, A, B, and C, lying on a horizontal line below O, proving that BC appears to be higher up than AB. The currently known proof introduces a line perpendicular to AC intersecting the visual rays OA, OB, and OC in D, E, and F, respectively. It is then argued that because F is situated higher than E, and E higher than D, and because BC is seen between the lines OC and OB, and AB is seen between the lines OB and OA, the line segment BC appears to be situated higher than AB. The line DF can be interpreted as representing a plane of projection, but in the proof its function was to get the rays OA, OB, and OC orientated with respect to above and below. The important thing in the proof was that AB is seen within the angle DOE, not that it is projected upon DE.

AB C

FIGURE 1. Euclid’s remoteness theorem.

1In current editions of Euclid’s Optics, this is theorem 10, but according to David C. Lindberg it was number 11 in the edition most likely used in the early fifteenth century (LindbergS 1976, 264, note 23). Ancient Roots of Perspective 725

Wilbur Knorr has convincingly argued that the intersecting line is a later addition, and that Euclid’s original proof was different (KnorrS 1991, 195–197). Knorr’s findings are, of course, an important support for the idea that Euclid did not think of projections in his Optics. Nevertheless, it is still possible that practitioners and theorists in antiquity thought that the practice of drawing more remote things higher up in a picture was an application of the remoteness theorem. The edition of Euclid’s Optics known in the Renaissance contains the proof of the remoteness theorem that I have just paraphrased. It may be, as suggested by Samuel Edgerton, that the proof, and in particular its accompanying diagram, influenced Alberti in creating his construction of the image of a square (EdgertonS 1966, 373), but he could as well have been inspired by something else.

The Convergence Theorem he optical theory considered thus far is in agreement with perspective in Tthe sense that the optical results also apply for a perspective projection. Throughout history, however, scholars and painters have also used arguments from the theory of appearances that are not valid in the theory of perspective. There seem to be two reasons for this application, the one being that in some cases a discrepancy between the two theories was not observed. The other rea- son was that, as noted elsewhere, some perspectivists considered perspective to be a science used for reproducing a visual impression (pages 111, 559, 619). The most famous example of an optical result that is not compatible with the theory of perspective is the following result from Euclid’s Optics, which I call the convergence theorem. Parallel lengths, seen from a distance, appear not to be equally distant from each other. [Translated from EuclidS Optics/1959, 4] Euclid considered two parallel lines and looked at the cases in which the eye point is either in the plane of the parallel lines or above them. In the first case he implicitly assumed that the eye point lies between the parallel lines, and in the second that its projection upon the plane of the parallel lines falls between them (figure 2). To prove his claim, Euclid introduced line segments lying on normals to the two parallel lines and having their end points on the two lines, and then showed that the visual angles determined by the eye point O and these line segments decrease as the distance between the eye and the normals increases. The angle AOB is thus larger than the angle COD, which is in turn larger than the angle EOF, and so forth. Because the visual angles become smaller and smaller, the two parallel lines seem to converge. The convergence theorem may, at first, seem to be in accordance with the vanishing point theorem. A closer examination shows, however, that this accordance is not complete because Euclid’s result is only valid for situations in which the eye point, or its projection upon the plane of the parallel lines, lies between the two parallel lines. Thus, if we apply Euclid’s method of argumentation to an eye point in another position, we end up with different results for how the 726 Appendix One

AC E G

BD F H

O E

C H A F

FIGURE 2. Euclid’s convergence theorem. In the upper diagram the eye point and the parallel lines are situated in the same plane, and in the lower the eye point lies above the plane of the parallel lines. parallel lines appear and how they should be drawn in perspective. In the early eighteenth century, Humphry Ditton phrased the visual result as follows: If the Eye be seated anywhere without the Parallels, they will seem to go further from each other (or their Intervals to widen) to a certain Term of Distance; and after that continually to approach each other. [Ditton 1712, 17] In other words, some sections of the two parallel lines appear to diverge, while other parts appear to converge2 – implying that the lines appear as curves. This conclusion is obviously different from the result obtained by the rules of perspective, according to which the images of the two parallel lines (when neither of them passes through the eye point) are either two converging straight lines or two parallel lines. The convergence theorem is not the only case of non-corresponding results in the theories of vision and perspective, but this one example suffices to show that the different aims of two disciplines may also lead to different results.3 Although it is conceptually important to be aware of the fact that some optical results cannot be applied in perspective, it is historically less relevant because this insight may not have existed in earlier times. It is therefore quite possible that the convergence theorem inspired some drawers in antiquity and other drawers during the Renaissance to depict orthogonals as converging lines.

2 S For an argument supporting this conclusion, see Andersen 19872, note 4. 3Another often-discussed example is proposition 8 in Euclid’s Optics and its seeming conflict with the law of inverse proportionality, which was discussed in chapter III (page 95). Ancient Roots of Perspective 727

Optics and Perspective in Harmony ome historians have seen optics and linear perspective as two conflicting dis- Sciplines. Erwin Panofsky’s influential paper Die Perspektive als symbolische Form (Perspective as symbolic form) has undoubtedly contributed significantly to this opinion. In discussing classical optics, Panofsky concluded that it was antiplanperspektivisch (“antithetical to linear perspective”, PanofskyS 1927/1991, 264/35). Panofsky’s point of view has been questioned by some scholars, among them C.D. Brownson, who, in arguing in favour of the compatibility of the two disciplines, focussed much upon their similarities (BrownsonS 1981). For the present purpose, the arguments on the relationship between optics and linear perspective need not to be discussed further. It is sufficient to be aware that some parts of the theory of appearances were fruitful for perspective by providing, as pointed out by David C. Lindberg, a mathematical skeleton for perspective (LindbergS 1976, 154) – while other parts were of no use for perspective, as I just noted. The circumstance that some optical results are not applicable to perspectival representations does not mean that the two disciplines are in disharmony. As Brownson, too, pointed out, a conflict only arises if one requires perspective to reproduce what the eye sees (BrownsonS 1981, 189). As stressed earlier, this requirement does, indeed conflict with what most perspectivists considered to be the aim of their discipline, namely to produce an image of a tableau that has the same effect on the eye as the tableau itself.

Cartography

o construct, on a flat surface, a map of a section of a spherical surface Tmeans establishing a correspondence, called a projection or a mapping, from the surface of the sphere to a plane. The ideal mapping would be one that preserves angles and lengths, but such a mapping does not exist. Down through the ages cartographers have searched for mappings with properties near to the ideal. These do not include a central projection, because it dis- torts either angles, or lengths, or both. Nevertheless, there are two ancient examples of applying a central projection to create maps.

Ptolemy’s Geography n his Geography Ptolemy described three methods of constructing maps. The Ilast of these is technically a very complicated procedure, which, as one of its several steps, involves a central projection (for technical details, see NeugebauerS S S S 1959, Andersen 19873, Berggren 1991, and Ptolemy Geo, 38–40). Edgerton has suggested that the arrival in Florence of the manuscript of Ptolemy’s Geography, and the eagerness with which the quattrocento scholars studied it, may have influenced Brunelleschi and Alberti in their perspective investigations (EdgertonS 1975, 93–120). Considering how difficult Ptolemy’s 728 Appendix One text is, I do not find this very likely (an opinion also expressed in KempS 1978 and VeltmanS 1980). Ptolemy’s Planisphaerium tolemy’s oeuvres offer a much more straightforward central projection than Pthe one from his Geography, namely a stereographic projection presented in a work that was translated into Latin from an Arabic manuscript in the mid- twelfth century and became known as the Planisphaerium. As described in chapter IV, in this work Ptolemy obtained a representation of the celestial sphere on the plane of the equator by means of a central projection from the south pole (page 139). This could have been a source of inspiration for perspectival representation, but there is no indication that this was the case. As far as I am aware, the first one to comment upon the connection between Ptolemy’s stereographic projection and perspective was Federico Commandino in 1558 (page 140) – long after the emergence of geometrical perspective. Scenography

t has often been discussed whether drawing in ancient Greece and Rome Iwas based on rules, and if so whether these rules were related to any theory. Unfortunately there is very little material that can help us to find an answer. One sign that some ancient theorists reflected on how to draw is the existence of a discipline called scenography. In his De architectura from the first century B.C.E., Vitruvius – having presented ichnography and orthography – wrote: Item scaenographia est frontis et laterum abscedentium adumbratio ad circinique cen- trum omnium linearum responsus. [VitruviusS Arch, book I, chapter 2, §2] Later in the work he hinted that scenography is related to the theatrical stage design and reported that Democritus and Anaxagoras showed how ad aciem oculorum radiorumque extentionem certo loco centro constituto, ad lineas ratione naturali respondere, uti de incerta re incertae4 imagines aedificiorum in scaenarum picturis redderent speciem et, quae in directis planisque frontibus sint figurata, alia absce- dentia, alia prominentia esse videantur. [VitruviusS Arch, book VII, preface, §11] These two descriptions have been interpreted and translated in a variety of different ways.5 Some have taken the centre mentioned in the first quotation

4Some copies have incertae and others certae. 5Inspired by Christian Wiener’s and John White’s translations (WienerS 1884, 8; WhiteS 1987, 251), I suggest the following interpretations: Likewise, scenography is the drawing of the outline of the front and of the receding sides and the representation of all the lines to the centre of a circle [literally: a pair of compasses]. ... when the centre is fixed at a certain place, the lines must correspond naturally to the sight of the eyes and the extension of the rays, so that images of an object render the appearance of buildings in the stage paintings, and so that which is shaped upon vertical and frontal planes is seen as partly receding, and partly projecting. For alternative suggestions, see PanofskyS 1927/1991, 38, and notes 18 and 19. Ancient Roots of Perspective 729 to mean a vanishing point, while the certo loco centro introduced in the second quotation has been understood as referring either to an eye point or a vanishing point. Panofsky has criticized his predecessors’ way of reading the text and instead suggested an interpretation that is in accordance with the angle axiom (PanofskyS 1927/1991, 266/38). Despite the various interpretations, it seems safe to assume that Vitruvius described a procedure for making stage sets that looks “natural”. However, as long as we do not have more source material it is fairly hopeless to reconstruct the technique he had in mind. In the fifth century Proclus commented upon the first book of Euclid’s Elements. In a prologue, Proclus described the virtues of mathematics and touched in this connection upon scenography. His description has also been interpreted in rather different ways.6 He presented scenography as a part of optics, and it seems he related the topic to a concern that an image should not seem disproportionate. We cannot be sure that Vitruvius and Proclus meant exactly the same thing by scenography. Proclus apparently did not describe a central projection, but a representation that somehow took the angle axiom into account. This fits in with his great affinity for Plato, and with the fact that in his Sophist, Plato described how, in some large sculptures and paintings, objects are not reproduced in their true proportions, because this would make the upper parts seem too small (PlatoS Soph, 236A). Most likely, Plato referred to the procedure we met in Dürer’s illustration Dürer (figure III.16, page 99), that is, representing highly elevated objects in a larger scale than lower objects of the same height so that the objects will be seen within equal angles. As I have already stressed, it is more difficult to know which technique Vitruvius was describing. It may have involved points of convergence for orthogonals lying in the same plane, or even a common convergence point for all orthogonals. As John White documented, a few examples from antiquity document the practice of using points of convergence for orthogonals in the same plane (WhiteS 1987, 258–267). In general, different points of convergence were used for different planes, but there is one case in which it strongly looks as if almost all orthogonals are converging towards one and the same point (figure 3).

6The translations include the following: ... die zeigt, wie es zu erreichen ist, dass in den Bildern dargestellten Dinge nicht als ver- worrene und verzerrte Gebilde erscheinen, sondern der Entfernung und Grösse der dargestellte Objekte entsprechen. [P. Leander Schönberger and Max Steck in ProclusS Comm/1945, 191] ... qui enseigne à faire voir dans des images des aspects non déformés ni disproportionnés par les distances et par la hauteur des dessins. [Paul ver Eecke in ProclusS Comm/1948, 34–35] ... showing how objects can be represented by images that will not seem disproportionate or shapeless when seen at a distance or an elevation. [Glenn R. Morrow in ProclusS Comm/1970, 33] 730 Appendix One

FIGURE 3. Wall painting in the “Room of the Masks”, right-hand wall in the House of Augustus, Palatine Hill, Rome. First century B.C.E.

Conclusion s there is such a paucity of factual knowledge about procedures of draw- Aing in antiquity, it becomes a matter of personal discretion how much theory one ascribes to the ancient art of drawing. In my view, it is more than likely that some results from optics were applied in the practice of drawing. I do not think, however, that practitioners and theoreticians pooled their requirements and insights to create a complete theory of drawing. This task was left to Renaissance artists and scholars. As it turned out, all the concepts they needed, and actually also all the geometry required for developing a mathematical theory of perspective, were available as an inheritance from ancient Greece. The question of what inspired the introduction of a perspectival projection in the Renaissance is as difficult to address as the matters dealt with in this appendix – but the problem is discussed in chapter I. Appendix Two

The Appearance of a Rectangle à la Leonardo da Vinci

In this appendix, I investigate how well Leonardo da Vinci’s answer to the question of “whether a vertical rectangle appears as rectilinear or curvilinear” (page 796) agrees with the theory he applied. In deciding on how a rectangle appears, Leonardo seems to have conceived of it as composed of an infinity of vertical line segments. To handle this idea mathematically, I introduce a movement and imagine that the rectangle ABCD (figure 1) has been produced by a moving line segment that starts in the position AB and ends as DC. I would like to apply Leonardo’s own mathematical tool – that is, the law of inverse proportionality – and to do so I begin with the situation in which the orthogonal projection of the eye point upon the rectangle is the point A. Setting OA = a, AD = x, and OD = y,I deduce from Pythagoras’s theorem that

yax=+22, and from relation (iii.1) that the apparent ratio between the two sides AB and CD is

vv(,ya )=+=+ ( a22 x , a ) a : a22 x. Taking the apparent size of AB as a unit, I define the apparent size of DC as a (x) = s (y,a),

a D

O B

FIGURE 1. The apparent size of DC as a function of DC’s distance, x, to AB. C

731 732 Appendix Two

B' C'

FIGURE 2. Introduction of the lines BC and B′C′.

implying that

a ()xaax=+ :22 . (1) This relation shows that when DC’s distance x to AB increases, the apparent size of DC decreases, as claimed by Leonardo, but it also shows that, con- trary to what he believed, the decrease is not linear. In the following I elaborate on what relation (1) actually shows. Let us assume (figure 2) that an eye is looking at the lines BC and B′C′ parallel to and at equal distance from the line AD, and that the orthogonal projection of the eye point upon the plane of the figuration falls in A. Following Leonardo, we want to find the apparent shapes of the lines BC and B′C′. When it is assumed that the line AD is seen as a straight line, a(x) in relation (1) provides for each x the apparent distance from AD of a point on BC,or, in other words, the collection of points on BC will be seen as a curve whose equation is given by (1).1 The same argument shows that the apparent shape of B′C′ is a curve symmetrical to the first with respect to the line AD. Equation (1) also shows that the graphs of these curves are dependent on the viewing distance a.

The Curves for Three Different Distances o see how well Leonardo’s solution approximates the mathematical solu- Ttion, I look at the curves defined by relation (1) for three different values of a. Returning to the situation outlined in figure 1, I have illustrated in figure 3 a horizontal section through the point A containing three eye points O1, O2, and O3 corresponding to the three values of a. Taking, as before, the line segment AB in figure 1 as the unit, I have depicted the situation in which the

1Provided it is accepted as a premise that the law of inverse proportionality is valid and can be applied as I do. Leonardo da Vinci’s Rectangle 733

AR S T

O 1

O 2

O 3

FIGURE 3. Different viewing distances from the line AD, depicted in figure 1.

distances a between A and the three eye points O1, O2, and O3 are 1, 3, and 10, and the maximum viewing angle is 90˚. Thus the points R, S, and T are the points of intersection between the transversal through A and the horizontal diagonals through O1, O2, and O3. In figures 4–6, for points in the interval [−a,a] and for a equal to 1, 3 and 10, I have drawn the curves defined by equation (1) – that is, the supposed apparent graphs of the lines BC and B′C′ both to the right and left of B and B′. Leonardo himself drew these apparent lines as two straight lines sloping towards the line AR at both ends (figure III.12). My figures show, among other things, that: The smaller a is, the more the curve deviates from two straight lines. Each of the considered sections of any of the curves does, however, lie near two straight and symmetrical lines – except in an interval around

FIGURE 4. The curvilinear appearance for a = 1. 734 Appendix Two

AR S

FIGURE 5. The curvilinear appearance for a = 3.

AR S T B

FIGURE 6. The curvilinear appearance for a = 10.

the midpoint. Thus, Leonardo’s intuitive solution is, to some extent, in accordance with the mathematical solution.*

The Angle Between the Line Segments n a different manuscript from the one in which he discussed whether a rec- Itangle would appear rectilinear or curvilinear, Leonardo stated that the angle between his two line segments in his figure (reproduced as figure III.12) increases with an increasing viewing distance (Manuscript G, fol. 32r; S Veltman 19861, 158–159). He did not give any argument for this result. Perhaps he thought that the longer the distance to a rectangle, the less it would appear distorted. At any rate, his conclusion is in accordance with what my curves demonstrate. Thus, when a is equal to 1, the angle between the almost linear parts of the curve is smaller than the corresponding angle for a equal to 3, and this is in turn smaller than the angle for a equal to 10.

*I am thankful to Hans Anton Salomonsen for having drawn the curves in this and the two previous figures. Appendix Three

’sGravesande Taking Recourse to the Infinitesimal Calculus to Draw a Column Base in Perspective

his appendix is devoted to describing how ’sGravesande applied his Tknowledge of the calculus to solve an intricate problem of determining the visible part of the column base shown in figure VII.61 (page 356, ’sGravesande 1711, §§65–68). Initially (figure 1), ’sGravesande considered the quarter ABCDE of a vertical section of the column base, in which the curve BC is a quarter of a circle whose centre is D. The upper half of the column base is then obtained by rotating ABCDE around the line AE, implying that the horizontal sections in

B A

H G T

S H' J R G' I F C D E

FIGURE 1. A section in a quarter of the column base.

735 736 Appendix Three the base are circles with centres on the line AE and radii varying from AB to EC. ’sGravesande placed the eye point O in his chosen vertical plane and set his mind on determining the part of the base that is visible from O. He conceived of the base as consisting of an infinite number of infinitely close horizontal discs or circles and wanted to find out how much of each horizontal circle can be seen from O – the view to each disc being obstructed by the disc lying above it. To be able to solve this problem, ’sGravesande looked at an arbitrary section, for instance the one with GH1 as its radius, and constructed on its circumference two points, to be defined later, which I call the boundary points of visibility – although ’sGravesande did not give them a name.

The First Step efore introducing the boundary points of the circle GH, ’sGravesande Blooked at how the upper of two discs, having a finite distance, blocks the view to the lower disc. For this purpose, together with the circle GH he considered the circle IJ, and, from O projected the lower circle upon the plane of the upper circle. Since the calculations become a bit more straightforward by projecting, instead, the upper circle on the plane of the lower, and since this procedure does not change the final result,2 I choose the latter. Therefore, let the projection of the upper circle GH on the plane of the lower circle IJ be the circle G′H′ (figure 2), and let the points of intersection of the two latter

JH' IG' M NP

FIGURE 2. The upper circle projected upon the plane of the lower circle.

1In the following I call a circle with the radius XY ‘the circle XY’. 2Because at the end ’sGravesande took a step corresponding to taking a limit. ’sGravesande’s Column Base 737 circles be K and L. These two points determine the ‘crescent moon’ KPLN of the circle IJ that can be seen from O. Let M be the point of intersection of KL and IJ. ’sGravesande set IJ = a, G′H′ = b, and the distance between the two centres I and G′ as IG′ = c. By a simple calculation he then found that 22- IM = ba- c. (1) 22c Based on this equation it is easy to determine the points K and L on the circle IJ.

The Infinitesimal and Limit Situation et us now, with ’sGravesande, turn to the situation in which the distance Lbetween circles GH and IJ is infinitesimal. Taking a step that corresponds to taking the limit, ’sGravesande obtained a situation (figure 1) in which the three points G, G′, and I coincide, as do the two circles GH and IJ, and in which the points K and L in figure 2 determine the arc of circle GH that can be seen from the eye point. In this limit situation I refer to the points K and L as the boundary points of visibility for the circle GH. To determine the position of the boundary points with the aid of the point M, ’sGravesande first calculated the a, b, and c corresponding to the infinitesimal situation. To present his calculations (figure 1), I let F be the point of intersection of the vertical line through O and the line CE, and S and T the points of intersection of OF and the lines IJ and GH. Finally, I let R be the point of intersection of the vertical through the point H and the line IJ. ’sGravesande set FE = GT = e, OT = x, TS = GI = HR = dx, GH = y, and RJ = dy. Since IR = GH, the last assumption implies that IJ = y + dy. By looking at similar triangles, ’sGravesande found results corresponding to + ll==dx ye IG e x and RH x dx, and hence + ll=- l + l =-dx +ye = y GH IR GI RH y e x x dx x dx Inserting these three expressions instead of a, c, and b in (1) results in ((/))(yyxdxydy+-+22 ) IM = - edx . 2edx/ x 2x Taking a limit step, ’sGravesande obtained the following result: y2 xy dy GM==- IM . e e dx 738 Appendix Three

Constructing the right-hand side geometrically, ’sGravesande first constructed the length dy y (2) dx as the subnormal – without using the word – to the section of the base in the point H with respect to the axis AE. When U is the point of intersection of the normal HD to the circle and the line AE, the above-mentioned subnormal is the projection GU of the normal in H upon the line AE. With the length (2) at his disposal, ’sGravesande straightforwardly constructed the length GM, thereby obtaining the boundary points K and L.

The Perspective Image of the Visible Part of the Column Base o perform his construction of the perspective image of the column base, T’sGravesande suggested to determine the boundary points for a few more horizontal sections, then throwing the visible arcs between the boundary points into perspective and making smooth curves between these arcs. His result is shown in figure VII.61. Appendix Four

The Perspective Sources Listed Countrywise in Chronological Order

Introduction

ollowing is a list of the literature containing presentations of perspective Fconstructions up to 1800, arranged chronologically and countrywise in the following order: Italy; France and the Southern Netherlands; Germany, Austria and Switzerland; the Northern Netherlands; and Britain. To make it easier to get an overview, abbreviated titles have been used, and in general only the first edition of a publication is included.1 Consequently translations have also been left out.

Italy 1435 Leon Battista Alberti, De pictura; first printing 1540. ~1460s Filarete, byname of Antonio Averlino, Trattato di architettura; first printing 1890. ~1470s Piero della Francesca, De prospectiva pingendi; first printing 1899. ~1480s Francesco di Giorgio Martini, Trattato di architettura civile e militare; first printing 1841. 1504 Pomponio Gaurico, De sculptura. 1530s Jacopo Barozzi da Vignola, Perspective manuscript; printed as Le due regole della prospettiva pratica con i commentarii del R. P. M. Egnatio Danti, 1583. 1545 Sebastiano Serlio, D’Architettura/L’Architecture. Il secondo libro di perspettiva/Le second livre de perspective. 1558 Federico Commandino, In planisphaerium Ptolemaei commentarius. 1567 Pietro Cataneo, L’architettura. 1568 Daniele Barbaro, La pratica della perspettiva. 1583 Jacopo Barozzi da Vignola, Le due regole della prospettiva pratica con i commentarii del Egnatio Danti. 1584 Giovanni Paolo Lomazzo, Trattato dell’arte della pittura, scoltura, et architettura.

1Also in cases where I have not seen the first edition, I have listed this here and then referred to the edition included in the first bibliography. Books which have no year of publication I have placed where I considered it likely they appeared.

739 740 Appendix Four

1585 Giovanni Battista Benedetti, Diversarum speculationum mathematicarum et physicarum liber. 1596 Lorenzo Sirigatti, La pratica di prospettiva. 1600 Guidobaldo del Monte, Perspectivae libri sex. ~1600 Scipione Chiaramonti, Delle scene, e teatri; published posthumously in 1675. ~1610 Lodovico Cardi (called il Cigoli), Trattato della prospettiva pratica; first printing 1992. ~1620 Matteo Zaccolini, Prospettiva lineale; manuscript. 1620 Pietro Antonio Barca, Avvertimenti e regole circa l’architettura ... prospettiva. 1625 Pietro Accolti, Lo inganno degl’occhi, prospettiva pratica. 1628 Ferdinando di Diano, L’occhio errante dalla ragione emendate, prospettiva. 1629 Giuseppe Viola-Zanini, Della architettura ... con ... regole prospettiva. 1638 Niccolò Sabbatini, Pratica di fabricar scene e machine ne’ teatri. 1642 Mario Bettini, Apiaria universae philosophiae mathematicae. 1643 Bernardino Contino, La prospettiva pratica; cf. Contino 1645. ~1645 Evangelista Torricelli, Prospettiva pratica; unfinished, undated manuscript. 1651 Leonardo da Vinci, Trattato della pittura. A collection of texts gathered from various Leonardo manuscripts from the end of fifteenth and the beginning of sixteenth century. 1653 Christoph Scheiner, Prattica del parallelogrammo da disegnare del P. Christoforo Scheiner, ed. Giulio Troili. 1671 Guarino Guarini, Euclides adauctus et methodicus mathematicaque universalis. 1672 Giulio Troili, Paradossi per pratticare la prospettiva senza saperla; cf. Troili 1683. 1693 Andrea Pozzo, Perspectiva pictorum et architectorum/prospettiva di pittori e architetti, vol. 1. 1700 Andrea Pozzo, Perspectiva pictorum et architectorum/prospettiva di pittori e architetti, vol. 2. 1711 Ferdinando Galli-Bibiena, L’architettura civile preparata sul la geometria e ridotta alla prospettiva. 1714 Paolo Amato, La nuova pratica di prospettiva. 1731 Ferdinando Galli-Bibiena, Direzioni al giovani studenti nel disegno dell’architettura civile. 1740 Giuseppe Galli-Bibiena, Architettura & prospettiva. 1744 Giovanni Lodovico Quadri, La prospettiva pratica delineata in tavola a norma della secondo regola di Giacomo Barozzi da Vignola. 1747 Giovanni Francesco Costa, Elementi di prospettiva per uso degli architetti e pittori. 1750 Giovanni Biago Amico, L’architetto pratico. 1750 Giovanni Battista Piranesi, Opere varie de architettura ... prospettiva. 1753 Ferdinando Galli-Bibiena, Direzioni della prospettiva teorica. 1755 Eustachio Zanotti, “De perspectiva in theoremam unum redacta”. 1760 Bernardo Antonio Vittone, Istruzioni elementari per indirizzo de’giovani allo studio dell’Architettura civile. 1766 Eustachio Zanotti, Trattato teorico-pratico di prospettiva. 1770 Giovanni Battista Spampani & Carlo Antonini, Il Vignola illustrato proposto Giambattista Spampani e Carlo Antonini studenti d’ architettura. 1773 Baldassare Orsini, Della geometria e prospettiva pratica. 1788 Giuseppe Torelli, Elementorum prospectivae libri duo. The Perspective Sources Countrywise 741 France and the Southern Netherlands 1505 Viator (Jean Pélerin), De artificiali perspectiva. 1531 Joachim Fortius Ringelberg, Opera. 1560 Jean Cousin, Livre de perspective. 1576 Jaques Androuet du Cerceau, Lecons de perspective positive. 1612 Salomon de Caus, La perspective avec la raison des ombres et miroirs. 1613 François Aguilon, Opticorum libri sex. 1628 Jacques Aleaume, Introduction à la perspective, printed posthumously, but not published and now lost. 1630 Jean Louis Vaulezard, Perspective cilindrique et conique ou traicté des apparences veuës par le moyen des miroirs. 1631 Jean Louis Vaulezard, Abrégé ou racourcy de la perspective. 1636 Girard Desargues, Exemple de l’une des manieres universelles de S.G.D.L. touchant la pratique de la perspective sans emploier aucun tiers point, de distance ny d’autre nature qui soit hors du champ de l’ouvrage. 1637 Pierre Hérigone, Cursus mathematicus/Cours mathématique, vol. 5. 1638 Claude Mydorge, Examen du livre des recreations mathématiques. 1638 Jean François Niceron, La perspective curieuse, ou magie artificielle des effets merveilleux. 1640 Henry Guenon, Pratique ... de la perspective sur les seules parties egales du compas de proportion sans y adiouster aucune ligne d’optique. 1642 Pierre Hérigone, Supplementum cursus mathematici. 1642 Jean Dubreuil, La perspective pratique.... 1642 Jean Dubreuil, Diverses methodes universelles et nouvelles ... Tirées pour la pluspart du contenu du livre de la Perspective pratique. Ce qui servira de plus de response aux deux affiches du Sieur Desargues contre ladite Perspective pratique. 1643 Jacques Aleaume, La perspective speculative et pratique ... Ensemble la maniere universelle de la pratiquer non seulement sans plan géométral & sans tiers poinct, dedans ni dehors de la champ du tableau. Mais encore par le moyen de la ligne communément appelée horisontale. 1643 Girard Desargues, Livret de perspective adressé aux théoriciens; lost. 1644 Jacques Curabelle, Examen des oeuvres du Sieur Desargues. 1644 Nicolas Baytaz, Abbreviations des plus difficiles operations de perspective pratique ... principalement aux vrais peintres. 1644 Marin Mersenne, Universae geometriae mixtae. 1646 Jean François Niceron, Thaumaturgus opticus seu admiranda optices. 1647 Jean Dubreuil, Second partie de la perspective pratique. 1648 Emmanuel Maignan, Perspectiva horaria. 1648 Abraham Bosse, Maniere universelle de Mr Desargues pour pratiquer la perspective. 1648 René Gaultier de Maignannes, Invention nouvelle et brieve pour reduire en perspective par le moïen du quarré ... sans se servir d’autres points soit tiers, ou accidentaux, que de ceux qui peuvent tomber dans le tableau.. 1649 Jean Dubreuil, Troisiesme et derniere partie de la perspective pratique. 1653 Abraham Bosse, Moyen universel de pratiquer la perspective sur les tableaux, ou surfaces irrégulières. 1660 Jacques Le Bicheur, Traité de perspective. 1661 Charles Bourgoing, La perspective affranchie. 1661 Pierre Bourdin, Le cours de mathematique. 742 Appendix Four

1665 Abraham Bosse, Traité des pratiques géométrales et perspectives enseignées dans l’Académie royale de la peinture et sculpture. 1669 Andreas Tacquet, Opera mathematica. 1670 Grégoire Huret, Optique de portraiture et peinture. 1674 Claude François Milliet Dechales, Cursus seu mundus mathematicus. 1682 Jacques Rohault, Oeuvres posthumes. 1689 Sébastien Leclerc, Discours touchant le point de veue. 1690 Claude François Milliet Dechales, Cursus seu mundus mathematicus; revised edition of Dechales 1674. 1693 Jacques Ozanam, Cours de mathématique. 1701 Bernard Lamy, Traité de perspective. 1706 Louis Bretez, La perspective practique de l’architecture. 1725 Jean Courtonne, Traité de la perspective pratique. 1744 Abbé Deidier, Traité de perspective théorique et pratique. 1745 Abbé Deidier, Elemens generaux des principales parties des mathematiques neccesaires à l’artellerie et au génie. 1750 Edme Sébastien Jeaurat, Traité de perspective à l’usage des artistes. 1756 Nicolas Louis Lacaille, Leçons élémentaires d’optiques; second edition. 1756 Claude Roy, Essai sur la perspective pratique par le moyen du calcul. 1757 Jacques Silvabelle, “Méthode generale, pour trouver la perspective d’un objet donné”. 1758 Ennemond Alexandre Petitot, Raisonnement sur la perspective pour en faciliter l’usage aux artistes/Ragionamento sopra la prospettiva. 1759 Johann Heinrich Lambert, La perspective affranchie de l’embaras du plan géometral. 1766 Nicolas François de Curel, Essai sur la perspective linéaire. 1769 Guillaume Germain Guyot, Nouvelles récréations physiques et mathématique. 1771 S. N. Michel, Traité de perspective linéaire. 1773 Charles Dupuis, Cours de géométrie pratique, ..., de perspective. s.a. Aléxandre Sobro, Traité de perspective à l’usage des artistes. 1800 Pierre Henri Valenciennes, Elémens de perspective pratique à l’usage des artistes.

Germany, Austria, and Switzerland 1508 Gregor Reisch, Margarita Philosophica Nova. 1509 Jörg Glockendon, Von der Kunnst Perspectiva. 1525 Albrecht Dürer, Underweysung der Messung mit dem Zirckel und Richtsheyt. 1531 Johann II von Simmern, Eyn schön nützlich Büchlin und Underweisung der Kunst des Messens mit dem Zirckel, Richtscheidt oder Lineal. 1538 Erhard Schön, Underweissung der Proportzion unnd Stellung der Possen. 1543 Augustin Hirschvogel, Ein aigentliche und grundtliche Anweysung, in die Geometria. 1547 Walther Hermann Ryff, Der furnembsten, notwendigsten, der ganzen Architectur angehörigen mathematischen und mechanischen Künst. 1564 Heinrich Lautensack, Des Circkels unnd Richtscheyts, auch der Perspectiva. 1567 Lorenz Stör, Geometria et Perspectiva. 1567 Hans Lencker, Perspectiva literaria. 1568 Wenzel Jamnitzer, Perspectiva corporum regularium. Das ist, ein fleyssige Fürweysung. The Perspective Sources Countrywise 743

1571 Hans Lencker, Perspectiva. Hierinnen auffs kürtzte beschrieben ... wie allerley Ding ... in die Perspectyf gebracht werden mag. 1583 Georg Hass, Künstlicher und zierlicher ... perspectifischer Stück. 1599 Paul Pfinzing, Ein schöner kurtzer Extract der Geometriae unnd Perspectivae. 1610 Johann Faulhaber, Newe geometrische und perspectivische Inventiones. 1615 Lucas Brunn, Praxis perspectivae, das ist von Verzeichnungen ein aussführlicher Bericht. 1616 Paul Pfinzing, Optica, das ist gründtliche doch kurtze Anzeigung wie notwendig die löbliche Kunst Geometriae seye inn der Perspectiv. 1623 Andreas Albrecht, Zwey Bücher. Das erste von der ohne und durch die Arithmetica gefundenen Perspectiva. Das andere von dem darzu gehörigen Schatten. 1625 Peter Halt, Perspektivische ... Reisskunst. 1626 Peter Halt, Drey wichtige newe Kunststück in underschidlichen perspectivischen Instrumenten inventiert und erfunden. 1630 Benjamin Bramer, Beschreibung eines sehr leichten Perspectiv und Grundreissenden Instruments. 1631 Christoph Scheiner, Pantographice. 1633 Johann Faulhaber, Ingenieurs Schul. 1646 Athanasius Kircher, Ars magna lucis et umbrae. 1652 Theodosius Haesell, Geistliche perspectiva. 1657 Gaspar Schott, Magia universalis naturae et artis, Pars I Optica. 1675 Joachim Sandrart, L’Academia todesca. 1677 Caspar Schott, Cursus mathematicus. 1680 Jacob Johann Füllisch, Compendium artis ... Das ist kurzer leichter ... Unterricht von der geometrisch-ignographischen Zeugnungs und Baukunst. 1683 Daniel Hartnack, Perspectiva mechanica und eigentliche Beschreibung derer vornehmsten Instrumenten. 1699 Johann Christoph Sturm, Mathesis juvenilis. 1713 Jakob Leupold, Anamorphosis mechanica nova, oder Beshreibung dreier neuen Maschinen. 1715 Christian Wolff, Elementa matheseos universae. 1717 Johann Wenceslaus Kaschube, Cursus mathematicus, oder deutlicher Begriff der mathematischen Wissenschaften. 1717 Anton Bernhard Lauterbach, Clavis perspectivae verticalis geometrica. 1718 Johann Friedrich Weidler, Institutiones matheseos; cf. Weidler 1736. 1719 Johann Jacob Schübler, Perspectiva Pes Pictura. Das ist kurze und leichte Verfassung der practicabelsten Regul zur perspectivischen ZeichnungsKunst. 1724 Johann Jacob Schübler & Johann Leonhard Rost, Mathematischer Lust und Nutzgarten ... sammt einer Anleitung zur Perspectiv. 1725 Johann Bernhard Wiedeburg, Einleitung zu denen mathematischen Wissenschaften. 1727 Paul Heinecke, Lucidum prospectivae speculum. Das ist ein heller Spiegel der Perspective. 1733 Friedrich WilhelmWeidemann, Kurtze Einleitung zu der optischen Perspectiv; cf. Weidemann 1746. 1737 Christian Wolff, Anfangsgründe aller mathematischen Wissenschaften; fifth edition.2

2Perspective is presumably also treated in some of the earlier editions. 744 Appendix Four

1741 Johann Christoph Bischoff, Kurtzgefasste Einleitung zur Perspectiv. 1747 Georg Erhard Hamberger, Dissertatio sistens leges perspectivae. 1747 Joachim Georg Darjes, Erste Gründe der gesammten Mathematik. 1752 Abraham Gotthelf Kästner, Perspectivae et projectionum theoria generalis analytica. 1752 Johann Heinrich Lambert, Anlage zur Perspektive; manuscript. 1753 Albrecht Ludwig Friederich Meister, Instrumentum scenographicum. 1758 Abraham Gotthelf Kästner, Anfangsgründe der Arithmetik, Geometrie ... und Perspectiv; cf. Kästner 1774. 1759 Johann Heinrich Lambert, La perspective affranchie ... and Die freye Perspektive. 1763 Georg Heinrich Werner, Die Erlernung der Zeichenkunst durch Geometrie und Perspectiv. 1768 Johann Heinrich Lambert, Kurzgefasste Regeln zu perspectivischen Zeichnungen vermittelst eines ... Proportional-Zirkels. 1770 Johann Friedrich Hennert, Elementa optices, perspectivae, catoptrices et phaometria. 1774 Johann Heinrich Lambert, Die freye Perspective ... mit Anmerkungen und Zusätzen vermehrt. 1775 Wenceslaus Johann Gustav Karsten, Lehrbegrif der gesamten Mathematik. Der siebende Theil. Die Optik und Perspectiv. 1779 Johann Andreas Segner, Gründe der Perspectiv. 1779 Johann Heinrich Lambert, Grundsätze der Perspectiv, aus Betrachtung einer perspectivisch gezeichneten Landschaft abgeleitet. 1780 Johann Leonhard Hoffmann, Anweisung zur Vertigung und Gebrauch des all- gemeinen Zeichnen-Instruments ohne Gläser. 1780 Lukas Voch, Abhandlung von der Perspektivkunst. 1781 Karl Scherffer, Beyträge zur Mathematik. 1784 Johann Michael Rödel, Abhandlungen von den zufälligen Punkten in der Perspectivkunst für Werkmeister; cf. Rödel 1796. 1787 Johann Georg Sulzer, Allgemeine Theorie der schönen Künste. 1791 Johann Friedrich Lorenz, Grundriss der reinen und angewandten Mathematik;cf. Lorenz 1799. 1794 Bernhard Friedrich Mönnich, Versuch die mathematischen Regeln der Perspektive für den Künstler ohne Theorie anwendbar zu machen; cf. Mönnich 1801. 1795 Abel Bürja, Der mathematische Maler oder gründliche Anweisung zur Perspektive. 1796 Georg Heinrich Werner, Gründliche Anweisung zur Zeichenkunst. 1797 Karl Gottlieb Horstig, Briefe über die mahlerische Perspektive. 1799 Johann Heinrich Lambert, “Grundsätze der Perspectiv”.

The Northern Netherlands 1560 Johan Vredeman de Vries, Artis perspectivae. 1560 Johan Vredeman de Vries, Scenographiae sive perspectivae. 1604 JohanVredeman de Vries, Perspective. 1605 Simon Stevin, Derde Stuck der Wisconstighe ghedachtnissen. Van de Deursichtighe. 1614 Samuel Marolois, La perspective contenant la theorie et la pratique. The Perspective Sources Countrywise 745

1623 Hendrik Hondius, Onderwijssinge in de perspective conste. 1660 Frans van Schooten, Mathematische Oeffeningen. 1676 Abraham de Graaf, De geheele mathesis of wiskonst. 1678 Samuel van Hoogstraten, Inleydung tot de hooge schoole der schilderkonst. 1699 Nicolaas Hartsoeker, Proeve der deursicht-kunde. 1703 Dirk Bosboom, Perspectiva of doorzicht-kunde. 1705 Hendrik van Houten, Verhandelinge van de grontregelen der doorzigtkunde of tekenkonst (perspectief). 1707 Gerard de Lairesse, Het groot schilderboek. 1711 Willem Jacob ’sGravesande, Essai de perspective. 1765 Caspar Jacobszoon Philips, Uitvoerig onderwys in de perspectiva of doorzichtkunde. 1769 Rienk Jelgerhuis, Nauwkeurige aanmerkingen op een vornaam gedeelte van de perspectiva of doorzigtkunde van Casper Philips Jacobsz. 1773 Jacob de Vlaming, Kort zaamenstel der perspectief. 1775 Caspar Jacobszoon Philips, Handleiding in de spiegelperspectief. 1786 Caspar Jacobszoon Philips, Wis-meet-en doorzichtkundige handleiding. 1786 Caspar Jacobszoon Philips, Zeemans onderwijser in de tekenkunst ... doorzichkundige en perspectivische regelen. 1788 Caspar Jacobszoon Philips, Handleiding om ... als ook de der perspectivische regelen.

Britain 1669 Henry Oldenburg (presumably), The Description of an Instrument, Invented Divers Years ago by Dr. Christopher Wren, for Drawing the Out-Lines of any Object in Perspective. 1670 Joseph Moxon, Practical Perspective, or, Perspective Made Easie. 1672 William Salmon, Polygraphice or the Art of Drawing. 1712 Humphry Ditton, A Treatise of Perspective, Demonstrative and Practical. 1715 Brook Taylor, Linear Perspective or, a New Method of Representing justly all Manner of Objects. 1719 Brook Taylor, New Principles of Linear Perspective. 1731 William Halfpenny, Perspective Made Easy or a New Method for Practical Perspective. 1738 John Hamilton, Stereography, or a Compleat Body of Perspective. 1743 James Hodgson, “The Theory of Perspective”; printed as introduction to Dubreuil 1743. 1746 Patrick Murdoch, Neutoni genesis curvarum per umbras seu perspectivae universalis elementa. 1751 Matthew Darly, A New Book of ... Chairs with the Manner of Putting them in Perspective According to Brook Taylor. 1754 Joseph Highmore, A Critical Examination of those two Paintings ... in which Architecture is introduced so far as relates to the Perspective. 1754 John Joshua Kirby, Dr. Brook Taylor’s Method of Perspective Made Easy, Both in Theory and Practice. 1755 Godfrey Smith, The Laboratory; or School of Arts ... and Easy Introduction to the Art of Drawing in Perspective. 1756 Thomas Bardwell, The Practice of Painting and Perspective Made Easy. 746 Appendix Four

1757? John Joshua Kirby, Dr. Brook Taylor’s Method of Perspective, compared with Examples lately publish’d on this Subject as Sirigatti’s; published s.a. 1761 John Joshua Kirby, The Perspective of Architecture ... deduced from the Principles of Dr. Brook Taylor. 1761 Daniel Fournier, A Treatise of the Theory and Practice of Perspective. Wherein the Principles ... by Dr. B. Taylor are fully and clearly explained. 1763 Joseph Highmore, The Practice of Perspective. On the Principles of Dr. Brook Taylor, written many years since, but now first published. 1764 Benjamin Martin, A New and Comprehensive System of Mathematical Institutions. 1765 John Muller, Elements of Mathematics; third edition. 1765 John Lodge Cowley, The Theory of Perspective, Demonstrated in a Method Entirely New. 1765 William Emerson, Cyclomathesis Or an Easy Introduction to the several Branches of the Mathematics. 1768 William Emerson, Perspective Or the Art of Drawing the Representations of all Objects upon a Plane. 1770 Joseph Priestley, A Familiar Introduction to the Theory and Practice of Perspective. s.a. Benjamin Martin, The Principles of Perspective. 1771 Benjamin Martin, The Description and Use of a Graphical Perspective. 1771 Edward Noble, The Elements of Linear Perspective. 1772 Joseph Priestly, History and Present State of Discoveries Relating to Vision, Light and Colours. 1772 John Wright, Elements of Trigonometry. 1774 William Hooper, Rational Recreations. 1775 James Ferguson, The Art of Drawing in Perspective Made Easy. 1775 Thomas Malton, A Compleat Treatise on Perspective in Theory and Practice on the True Principles of Dr. Brook Taylor, Made Clear. 1776 Henry Clarke, Practical Perspective. 1783 Thomas Malton, An Appendix or Second Part to the Compleat Treatise on Perspective. 1790 Robert Bradberry, The Principles of Perspective. Explained in a Genuine Theory and Applied in an Extensive Practice. 1791 George Adams, Geometrical and Graphical Essays. 1793 Thomas Sheraton, The Cabinet-maker and Upholsterer’s Drawing Book. 1794 A. Cobin, Short and Plain Principles of Linear Perspetive Adapted to Naval Architecture. 1799 John Wood, Elements of Perspective, Containing the Nature of Light and Colours and the Theory and Practice of Perspective. 1800 James Malton, The Young Painter’s Maulstick being a Practical Treatise on Perspective founded on the process of Vignola and Sirigatti, ... united with the theoretic principles of ... B. Taylor. First Bibliography

Pre-Nineteenth Century1 Publications on Perspective

Accolti, Pietro 1625 Lo inganno degl’occhi, prospettiva pratica, Firenze. Facsimile reprint by William Clowes, s.l. 1972. Adams, George 1791 “An Essay on Perspective, and a Description of some Instruments for Facilitating the Practice of that Useful Art”, in Geometrical and Graphical Essays, London, 461–485. Second edition London 1797. Aguilon, François 1613 “De scenographice”, part of “Liber VI. De proiectionibus” in Opticorum libri sex, Antwerpen, 637–681. Alberti, Leon Battista 1435 De pictura, manuscript containing some sections on perspective, first published Basel 1540. In 1436 Alberti wrote an Italian version, Della pittura. There are numerous editions and translations of the two manuscripts (for a survey, see Alberti 1992, 253–255), of which three recent ones are listed as the following items. 1972 On Painting and On Sculpture. The Latin Texts of De Pictura and De Statua, ed. and tr. Cecil Grayson, London. The English translation of De pictura is reedited in Alberti 1991. 1991 On painting, ed. and tr. Cecil Grayson and Martin Kemp, London. 1992 De la peinture. De Pictura (1435), tr. Jean Louis Schefer, Paris. Albrecht, Andreas 1623 Zwey Bücher. Das erste von der ohne und durch die Arithmetica gefundenen Perspectiva. Das andere von dem darzu gehörigen Schatten, Nürnberg. Later posthumous editions, some in Latin, among them the next item. 1671 Duo libri. Prior de perspectiva ... Posterior de umbra, Nürnberg. Aleaume, Jacques 1628 Introduction à la perspective, ensemble l’usage du compas optique et perspective, Paris.* The book seems to have existed in a print which was never published, at present no copies of it are known.

1The bibliography contains a few nineteenth century titles related to discussions about the further development in particular fields. A star * at a title indicates that I have not seen the publication, and a (*) that the illustrations were missing in the copy I studied.

747 748 First Bibliography

1643 La perspective speculative et pratique ... Ensemble la maniere universelle de la pratiquer non seulement sans plan géométral & sans tiers poinct, dedans ni dehors de la champ du tableau. Mais encore par le moyen de la ligne communément appelée horizontale, ed. Étienne Migon, Paris. The same book with a new title page Paris 1663. Amato, Paolo 1736 La nuova pratica di prospettiva, Palermo.(*) Amico, Giovanni Biago 1750 “Compendio della prospettiva pratica” in L’architetto pratico, Palermo, vol. 2, 122–150. Androuet du Cerceau, Jacques, see Cerceau Antonini, Carlo, see Spampani & Antoni Averlino, Antonio, see Filarete Barbaro, Daniele 1569 La pratica della perspettiva, Venezia. First edition 1568. Facsimile of the 1569 edition, Sala Bolognese 1980. Barca, Pietro Antonio 1620 “Prospettiva” in Avvertimenti e regole circa l’architettura ... prospettiva ..., Milano, 25–27. Bardwell, Thomas 1756 “The Principles of Perspective” in The Practice of Painting and Perspective Made Easy, London, 42–64. Barozzi da Vignola, Giacomo, see Vignola Baytaz, Nicolas 1644 Abbreviations des plus difficiles operations de perspective pratique ... principalement aux vrais peintres ..., Annecy. Benedetti, Giovanni Battista 1585 “De rationibus operationum perspectivae”, in Diversarum speculationum mathematicarum et physicarum liber, Torino, 119–140. “De rationibus ...” was also printed in two later editions of Benedetti’s work, Speculationum mathematicarum et physicarum ... tractatus, Venezia 1586 and Speculationum liber, Venezia 1599. Bettini, Mario 1642 “Apiarium V” in Apiaria universae philosophiae mathematicae, Bologna. Later editions. The section has the heading optics and scenography, but it mainly treats anamorphoses. Bicheur, Jacques Le 1660 Traité de perspective faict par un peintre de l’Académie Royale, dédié à Monsiuer Le Brun ..., Paris.* Bischoff, Johann Christoph 1741 Kurtzgefasste Einleitung zur Perspectiv, darinnen nebst dem wahren Fundamente derselben ... dem noch beygefüget eine neue Erfindung eines Instruments, Halle. Publications on Perspective 749

Blacker, George O. 1885 John Heywood’s Second Grade Perspective ... adapted from Dr. Brook Taylor, Manchester 1885–1888. Bosboom, Dirk 1703 Perspectiva of doorzicht-kunde, Amsterdam. Later edition Amsterdam 1729. Bosse, Abraham 16482 Maniere universelle de Mr Desargues pour pratiquer la perspective par petit-pied, comme le geometral ..., Paris. Facsimile reprint Alburgh 1987. Dutch transla- S tion Bosse 16641. Also a Japanese edition (Taton 1951, 57). 1653 Moyen universel de pratiquer la perspective sur les tableaux, ou surfaces irreg-

ulieres, Paris. Dutch translation Bosse 16642. r 16641 Algemeene manier van de H Desargues, tot de practyk der perspectiven, gelyk tot die der meet-kunde met de kleine voet-maat ..., tr. J. Bara, Amsterdam. Second edition Amsterdam 1686.

16642 Algemeen middel tot de practijk der doorsicht-kunde op tafereelen of regel-lose buyten gedaanten, Amsterdam. Second edition Amsterdam 1686. 1665 Traité des pratiques géométrales et perspectives enseignées dans l’Académie Royale de la Peinture et Sculpture ..., Paris. Bourdin, Pierre 1661 Le cours de mathematique, third edition, Paris. In the text to plate 172 Bourdin touched upon perspective. Bourgoing, Charles 1661 La perspective affranchie, contenant la vraye et naturele pratique jusques icy inconnue ..., par laquelle l’on peut representer toutes sortes de figures ... sans tracer ny supposer le plan geometral ordinaire, Paris. Bradberry, Robert 1790 The Principles of Perspective. Explained in a Genuine Theory and Applied in an Extensive Practice, Edinburgh. By and large a copy of Martin s.a. Bramer, Benjamin 1630 Beschreibung eines sehr leichten Perspectiv und Grundreissenden Instruments auff einem Stande: Auff Joh. Faulhabers, Ingenieurs zu Ulm, weitere Continuation seines mathematischen Kunstspiegels geordnet, Kassel. Bretez, Louis 1706 La perspective practique de l’architecture ..., Paris. Later edition Paris 1751. Brunn, Lucas 1615 Praxis perspectivae, das ist von Verzeichnungen ein aussführlicher Bericht, Leipzig. Bürja, Abel 1795 Der mathematische Maler oder gründliche Anweisung zur Perspektive, Berlin. Cardi, Lodivico, see Cigoli

2According to Jean Pierre Le Goff the first copies appeared in 1647 (Le GoffS 1994). 750 First Bibliography

Cataneo, Pietro 1567 “Libro ottavo dove si mostra a operare praticamente nelle cose di prospettiva ...” in L’architettura, Venezia. An earlier edition of L’architettura (Venezia 1554) does not contain book eight. Cerceau, Jaques Androuet du 1576 Lecons de perspective positive, Paris. Later editions, facsimile Paris 1978. Chiaramonti, Scipione 1675 Delle scene, e teatri opera postuma, Cesena.*3 Cigoli, il byname of Ludovico Cardi Pros Prospettiva pratica, manuscript published as Trattato pratico di prospettiva di Ludovico Cardi detto il Cigoli, ed. Rudolfo Profumo, Roma 1992. Clarke, Henry 1776 Practical Perspective being a Course of Lessons Exhibiting Easy and Concise Rules for Drawing Justly all Sorts of Objects, London. Cobin, A. 1794 Short and Plain Principles of Linear Perspetive Adapted to Naval Architecture, London.* Fourth edition. Commandino, Federico 1558 In planisphaerium Ptolemaei commentarius; in quo universa scenographices ratio quam brevissime traditur, ac demonstrationibus confirmatur, Venezia. Fol. 2r–19r deal with perspective. Contino, Bernardino 1645 La prospettiva pratica, Venezia. First issue 1643, later edition Venezia 1684. Costa, Giovanni Francesco 1747 Elementi di prospettiva per uso degli architetti e pittori, Venezia. Courtonne, Jean 1725 Traité de la perspective pratique avec des remarques sur l’architecture ..., Paris. Cousin, Jean 1560 Livre de perspective, Paris. Facsimile reprint Unterschneidheim 1974. Cowley, John Lodge 1765 The Theory of Perspective, Demonstrated in a Method Entirely New ... Invented, and now Published for the Use of the Royal Academy at Woolwich, London. Curabelle, Jacques 1644 “L’examen de l’une des manieres universelles de Sieur Desargues touchant la pratique de la perspective” in Examen des œuvres du Sieur Desargues, Paris, 66–81. Curel, Nicolas François de 1766 Essai sur la perspective linéaire et sur les ombres, Strasbourg. Danti, Egnazio, see Vignola

3According to G. Benzoni the book was composed before 1610 (BenzoniS 1980, 542). Publications on Perspective 751

Darjes, Joachim Georg 1747 “Elementa perspectivae” in Erste Gründe der gesamten Mathematik, Jena, 587–600. Later editions. Darly, Matthew 1751 A New Book of Chinese, Gothic, and Modern Chairs with the manner of putting them in Perspective according to Brook Taylor, London* (RococoS 1984, 167–168). De Caus, Salomon 1612 La perspective avec la raison des ombres et miroirs, London. Dechales, Claude François Milliet 1674 “Perspectiva” in Cursus seu mundus mathematicus, Lyon, vol. 2, 465–532, reprinted in revised version in Dechales 1690, vol. 3, 491–566. 1690 Cursus seu mundus mathematicus, 4 vols., ed. Amati Varcin, Lyon. Deidier, (Abbé) 1744 Traité de perspective théorique et pratique, Paris. Second edition Paris 1770. Despite the different titles the contents of this book and the next item are very close. 1745 “Pratique de la perspective” in Elemens generaux des principales parties des mathematiques neccesaires à l’artellerie et au génie, Paris, vol. 2., 279–379. Second edition Paris 1773. Desargues, Girard 1636 Exemple de l’une des manieres universelles de S.G.D.L. touchant la pratique de la perspective sans emploier aucun tiers point, de distance ny d’autre nature qui soit hors du champ de l’ouvrage, Paris. Reprinted in Bosse 1648, 321–334, and in Desargues Œuvres, vol. 1, 55–84. Facsimile of the first printing together with an English translation in Field and GrayS 1987, 190–201 and 144–160. 1643 Livret de perspective adressé aux théoriciens.* This booklet is mentioned by Curabelle (1644, 70), but it is lost and its exact title is unknown. Its content was presumably presented in the section Aux théoriciens in Bosse 1648. This section is not so easy to find because its text claims to be comments to plates 112–119 which Bosse later renumbered so they became plates 141–148. Moreover the page numbers are missing, but according to the order of the book they should be 313–320. Bosse’s presentation is reprinted in Œuvres, vol. 1, 439–462. Œuvres Œuvres de Desargues réunies et analysées ..., 2 vols., ed. N. Poudra, Paris 1864. Diano, Ferdinando di 1628 L’occhio errante dalla ragione emendate, prospettiva, Venezia. The section cov- ering the pages 153–182 deals with perspective. Ditton, Humphry 1712 A Treatise of Perspective, Demonstrative and Practical, London. Dubreuil, Jean

16421 La perspective pratique ... par un religieux de la compagnie de Jesus, Paris 1642. Published anonymously. For a second and third part, see Dubreuil 1647 and 1649. Particularly the first part of La perspective pratique, known as the “Jesuit’s perspective”, became very popular, it was reissued Paris 1651, and thereafter often. Two English and one German translations are listed separately. 752 First Bibliography

16422 Diverses methodes universelles et nouvelles, en tout ou en partie pour faire des perspectives ... Tirées pour la pluspart du contenu du livre de la Perspective pratique. Ce qui servira de plus de response aux deux affiches du Sieur Desargues contre ladite Perspective pratique, Paris. 1647 Second partie de la perspective pratique ..., Paris. Second edition Paris 1657. 1649 Troisiesme et derniere partie de la perspective pratique ..., Paris. Second edition Paris 1659. 1672 Perspective practical, tr. Robert Pricke, London. Second edition London 1698. 1710 Perspectiva practica, oder Vollständige Anleitung zu der Perspectiv-Reia-Kunst ..., tr. Johann Christoph Rembold, Augsburg. Facsimile reprint Hannover 1977. 1743 The Practice of Perspective. Or an Easy Method of Representing Natural Objects According to the Rules of Art ..., tr. E. Chambers. Dürer, Albrecht 1525 Underweysung der Messung mit dem Zirckel und Richtsheyt in Linien, Ebnen, unnd gantzen Corporen, Nürnberg. Enlarged, posthumous edition Nürnberg 1538. Latin editions with the title Institutiones geometricae, Paris 1532 and later. Abbreviated edition in modernised language in Albrecht Dürer’s Unterweisung der Messung, ed. Alfred Peltzer, München 1908, facsimile Vaduz 1970. Facsimile reprint of the 1525 text, eds. Alvin Jaeggli & Christine Papesch, Zürich 1966, further facsimile reprints Portland, Oregon 1972, Unterschneidlin 1972, in Dürer 1977, and Nördlingen 1983. English and French translations in the next items. 1977 The Painter’s Manual. A Manual of Measurement of Lines, Areas, and Solids by Means of Compass and Ruler, ed. and tr. Walter L. Strauss, New York. Besides an English translation,the book contains a facsimile of the 1525 edition and of the changes and additions in the 1538 edition of Underweysung der Messung. 1995 “Instructions pour la mesure à la regle et au compas des lignes, plans et corps solides” in Géométrie, ed. and tr. Jeanne Peiffer, Paris, 132–353. Dupuis, Charles 1773 Cours de géométrie pratique, ..., de perspective. Paris.* Edwards, Edward 1803 A Practical Treatise of Perspective, on the Principles of Dr. B. Taylor, London. Emerson William 1765 “Perspective” in Cyclomathesis: Or an Easy Introduction to the several Branches of the Mathematics, London, vol. 6* (JonesS 1947, 221). 1768 Perspective: Or the Art of Drawing the Representations of all Objects upon a Plane, London. Appeared as a separate part of Emerson’s The Elements of Optics, London. Eytelwein, Johann Albert 1810 Handbuch der Perspektive, Berlin. Faulhaber, Johann 1610 Newe geometrische und perspectivische Inventiones, Frankfurt am Main. 1633 Ingenieurs Schul. Dritter Theil ... die irregular Figuren zu fortificern, Ulm. Ferguson, James 1775 The Art of Drawing in Perspective Made Easy ..., London. Publications on Perspective 753

Filarete, byname of Antonio Averlino Arch Book 23 of Trattato di architettura, manuscript from around 1460. The tract was first published together with a German translation in Antonio Averlino Filarete’s Tractat über die Baukunst, ed. and tr. Wolfgang von Oettingen, Wien 1890. The following titles are later editions. References are to Filarete 1972. 1965 Filarete’s Treatise on Architecture, 2 vols., ed. and tr. John R. Spencer, New Haven. 1972 Trattato di architettura, 2 vols., ed. Anna Maria Finoli & Liliana Grassi, Milano. Fortius, see Ringelberg Fournier, Daniel 1761 A Treatise of the Theory and Practice of Perspective. Wherein the Principles ... by Dr. B. Taylor are fully and clearly explained by the means of moveable Schemes, London. Later editions London 1762, 1763, 1764. Francesco di Giorgio Martini Arch “Geometria e modi di misurare distanze altezze e profundità” in Trattati di architettura ingegneria e arte militare, this section contains a page on perspective. Manuscript from around 1480, first published in Torino 1841. References are to Francesco 1967. 1967 Trattati di architettura ingegneria e arte militare, 2 vols., ed. Corrado Maltese & Livia Maltese Degrassi, Milano. Füllisch, Johann Jacob 1680 “Von Perspectiven” part 6 of Compendium artis ... Das ist kurzer leichter ... Unterricht von der geometrisch-ignographischen Zeugnungs und Baukunst, Nerolingen. Galli-Bibiena, Ferdinando 1711 “Della prospettiva in generale” part 3 of L’architettura civile preparata sul la geometria e ridotta alla prospettiva, Parma, 77–114. A lavish edition, the text reappeared slightly revised in a more economical edition being the next item. 1731 Direzioni al giovani studenti nel disegno dell’architettura civile ..., 2 vols., Bologna 1731 and 1732. The second volume of this work was edited posthumously with yet another title, namely the next item. 1753 Direzioni della prospettiva teorica ..., Bologna. Galli-Bibiena, Giuseppe 1740 Architettura & prospettiva, Augusta. Gaultier de Maignannes, René 1648 Invention nouvelle et brieve pour reduire en perspective, par le moïen du quarré, toutes sortes de plans ... sans se servir d’autres points de tiers, ou accidentaux, que de ceux qui peuvent tomber dans le tableau, La Fleche. Gaurico, Pomponio 1504 “De perspectiva” in De sculptura, Firenze. Numerous later editions. In modern times edited by Heinrich Brockhaus with a German translation, Leipzig 1886 and in the following title. 1969 “De perspectiva” in De sculptura, Latin text and French translation, ed. and tr. André Chastel & Robert Klein, Genève, 182–201. 754 First Bibliography

Glockendon, Jörg 1509 Von der Kunnst Perspectiva, Nürnberg. A pirated German version of Viator 1505. Graaf, Abraham de 1676 “Perspectief of tekenkonst” the tenth book in De geheele mathesis of wiskonst, herstelt in zijn natuurlijke gedaante, Amsterdam, 213–226. A revised version in 1694, where perspective occurs on the pages 213–222. Several later editions. ’sGravesande, Willem Jacob 1711 Essai de perspective, Den Haag. Later edition Rotterdam 1717. Reprint ’sGravesande 1774. An English translation in the next item and a free Dutch translation in ’sGravesande 1837. 1724 An Essay on Perspective ..., tr. E. Stone, London. 1774 “Essai de perspective” in Œuvres philosophiques et mathématiques de Mr G.J. ’sGravesande, ed. Nicolas Sébastien Allamand, Amsterdam, vol. 1, 1–88. 1837 Beginselen der doorzigtkunde door G.J. ’sGravesande. Vrij vertaald uit het fran- sch en met bijvoegselen vermeerderd, ed. and tr. H. van Blanken, Zwolle. Guarini, Guarino 1671 “Tractatus XXVI de stereographia” in Euclides adauctus et methodicus mathematicaque universalis, Torino, 452–462. Guenon, Henri 1640 Pratique nouvelle et universelle de la perspective sur les seules parties egales du compas de proportion, sans y adiouster aucune ligne d’optique, Paris. This is a booklet of 11 pages. Guidobaldo del Monte 1600 Perspectivae libri sex, Pesaro. Reproduction of the Latin text and an Italian translation in the following title. 1984 I sei libri della prospettiva di Guidobaldo dei marchesi Del Monte, tr. Rocco Sinisgalli, Roma. Guyot, Guillaume Germain 1769 Nouvelles récréations physiques et mathématiques ..., Paris,* numerous other editions. According to Hooper, Guyot treated anamorphoses, and it seems most likely that he did so in this work (Hooper 1774, 172). Haesell, Theodosius 1652 Geistliche perspectiva, Dresden. Halfpenny, William 1731 Perspective Made Easy: Or a New Method for Practical Perspective, London. Halt, Peter 1625 Perspektivische allen Bauleuten dienende Reisskunst ..., Augsburg. 1626 Drey wichtige newe Kunststück in underschidlichen perspectivischen Instrumenten inventiert und erfunden, Augsburg.* Hamberger, Georg Erhard 1747 Dissertatio mathematica sistens leges perspectivae ad situm plani transparentis mutatum adplicatas, Jena; mathematical dissertation defended 1719. Publications on Perspective 755

Hamilton, John 1738 Stereography, or a Compleat Body of Perspective ..., London. Later editions London 1740, 1748, 1749. Hartnack, Daniel 1683 Perspectiva mechanica und eigentliche Beschreibung derer vornehmsten Instrumenten ... zum perspectivischen Reissen bissher erfunden worden, Lüneburg. Hartsoeker, Nicolaas 1699 Proeve der deursicht-kunde in het frans beschreeven ... en vertaald door A. Block, Amsterdam.* Hass, Georg 1583 Künstlicher und zierlicher newer vor nie gesehener funffzig perspectifischer Stück ..., Wien. Heinecke, Paul 1727 Lucidum prospectivae speculum. Das ist ein heller Spiegel der Perspective, Augsburg. Hennert, Johann Friedrich 1770 “Perspectivae” in Elementa optices, perspectivae, catoptrices, dioptrices et phaometriae, Utrecht, 37–51. Hérigone, Pierre 1637 “Perspective” in Cursus mathematicus/Cours mathématique, Paris, vol. 5, 190–21. Later edition Paris 1654. 1642 “De la perspective” in Supplementum cursus mathematici, 99–116, Paris. Highmore, Joseph 1754 A Critical Examination of those two Paintings on the Ceiling of the Banqueting- House at Whitehall, in which Architecture is introduced, so far as relates to the Perspective, London. 1763 The Practice of Perspective on the Principles of Dr. Brook Taylor, ... Written many years since, but now first published, London. Hirschvogel, Augustin 1543 “Anfang des Perspectiva” in Ein aigentliche und grundtliche Anweysung, in die Geometria, sonderlich aber, wie alle regulierte, und unregulierte Corpora in den Grund gelegt, und in das Perspecktiff gebracht ... sollen werden, fol. fiiv– hiiir, Nürnberg. Hodgson, James 1743 “The Theory of Perspective” printed as introduction to Dubreuil 1743, 1–16. Hoffmann, Johann Leonhard 1780 Anweisung zur Vertigung und Gebrauch des algemeinen Zeichnen-Instruments ohne Gläser, Anspach. Hondius, Hendrik 1623 Onderwijssinge in de perspective conste, Den Haag. Without many changes the book was reedited as Grondige onderrichtinge in de optica of te perspective kon- ste, one edition is from Amsterdam without a year of printing, another appeared in Amsterdam 1647 and a third in den Haag 1647 (where the title is written 756 First Bibliography

Grondighe onderrichtinghe ...). All the editions – including the French mentioned below – have the same frontispiece decorated with the title Institutio artis perspectivae, hence references to such a work by Hondius occur frequently. 1625 Instruction en la science de perspective, den Haag. Facsimile reprint Alburgh 1987. Hoogstraten, Samuel van 1678 Inleyding tot de hooge schoole der schilderkonst, Rotterdam. Facsimile reprint Davaco Publishers, s.l. 1969. Later editions. Hooper, William 1774 “Perspective Recreations” in Rational Recreations, London, vol. 2, 168–188. This section contains an instruction in making anamorphoses. Horstig, Karl Gottlieb 1797 Briefe über die mahlerische Perspektive, Leipzig. Houten, Hendrik van 1705 Verhandelinge van de grontregelen der doorzigtkunde of tekenkonst (perspectief), Amsterdam. Hummel, Johann Erdmann 1824 Die freie Perspektive, erlaütert durch praktische Aufgaben und Beispiele, haupt- sächlich für Maler und Architekten, 2 vols., Berlin 1824 and 1825. Huret, Grégoire 1670 Optique de portraiture et peinture, Paris. Later edition Paris 1672. Jamnitzer, Wenzel 1568 Perspectiva corporum regularium. Das ist, ein fleyssige Fürweysung, wie die fünff regulirten Cörper ... inn die Perspectiva gebracht ... werden mügen, Nürnberg. Reprint Graz 1973. Facsimile reprint together with a French translation in FloconS 1964. The work seems to be copied in Sintagma, in quo variae eximi- aque corporum diagrammata ex praescriptio opticae exibentur ..., Amsterdam 1608 and 1618 (JonesS 1947, 155 and VagnettiS 1979, 335). Jeaurat, Edme Sébastien 1750 Traité de perspective à l’usage des artistes, Paris. Jelgerhuis, Rienk 1769 Nauwkeurige aanmerkingen op een vornaam gedeelte van de perspectiva of doorzigtkunde van Casper Philips Jacobsz, Leeuwarden. Johann II, Simmern von 1531 Eyn schön nützlich Büchlin und Underweisung der Kunst des Messens mit dem Zirckel, Richtscheidt oder Lineal. Zu Nutz allen ... denen so sich der Kunst ... Perspectiva ... zugebrauchen Lust haben, Simmern. Facsimile reprint Graz 1970. Later edition Frankfurt 1546. Kästner, Abraham Gotthelf 1752 Perspectivae et projectionum theoria generalis analytica, Leipzig. 1774 “Die Perspective” in Anfangsgründe der Arithmetik, Geometrie ... und Perspectiv, third revised edition Göttingen, 460–469. First edition appeared in Göttingen 1752 and the fifth enlarged in Göttingen 1792. Publications on Perspective 757

Karsten, Wenceslaus Johann Gustav 1775 “Die Perspectiv” in Lehrbegrif der gesamten Mathematik, Greifswald, vol. 7, 110–928. Kaschube, Johann Wenceslaus 1717 “Die Perspectiv-Kunst” in Cursus mathematicus, oder deutlicher Begriff der mathematischen Wissenschaften ..., Jena, 353–361. Kirby, John Joshua 1754 Dr. Brook Taylor’s Method of Perspective Made Easy, Both in Theory and Practice, Ipswich. Second edition Ipswich 1755, this contains an appendix which was issued separately in 1754. For later editions, see Kirby 1765. s.a. Dr. Brook Taylor’s Method of Perspective, compared with Examples lately publish’d on this Subject as Sirigatti’s by Isaac Ware, London. According to De MorganS 1861 this book was published in 1757. 1761 The Perspective of Architecture ... Deduced from the Principles of Dr. Brook Taylor, Part First Contains the Description and Use of a new Instrument Called the Architectonic Sector, Part the Second, a New Method of Drawing ... in Perspective, London. The first part also appeared as a separate book London 1761. 1765 Dr. Brook Taylor’s Method of Perspective Made Easy, Both in Theory and Practice, third revised and enlarged editon of Kirby 1754, in folio as well as in quarto both of which were reissued London 1768. Kircher, Athanasius 1646 “De arte scenographica” in Ars magna lucis et umbrae, Roma, 161–196. Second edition Amsterdam 1671, 124–143. Koutny, E., see Peschka & Koutny Lacaille, Nicolas Louis 1756 “Traité de perspective” in Leçons élémentaires d’optiques, second edition, Paris, 128–198. In the first edition of his book on optics, Lacaille did not treat perspective. Later edition Paris 1808. Lairesse, Gerard de 1707 Het groot schilderboek, 2 vols., Amsterdam. Several later editions, among them Amsterdam 1712, Haarlem 1740. English translation next title. 1738 The Art of Painting in all its Branches, tr. John Frederick Fritsch, London. Lambert, Johann Heinrich 1752 Manuscript entitled Anlage zur Perspektive edited in Lambert 1943, 161–186, and translated into French in Lambert 1981. 1759 Lambert 1759 refers to both the two following items.

17591 La perspective affranchie de l’embaras du plan géométral, Zürich. Facsimile reprints Paris 1977 and Alburgh 1987. German edition below.

17592 Die freye Perspektive, oder Anweisung jeden perspektivischen Aufriss von freyen Stücken und ohne Grundriss zu verfertigen, Zürich. Second edition as part of Lambert 1774. Reprinted in Lambert 1943, 192–301. 1768 Kurzgefasste Regeln zu perspectivischen Zeichnungen vermittelst eines ... Proportional-Zirkels, Augsburg. 1774 Die freye Perspective ... mit Anmerkungen und Zusätzen vermehrt, Zürich. Reprinted in Lambert 1943, 309–380. French translation of the Anmerkungen 758 First Bibliography

in LaurentS 1987, 193–284. Page references to Lambert 1774 are to the part containing the Zusätze. 1799 “J.H. Lamberts Grundsätze der Perspectiv, aus Betrachtung einer perspectivisch gezeichneten Landschaft abgeleitet”, ed. Johann Bernoulli, Archiv der reinen und angewandten Mathematik, vol. 9, 1–21. 1943 Johann Heinrich Lambert, Schriften zur Perspektive, ed. Max Steck, Berlin. 1981 Essai sur la perspective, ed. Roger Laurent and tr. Jeanne Peiffer, Coubron. Translation of Anlage zur Perspektive (Lambert 1752). Lamy, Bernard 1701 Traité de perspective, Paris. Later edition Amsterdam 1734. English translations in the next items. 1702 A Treatise of Perspective, tr. A. Forbes, London* (SothebyS 2002, 238). 1710 Perspective made Easie, tr. A. Forbes, London. Facsimile reprint Alburgh 1987. Lautensack, Heinrich 1564 Des Circkels unnd Richtscheyts, auch der Perspectiva, und Proportion der Menschen und Rosse, kurtze doch gründtliche Underweisung, des rechten Gebrauchs, Frankfurt. Lauterbach, Anton Bernhard 1717 Clavis perspectivae verticalis geometrica, Jena.* Le Breton, Adèle 1828 Traité de perspective simplifiée (linéaire) ..., Paris.* Second edition Paris 1832. Leclerc, Sébastien 1679 Discours touchant le point de veue, dans lequel il est prouvé que les choses qu’on voit distinctement, ne sont veuës que d’un oeil, Paris. Lencker, Hans 1567 Perspectiva literaria. Das ist ein clerliche Fürreyssung, wie man alle Buchstaben ... in die Perspectif ... bringen mag, Nürnberg. Several later editions. Reprint Frankfurt 1972. 1571 Perspectiva. Hierinnen auffs kürtzte beschrieben ... wird, ein newer ... Weg, wie allerley Ding ... in Grund zulegen ist, ... ferner in die Perspectyf gebracht werden mag ..., Nürnberg. Later edition Nürnberg 1595. Leonardo da Vinci Codex Atlanticus Biblioteca Ambrosiana, Milano, published in Leonardo 1894. Codex Urbinas 1270 compiled by Francesco Melzi around 1530, Biblioteca Vaticana, Roma, published in Leonardo 1956 and in Leonardo 1995. Manuscript A 1492, Institut de France, Paris, published in Leonardo 1881, vol. 1. Manuscript Arundel 1480–1518, British Library, London, published in Leonardo 1923. Manuscript Ash I 1487–1490, Institut de France, Paris, published in Leonardo 1881, vol. 6. Manuscript C 1490–1491, Institut de France, Paris, published in Leonardo 1881, vol. 3. Manuscript E 1513–1514, Institut de France, Paris, published in Leonardo 1881, vol. 3. Publications on Perspective 759

Manuscript Forster around 1505, Victoria and Albert Museum, London, published in Leonardo 1923. Manuscript G 1510–1515, Institut de France, Paris, published in Leonardo 1881, vol. 5. Manuscript W 1478–1518, Royal Library, Windsor, published in Leonardo 1957, Leonardo 1968, and Leonardo, 1978.

16511 Trattato della pittura di Lionardo da Vinci, ed. Raphael du Fresne, Paris. Numerous later editions in several languages, the first translations being the next items. For a list of editions from the period 1651–1956, see SteinitzS 1958.

16512 Traité de la peinture, tr. Roland Fréart de Chambray, Paris. 1721 A Treatise of Painting, tr. John Senex, London. 1724 Tractat von der Mahlerey, tr. Johann Georg Böhm, Nürnberg. Second edition Nürnberg 1747. 1802 A Treatise on Painting, tr. John Francis Rigaud, London. Reprinted New York 2002. 1881 Les manuscripts de Léonard de Vinci ... de la bibliothèque de l’Institut, 6 vols., ed. and tr. Charles Ravaisson-Mollien, Paris 1881–1891. 1894 Il codice Atlantico di Leonardo da Vinci nella Biblioteca Ambrosiana di Milano, 35 vols., ed. G. Piumati, Firenze, 1894–1904. 1923 I manoscritti e i disegni di Leonardo da Vinci, Roma 1923–1941. 1956 Treatise on Painting, ed. and tr. A. Philip McMahon, Princeton New Jersey. 1957 Leonardo da Vinci: Fragments at Windsor Castle from Codex Atlanticus, ed. Carlo Pedretti, London. 1964 Leonardo da Vinci on Painting. A Lost Book (Libro A) Reassembled from the Codex Vaticanus Urbinas 1270 and from the Codex Leiceister, ed. and tr. Carlo Pedretti, Berkeley. 1968 A Catalogue of Drawings by Leonardo da Vinci in the Collection of Her Majesty the Queen at Windsor Castle, 3 vols., ed. Kenneth Clark and Carlo Pedretti, London 1968–1969. 1970 The Notebooks of Leonardo da Vinci, 2 vols., ed. and tr. Jean Paul Richter, New York. Reprint of The Literary Works of Leonardo da Vinci, London 1883. 1977 Carlo Pedretti, The Literary Works of Leonardo da Vinci. A Commentary to Jean Paul Richter’s Edition, 2 vols., London. 1978 Leonardo da Vinci. Corpus of the Anatomical Studies in the Collection of Her Majesty the Queen at Windsor Castle, 3 vols., ed. Kenneth D. Keele and Carlo Pedretti, London 1978–1980. 1989 Leonardo on Painting. An Anthology of Writings by Leonardo da Vinci, ed. and tr. Martin Kemp and Magaret Walker, New Haven. 1995 Libro di pittura: Codice urbinate lat. 1270 nella Biblioteca apostolica Vaticana / Leonardo da Vinci, ed. Carlo Pedretti, tr. Carlo Vecce, Firenze. Leupold, Jakob 1713 Anamorphosis mechanica nova, oder Beschreibung dreyer neuen Maschinen mit welchen ... mancherley Bilder und Figuren können gezeichnet werden dass sie ganz ungestalt und unkäntlich fallen ..., Leipzig. First published in Acta eruditorum 1712. Lomazzo, Giovanni Paolo 1584 “Libro quinto della prospettiva” in Trattato dell’arte della pittura, scoltura, et architettura. Milano. Several later editions. Fascimile of the 1584 edition Hildesheim 1968. English translation next title. 760 First Bibliography

1598 A Tracte Containing Artes of Curious Paintinge, Carvinge & Buildinge, ed. Richard Haydock, Oxford. Lorenz, Johann Friedrich 1799 “Von den ersten Gründen der Perspectiv” in Grundriss der reinen und angewandten Mathematik. Zweyter Theil. Die angewandte Mathematik, second edition Helmstedt, 132–138. First edition Helmstedt 1791. Maignan, Emmanuel 1648 Perspectiva horaria ..., Roma. Proposition 77 in the third book, 438–449, deals with anamorphoses. Malton, James 1800 The Young Painter’s Maulstick: being a Practical Treatise on Perspective ... Founded on the Process ... of Vignola and Sirigatti, ... United with the Theoretic Principles of ... Dr. Brook Taylor ... Addressed to Students in Drawing, London. Malton, Thomas 1775 A Compleat Treatise on Perspective in Theory and Practice on the True Principles of Dr. Brook Taylor, Made Clear ..., London. Also London 1776, 1778 and 1779. 1783 An Appendix or Second Part to the Compleat Treatise on Perspective, London. Second edition London 1800. Marolois, Samuel 1614 La perspective contenant la theorie et la pratique, Den Haag. This work was reprinted often, among the years of publication are 1628, 1638, 1647 and 1662; it appeared in Dutch, German, French, and Latin separately and as part of Marolois’s Opera mathematical Œuvres mathematiques which appeared from 1614 onwards. There is some language confusion in several of the editions their title page being in one language and the main text in another. Martin, Benjamin 1764 “Universal Perspective” in A New and Comprehensive System of Mathematical Institutions, Agreeable to the Present State of Newtonian Mathesis, vol. 2, London, 148–228. s.a. The Principles of Perspective explained in a Genuine Theory and Applied in an Extensive Practice. With the Construction and Uses of all such Instruments as are Subservient to the Purpose of this Science, London. 1771 The Description and Use of a Graphical Perspective and Microscope for Drawing all Kinds of Objects in True Perspective ..., London. A booklet of a dozen pages of which nine deals with a perspective instrument. Mayer, Johann Tobias 1786 “Perspectivische Zeichnungen” & “Katoptriche Zeichnungen” in Unterricht zur praktischen Rechenkunst, zu geometrischen, perspectivischen und optischen Zeicnungen ... ehemals durch Schübler und Rost verfasset, nun aber umgeändert und mit Zusätzen vermehrt, Nürnberg, 211–262 and 265–272. Meister, Albrecht Ludwig Friedrich 1753 Instrumentum scenographicum, Göttingen. Publications on Perspective 761

Mersenne, Marin 1644 “De arte perspectivae” in Universae geometriae mixtae ..., Paris, 541–548. Michel, S.N. 1771 Traité de perspective linéaire, Paris. Mönnich, Bernhard Friedrich 1794 Versuch die mathematischen Regeln der Perspektive für den Künstler ohne Theorie anwendbar zu machen, Berlin. Second edition Berlin 1801. Mohr, Georg 1672 Euclides Danicus, Amsterdam. One edition in Danish and another in Dutch. The problems 19–22 in part two deal with perspective constructions. Monge, Gaspard 1820 “Théorie de la perspective” in Géométrie descriptive,4e édition augmentée d’une théorie des ombres et de la perspective, extraite des papiers de l’auteur, par M. Brisson, Paris, §§ 136–139, later edition Paris 1827. Reprinted in L’École nor- male de l’an III. Leçons de mathématiques, ed. Jean Dhombres et. al, Paris 1992. Moxon, Joseph 1670 Practical Perspective, or, Perspective Made Easie, London. Muller, John 1765 “Elements of Perspective” in Elements of Mathematics. Third edition which is “improved with an addition of a new treatise on perspective”, London, 304–312. Murdoch, Patrick 1746 “Perspectivae linearis principia”, Section I in Neutoni genesis curvarum per umbras seu perspectivae universalis elementa; exemplis coni sectionum et linearum tertii ordinis illustrata, London, 1–18. French translation in Taylor 1757. Mydorge, Claude 1638 Examen du livre des recreations mathématiques et des problemes en géometrie, mechanique, optique & catoptrique, Paris. Revised second edition with the title Recreations mathematiques ..., Paris 1661. Problem 2 touches upon perspective. Niceron, Jean François 1638 La perspective curieuse, ou magie artificiele des effets merveilleux ..., Paris. Later enlarged editions Paris 1652, Paris 1663, and Paris 1679. Revised Latin edition below. 1646 Thaumaturgus opticus ..., Paris. Noble, Edward 1771 The Elements of Linear Perspective, London. Oldenburg, Henry 1669 “The Description of an Instrument, Invented Divers Years ago by Dr. Christopher Wren, for Drawing the Out-Lines of any Object in Perspective”, Philosophical Transactions of the Royal Society, vol. 4, 898–899.4

4The text is not signed, but probably written by the secretary Henry Oldenburg (BennettS 1982, 75). 762 First Bibliography

Orsini, Baldassare 1771 Della geometria e prospettiva pratica, 2 vols., Roma 1771* and 1773* (SothebyS 2002, 293). Ozanam, Jacques 1693 La perspective théorique et pratique ..., vol. 4 of Ozanam’s Cours de mathéma- tique, 5 vols., Paris. The Cours was reissued Paris 1697 and Amsterdam 1699 and appeared in English as Cursus mathematicus: Or a Compleat Course of the Mathematicks, 5 vols., London 1712. Moreover La perspective was edited separately Paris, 1711, 1720, and 1769. Pélerin, Jean, see Viator Peschka, Gustav A. & Koutny, E. 1868 Freie Perspektive in ihrer Begründung und Anwendung, Hannover. Petitot, Ennemond Alexandre 1758 Raisonnement sur la perspective pour en faciliter l’usage aux artistes/ Ragionamento sopra la prospettiva ..., Parma; parallel French and Italian text. Pfinzing, Paul 1599 Ein schöner kurtzer Extract der Geometriae unnd Perspectivae, Nürnberg. Appeared in a second revised edition under the following title. 1616 Optica, das ist gründtliche doch kurtze Anzeigung wie notwendig die löbliche Kunst Geometriae seye inn der Perspectiv. Augsburg. Philips, Caspar Jacobszoon 1765 Uitvoerig onderwys in de perspectiva of doorzichtkunde, Amsterdam. Second printing, Amsterdam 1781. Edited in German as Ausführlicher Unterricht in der Perspective, Degen 1803. 1775 Handleiding in de spiegelperspectief, om door de regulen der doorzichtkunde alle voorwerpen in vlakke spiegels over te brengen, Amsterdam. Later editions Amsterdam 1780 and 1803.

17861 Wis-meet-en doorzichtkundige handleiding volgende welke men ten allen tyden en plaatse der stand der zonne en maane ..., Amsterdam.

17862 Zeemans onderwijser in de tekenkunst of handleiding om door geometrische, doorzichkundige en perspectivische regelen ..., Amsterdam. 1788 Handleiding om in de kunst-tafereelen den afstand het oog des zienders tot de zelve ... als ook de der perspectivische regelen ..., Amsterdam. Piero della Francesca Pros De prospectiva pingendi, manuscript from before 1492. Exists in an Italian and a Latin version – both with the Latin title. The earliest Italian version, a Parma codex, is partially an autograph. This was first printed together with a German translation in Piero 1899, and published again in 1942 as the first edition of Piero 1974. References are to Piero 1974. 1899 Petrus Pictor Burgensis: De prospectiva pingendi, tr. Constantin Winterberg, Strasbourg. 1974 De prospectiva pingendi, 2 vols., ed. Giusta Nicco Fasola, Firenze. First edition Firenze 1942 and third edition Firenze 1984. 1998 De la perspective en peinture, ed. Jean Pierre Le Goff, Paris. Publications on Perspective 763

Piranesi, Giovanni Battista 1750 Opere varie de architettura, prospettiva ..., ed. Giovanni Bouchard, Roma. Pozzo, Andrea 1693 Perspectiva pictorum et architectorum/Prospettiva de’ pittori e architetti, 2 vols., Roma 1693 and 1700. As the title indicates the work has parallel Latin and Italian text. Dozens of later editions of the first part in several languages and various combinations of languages (KerberS 1971, 267–270). In fact both volumes were available in French, German, and English rather early in the 18th century (ibid.). 1707 Rules and Examples of Perspective, in Latin and English, ed. John James with new engravings by John Sturt, London. This edition exists in two printings, one by B. Motte and one by J. Senex and J. Osborn which is undated. Facsimile reprint of the Motte edition New York 1991 and facsimile of the Senex and Osborn edition, in reduced size, New York 1989. Priestley, Joseph 1770 A Familiar Introduction to the Theory and Practice of Perspective, London. Second edition 1780. Reprinted New York 1970. 1772 “A Short History of Perspective”, in The History and Present State of Discoveries Relating to Vision, Light and Colours, 2 vols., London, 91–96. Quadri, Giovanni Lodovico 1744 La prospettiva pratica delineata in tavola a norma della secondo regola di Giacomo Barozzi da Vignola, Bologna. Reisch, Gregor 1508 “Introductio architecturae et perspectivae” in Margarita philosophica nova, Strassbourg. Copy without reference of parts of Viator 1505. Many later editions. Ringelberg, Joachim Fortius 1531 “Optice” in Opera, Lyon, 459–480. Facsimile reprint Niewkoop 1967. The section on optics is completely devoted to perspective. Rödel, Johann Michael 1796 Abhandlungen von den zufälligen Punkten in der Perspektivkunst für Werkmeister, Leipzig. The book has a preface by Abraham Gotthelf Kästner. First edition Coburg 1784. Rohault, Jacques 1682 “La perspective” in Œuvres posthumes, ed. Claude de Clerselier, Paris. In the second edition Den Haag 1690, “La perspective” appears in vol. 2, 259–284. Rost, Johann Leonhard (see also Schübler & Rost) 1745 Mathematischer Lust und Nutzgarten ... darinnen das Nothwendigste von der Arithmetica vulgari ... Sammt einer Einleitung zur Perspectiv, wie sie in des Herrn Desargues Anfangsgründe ..., Nürnberg.*5

5Most likely, this is a second edition of Schübler & Rost 1724 as the two books have the same title, but I have not had the occassion to examine Rost 1745. 764 First Bibliography

Roy, Claude 1756 Essai sur la perspective pratique par le moyen du calcul, Paris. Ryff, Walther Hermann (also known as Gualtherus Rivius) 1547 Der furnembsten, notwendigsten, der ganzen Architectur angehörigen mathematischen und mechanischen Künst ..., Nürnberg. Later editions Nürnberg 1558 and Basel 1582. Sabbatini, Niccolò 1638 Pratica di fabricar scene e machine ne’ teatri, Ravenna, second enlarged edition. First edition 1637. Facsimile of the 1638 edition together with a German translation by Willi Flemming, Weimar 1926. Part of it translated into English in HewittS 1958. Salmon, William 1672 “The General Practice of Perspective” in Polygraphice or the Art of Drawing ..., London, 73–79. The book reappeared frequently in the following decades. Sandrart, Joachim 1675 L’Academia todesca ... oder teutsche Academie der edlen Bau-Bild-und Mahlerey-Künste ... Darinn enthalten ein gründlicher Unterricht ... von der Perspectiv, Nürnberg. Edited by A.R. Peltzer, München 1925. Scheiner, Christoph 1631 Pantographice ... prior epipedographicen, sive planorum, posterior stereographi- cen, seu solidorum ..., Roma. Later editions in Italian among them the next item. 1653 Prattica del parallelogrammo da disegnare del P. Christoforo Scheiner, ed. Giulio Troili, Bologna. Scherffer, Karl 1781 “Perspektivische Aufgaben durch welche der Gebrauch des Tangentenmaassstabes ... erleichtert wird” in Beyträge zur Mathematik, Wien, 191–225. Schön, Erhard 1538 Underweissung der Proportzion unnd Stellung der Possen ... wie man das vor Augen sicht ..., Nürnberg. Enlarged editions Nürnberg 1540–1543 (SchülingS 1973, 40–42). Facsimile reprint ed. Leo Baer, Frankfurt a. M. 1920. Schooten, Frans van 1660 “Tractaet der perspective, ofte schynbaere teycken-konst. Waer in de fonda- menten derselbe konst op het kortste verhandelt en betoont worden”, published in Mathematische Oeffeningen, Amsterdam, 501–544. Schott, Gaspar 1657 “De magia anamorphosi optica”, Liber III of Magia universalis naturae et artis, Pars I: Optica, Würzburg, 99–169. Later edition Bamberg 1677. 1677 “Opticae practicae sive perspectivae” in Cursus mathematicus, Bamberg, 470. Posthumous edition. Schübler, Johann Jacob (see also Schübler & Rost) 1719 Perspectiva pes picturae. Das ist kurze und leichte Verfassung der practicabelsten Regul zur perspectivischen Zeichnungs-Kunst, 2 vols., Nürnberg 1719 and 1720. Several later editions with the title Perspectiva geometrico-practica. Publications on Perspective 765

Schübler, Johann Jacob & Rost, Johann Leonhard 1724 “Von der Perspectiv” and “Von der Anamorphosi Catoptrica” in Mathematischer Lust und Nutzgarten ... darinnen das nothwendigste von der Arithmetica vulgari ... sammt einer Anleitung zur Perspectiv wie sie in des Herrn Desargues Anfangsgründe ..., Nürnberg, 204–249 and 249–262. The title page only reveals that the book is written by S.R. On page 369, I have explained why I consider S. R. to be an abbreviation of Schübler and Rost. Segner, Johann Andreas 1779 Gründe der Perspectiv, Berlin. Serlio, Sebastiano 1545 D’Architettura/L’Architecture. Il secondo libro di perspettiva/Le second livre de perspective, Paris. This second book in Serlio’s work on architecture was, as the title indicates, printed with parallel Italian and French text. It became very popular, went through many editions and was translated into Dutch, English, German, Latin and Spanish. The first Dutch and English translations are listed separately. The Italian text appeared again in Serlio 1584. 1553 Den tweeden boeck van architecturen Sebastiani Serlii tracterende van perspec- tyven, tr. Pieter Coecke van Aelst, Antwerpen. 1584 “Il secondo libro di prospettiva”, in Tutte l’opere d’architettura, Venezia. Facsimile reprint Sala Bolognese 1987. Reprints 1600 and 1619, fascimile edition of the latter Ridgewood, New Jersey, 1966. 1611 The Second Booke of Architecture ... Entreating of Perspective which is Inspection or Looking into by Shortening of the Sight, tr. Robert Peake, London. This book was a translation of the Dutch edition. Sheraton, Thomas 1793 “Of Perspectives” in The Cabinet-maker and Upholsterer’s Drawing Book, London, 177–350. Silvabelle, Jacques 1757 “Méthode generale, pour trouver la perspective d’un objet donné, par le moyen des lignes perpendiculaires & paralleles” in Taylor 1757/1759, xxix–xxxvi. Sirigatti, Lorenzo 1596 La pratica di prospettiva, Venezia. Later edition Venezia 1625. English translation mentioned below. 1756 Practice of Perspective with Figures Engraved by Isaac Ware, London. Smith, Godfrey 1755 The Laboratory; or School of Arts ... and Easy Introduction to the Art of Drawing in Perspective ... 2 vols., London*. Sobro, Aléxandre s.a. Traité de perspective à l’usage des artistes ..., Paris.* Presumably published in the 1790s. Spampani, Giovanni Battista & Antonini, Carlo 1770 “Prospettiva pratica di M. Giacomo Barozzi da Vignola” in Il Vignola illustrato proposto Giambattista Spampani e Carlo Antonini studenti d’ architettura ... , Roma. 766 First Bibliography

Stevin, Simon

16051 “Van de verschaeuwing. Eerste bouck der deursichtighe” in Derde Stuck der Wisconstighe Ghedachtnissen, Leiden. Most of it is reprinted in Stevin 1978, on the even pages from 796 to 964. Translations listed below.

16052 “De optica” in Hypomnemata mathematica a Simone Stevino. Tomus tertius, ed. and tr. Willebrord Snellius, Leiden. Reprinted in SinisgalliS 1978.

16053 “Des perspectives” in Mémoires mathématiques par Simon Stevin. Livre trois, ed. and tr. Jean Tuning, Leiden. Slightly revised version of this translation in Stevin 1634. 1634 Les œuvres mathématiques de Simon Stevin ..., ed. and tr. Albert Girard, Leiden. 1958 The Principal Works of Simon Stevin, ed. and tr. Dirk J. Struik, Amsterdam,

vol. II.B. In this volume are included a facsimile of most of Stevin 16051 and an English translation of it. S 1978 Sinisgalli 1978 contains a reprint of Stevin 16052 together with an Italian translation. Stör, Lorenz 1567 Geometria et Perspectiva. Hierinn etliche zerbrochne Gebew den Schreinern in eingelegter Arbait dienstlich ... Augsburg. Reprint Frankfurt 1972. Sturm, Johann Christoph 1701 “Optica” in Mathesis juvenilis, Nürnberg, vol. 2., second edition, perspective and anamorphoses are dealt with on pages 154–164. First edition Nürnberg 1699. Many later editions also in German. Sulzer, Johann Georg 1787 “Perspectiv” in Allgemeine Theorie der schönen Künste, Leipzig, 552–569. Tacquet, Andreas 1669 “De perspectiva sive projectionis scenographicae theoria et praxi” in the posthumously published Opera mathematica, Antwerpen, 158–177. Later edition Antwerpen 1707. Taylor, Brook

17151 Linear Perspective: or, a New Method of Representing justly all Manner of S Objects, London. Facsimile reprint in Andersen 19921. 17152 “Accounts of Books: Linear Perspective ... by Brook Taylor ... London 1715”, Philosophical Transactions, vol. 29, 300–304. Published anonymously but its contents clearly show that Taylor is the author. 1719 New Principles of Linear Perspective: or the Art of Designing on a Plane the Representations of all sorts of Objects, in a more General and Simple Method than S has been done before, London. Facsimile reprint in Andersen 19921. Reissued as the third edition (because Taylor 1715 was counted as the first edition) by J. Colson 1749. Edited as Dr. Brook Taylor’s Method of Perspective by I. Ware, London 1767. A revised editon London 1811. Edited as Brook Taylor’s Principles of Linear Perspective by J. Jopling, London 1835. Translations listed below. 1755 Elementi di perspettiva secondo li principii di Brook Taylor, con varii aggiunti, ed. and tr. François Jacquier, Roma. 1757 Nouveaux principes de la perspective linéaire, traduction de deux ouvrages, l’un anglois de Docteur Brook Taylor, l’autre latin de M. Patrice Murdoch, Amsterdam. Publications on Perspective 767

Second edition 1759. The translator’s name is not mentioned, but there is a general agreement that the translation was made by Antoine Rivoire. The book also contain a section written by Jacques Silvabelle (Silvabelle 1757). 1782 Nuovi principii della prospettiva lineare, ed. and tr. Giacopo Stellini, published in StelliniS 1782. Torelli, Giuseppe 1788 Elementorum prospectivae libri duo, ed. J.B. Bertolini, Verona. Torricelli, Evangelista Pros “Prospettiva pratica”, unfinished, undated manuscript (Gal. 134 T.XXIV della Div. IV, Mss. Galileiani, Biblioteca Nazionale di Firenze), presumably from the 1640s; part of it is printed in Torricelli Opere, vol. 2, 313–320. Opere Opere di Evangelista Torricelli, 4 vols., ed. Gino Loria & Giuseppe Vassura, Faenza, 1919–1944. Troili, Giulio 1683 Paradossi per pratticare la prospettiva senza saperla, Bologna. First edition Bologna 1672. Valenciennes, Pierre Henri 1800 Elémens de perspective pratique à l’usage des artistes, Paris. An VIII. Vaulezard, Jean Louis 1630 Perspective cilindrique et conique ou traicté des apparences veuës par le moyen des miroirs ..., Paris. 1631 Abrégé ou racourcy de la perspective ..., Paris. Later editions Paris 1633, and Paris 1643. Viator byname of Jean Pélerin 1505 De artificiali perspectiva, Toul with Latin and French text. Facsimile in IvinsS 1975. Part of De artificiali perspectiva was pirated by Gregor Reisch under the name Introductio architecturae et perspectivae (Reisch 1508). Another pirated edition by the printer Jörg Glockendon appeared as Von der Kunnst Perspectiva (Glockendon 1509). Later editions, see below. 1509 De artificiali perspectiva, Toul; revised version of the 1505 edition with parallel Latin and Italian text. Facsimile reprint Paris 1860 and in IvinsS 1975. Republished in a slightly revised version Toul 1521. Later edition: La perspective positive de Viator, ed. Mathurin Jousse,6 La Fleche 1635. Critical edition of the text in Brion-GuerryS 1962. For a comparison of the four editions, see Brion-GuerryS 1962, Table de Concordance. Vignola, Giacomo Barozzi da 1583 Le due regole della prospettiva pratica con i commentarii del R. P. M. Egnatio Danti, Roma. Facsimile reprints Vignola 1974 and Alburgh 1987. During the seventeenth and eighteenth centuries a dozen editions of this book were issued. Facsimile of the Venezia 1743 edition Sala Bolognese 1985.

6Liliane Brion-Guerry has pointed out that Estienne Marlange helped with the prepa- ration of this edition, but his name disappeared for unknown reasons from the title page (Brion GuerryS 1962, 160–162). 768 First Bibliography

Viola-Zanini, Giuseppe 1629 Della architettura ... con ... regole prospettiva, Padova. Later edition 1677. Vittone, Bernardo Antonio 1760 “Della prospettiva ...” in Istruzioni elementari per indirizzo de’giovani allo studio dell’Architettura civile, Lugano, 527–545. Vlaming, Jacob de 1773 Kort zaamenstel der perspectief op eene geheele nieuwe wyze afgeleid uit de gron- den der driehoeksmeetinge, Amsterdam. Voch, Lukas 1780 Abhandlung von der Perspektivkunst. Worinnen nicht allein die algemeine, als auch die Sirigatische ... und ihre Gründen gelehret wird ... Zum Nützen derer Baumeister, Ingenieurs. Augsburg.* Vredeman de Vries, Johan 1560 Artis perspectivae ..., Antwerpen. Several later enlarged editions, some with the text in Dutch and at least one with the text in German. 1560 Scenographiae sive perspectivae, Antwerpen. Later enlarged editions. 1604 Perspective, 2 vols., Den Haag 1604 and 1605. For some later editions, see Vredeman de Vries 1615. Facsimile of the plates New York 1968. Facsimile of the entire work with comments in Dutch and English, a transcription of de Vries’s text into modern Dutch and a translation of it into English, ed. and tr. Peter Karstkarel, Mijdrecht 1979. 1615 Perspective ... augmentée et corrigée ... par Samuel Marolois, Den Haag. Several later editions in Marolois’s Opera mathematica (Marolois 1614) Weidemann, Friedrich Wilhelm 1746 Kurtze Einleitung zu der optischen Perspectiv nebst deren ersten Grund und Lehrsätzen, Berlin. First edition Berlin 1733. Weidler, Johann Friedrich 1736 “Ars perspectiva” in Institutiones matheseos, Wittenberg, 254–263. First edition Wittenberg 1718, several later editions. Weinbrenner, Friedrich 1817 Perspectivische Zeichnungslehre, Architektonisches Lehrbuch Teil 2, Tübingen.* Werner, Georg Heinrich 1763 Die Erlernung der Zeichenkunst durch Geometrie und Perspectiv, Erfurt. The second edition appeared under the title shown in the next item. 1796 “Von der Perspectiv” in Gründliche Anweisung zur Zeichenkunst ..., Erfurt, 61–122. Wiedeburg, Johann Bernhard 1735 “Von der Perspectiv und mancherley Verstellungen der Figuren” in Einleitung zu denen mathematischen Wissenschaften, Jena. First edition Jena 1725. Wolff, Christian 1715 “Elementa perspectivae” in Elementa matheseos universae, Halle, vol. 2, 89–115. Second edition in Elementa matheseos universae, Halle 1735, vol. 3, 103–134, facsimile of the latter Hildesheim 1968. Publications on Perspective 769

1737 “Perspectiv” in Anfangsgründe aller mathematischen Wissenschaften, fifth edition, Halle, vol. 3, 1065–1078. Wood, John 1799 Elements of Perspective, Containing the Nature of Light and Colours and the Theory and Practice of Perspective, Edinburgh. Wright, John 1772 “The Principles of Perspective” in Elements of Trigonometry ..., Edinburgh, 109–143. Zanotti, Eustachio 1755 “De perspectiva in theorema unum redacta”, De Bononiensi scientarum et artium instituto atque academia commentarii, vol. 3, 169–176. 1766 Trattato teorico-pratico di prospettiva, Bologna. Later editions Bologna 1782, Parma 1785, Milano 1825. Second Bibliography

Supplementary Literature

Aa, A. J. van der 1852 Biographisch Woordenboek der Nederlanden, Haarlem, vol. 3, reprint Amsterdam 1969. Abels, Joscijka Gabriele 1985 Erkenntnis der Bilder. Die Perspektive in der Kunst der Renaissance, New York. Ackerman, James S. 1978 “Leonardo’s Eye”, Journal of the Warburg and Courtauld Institutes, vol. 41, 108–146, reprinted in AckermanS 1994, 97–147. 1994 Distance Points. Essays in Theory and Renaissance Art and Architecture, Cambridge Massachusetts. Allgemeine 1875 Allgemeine Deutsche Biographie, 56 vols., Leipzig 1875–1912. Andersen, Kirsti (see also Andersen & Grattan-Guinness) 1985 “Some Observations Concerning Mathematicians’ Treatment of Perspective Constructions in the 17th and 18th Centuries”, Mathemata, Festschrift für Helmuth Gericke, ed. M. Folkerts & U. Lindgren, Stuttgart, 409–425.

19871 “The Problem of Scaling and of Choosing Parameters in Perspective Constructions, Particularly in the One by Alberti”, Analecta Romana, vol. 16, 107–128.

19872 “Ancient Roots of Linear Perspective”, From Ancient Omens to Statistical Mechanics. Essays on the Exact Sciences Presented to Asger Aaboe, ed. J.L. Berggren & B.R. Goldstein, Copenhagen, 75–89.

19873 “The Central Projection in one of Ptolemy’s Map Constructions”, Centaurus, vol. 30, 106–113. 1990 “Stevin’s Theory of Perspective. The Origin of a Dutch Academic Approach to Perspective”, Tractrix, vol. 2, 25–62. 1991 “Desargues’ Method of Perspective. Its Mathematical Content, Its Connection to Other Perspective Methods and Its Relation to Desargues’ Ideas on Projective Geometry”, Centaurus, vol. 34, 44–91.

19921 Brook Taylor’s Work on Linear Perspective. A Study of Taylor’s Role in the History of Perspective Geometry. Including Facsimiles of Taylor’s Two Books on Perspective, New York.

19922 “The History of Linear Perspective from 1435 to the End of the 18th Century Seen in Mathematical Perspective”, Transactions of the XVth Congress of the International Association of Bibliophiles, ed. Poul A. Christiansen, Copenhagen, 21–37.

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Sources and Studies in the History of Mathematics and Physical Sciences

Continued from page ii

E. Kheirandish The Arabic Version of Euclid’s Optics, Volumes I and II

J. Lützen Joseph Liouville 1809–1882: Master of Pure and Applied Mathematics

J. Lützen The Prehistory of the Theory of Distributions

G.H. Moore Zermelo’s Axiom of Choice

O. Neugebauer A History of Ancient Mathematical Astronomy

O. Neugebauer Astronomical Cuneiform Texts

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B.A. Rosenfeld A History of Non-Euclidean Astronomy

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J. Sesiano Books IV to VII of Diophantus’ Arithemetica: In the Arabic Translation Attributed to Qustä ibn Lüqä

L. Sigler Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation

B. Stephenson Kepler’s Physical Astronomy

N.M. Swerdlow/O. Neugebauer Mathematical Astronomy In Copernicus’ De Revolutionibus

G.J. Toomer (Ed.) Apolonius Conics Books V to VII: The Arabic Translation of the Lost Greek Original in the Version of Banu¯Mu¯sa¯, Edited, with English Translation and Commentary by G.J. Toomer

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C. Truesdell The Tragicomical History of Thermodynamics, 1822–1854 Continued from previous page

I. Tweddle James Stirling’s Methodus Differentialis: An Annotated Translation of Stirling’s Text

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K. von Meyenn (Ed.) Wolfgang Pauli:Scientific Correspondence III: 1940–1949

K. von Meyenn (Ed.) Wolfgang Pauli:Scientific Correspondence IV, Part I: 1950–1952

K. von Meyenn (Ed.) Wolfgang Pauli:Scientific Correspondence IV, Part 2: 1953–1954

J. Stedall The Arithmetic of Infinitesimals: John Wallis 1656