The Trattato As Textbook: Francesco Di Giorgio's
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Symmetry As an Aesthetic Factor
Comp. & Maths. with Appls, Vol. 12B, Nos. I/2, pp. 77-82. 1986 0886-9561/86 $3,1)0+ .00 Printed in Great Britain. © 1986 Pergamon Press Ltd. SYMMETRY AS AN AESTHETIC FACTOR HAROLD OSBORNEt Kreutzstrasse 12, 8640 Rappersvill SG, Switzerland Abstract--In classical antiquity symmetry meant commensurability and was believed to constitute a canon of beauty in nature as in art. This intellectualist conception of beauty persisted through the Middle Ages with the addition doctrine that the phenomenal world manifests an imperfect replica of the ideal symmetry of divine Creation. The concept of the Golden Section came to the fore at the Renaissance and has continued as a minority interest both for organic nature and for fine art. The modern idea of symmetry is based more loosely upon the balance of shapes or magnitudes and corresponds to a change from an intellectual to a perceptual attitude towards aesthetic experience. None of these theories of symmetry has turned out to be a principle by following which aesthetically satisfying works of art can be mechanically constructed. In contemporary theory the vaguer notion of organic unity has usurped the prominence formerly enjoyed by that of balanced symmetry. From classical antiquity the idea of symmetry in close conjunction with that of proportion dominated the studio practice of artists and the thinking of theorists. Symmetry was asserted to be the key to perfection in nature as in art. But the traditional concept was radically different from what we understand by symmetry today--so different that "symmetry" can no longer be regarded as a correct translation of the Greek word symmetria from which it derives--and some acquaintance with the historical background of these ideas is essential in order to escape from the imbroglio of confusion which has resulted from the widespread conflation of the two. -
Engineers of the Renaissance
Bertrand Gille Engineers of the Renaissance . II IIIII The M.I.T.Press Massachusetts Institute of Technology Cambridge, Massachusetts ' ... � {' ( l..-'1 b 1:-' TA18 .G!41J 1966 METtTLIBRARY En&Jneersor theRenaissance. 11111111111111111111111111111111111111111111111111111111111111111 0020119043 Copyright @ 1966 by Hermann, Paris Translated from Les ingenieurs de la Renaissance published by Hermann, Paris, in 1964 Library of Congress Catalog Card Number 66-27213 Printed in Great Britain Contents List of illustrations page 6 Preface 9 Chapter I The Weight of Tradition 15 2 The Weight of Civilization 3 5 3 The German School 55 4 The First Italian Generation 79 5 Francesco di Giorgio Martini 101 Cj 6 An Engineer's Career -Leonardo da Vinci 121 "'"" f:) 7 Leonardo da Vinci- Technician 143 ��"'t�; 8 Essay on Leonardo da Vinci's Method 171 �� w·· Research and Reality ' ·· 9 191 �' ll:"'t"- 10 The New Science 217 '"i ...........,_ .;::,. Conclusion 240 -... " Q: \.., Bibliography 242 �'� :::.(' Catalogue of Manuscripts 247 0 " .:; Index 254 � \j B- 13 da Page Leonardo Vinci: study of workers' positions. List of illustrations 18 Apollodorus ofDamascus: scaling machine. Apollodorus of Damascus: apparatus for pouring boiling liquid over ramparts. 19 Apollodorus ofDamascus: observation platform with protective shield. Apollodorus of Damascus: cover of a tortoise. Apollodorus ofDamascus: fire lit in a wall andfanned from a distance by bellows with a long nozzle. 20 Hero of Byzantium: assault tower. 21 Hero of :Byzantium: cover of a tortoise. 24 Villard de Honnecourt: hydraulic saw; 25 Villard de Honnecourt: pile saw. Villard de Honnecourt: screw-jack. , 26 Villard de Honnecourt: trebuchet. Villard de Honnecourt: mechanism of mobile angel. -
Transfer of Islamic Science to the West
Transfer of Islamic Science to the West IMPORTANT NOTICE: Author: Prof. Dr. Ahmed Y. Al-Hassan Chief Editor: Prof. Dr. Mohamed El-Gomati All rights, including copyright, in the content of this document are owned or controlled for these purposes by FSTC Limited. In Production: Savas Konur accessing these web pages, you agree that you may only download the content for your own personal non-commercial use. You are not permitted to copy, broadcast, download, store (in any medium), transmit, show or play in public, adapt or Release Date: December 2006 change in any way the content of this document for any other purpose whatsoever without the prior written permission of FSTC Publication ID: 625 Limited. Material may not be copied, reproduced, republished, Copyright: © FSTC Limited, 2006 downloaded, posted, broadcast or transmitted in any way except for your own personal non-commercial home use. Any other use requires the prior written permission of FSTC Limited. You agree not to adapt, alter or create a derivative work from any of the material contained in this document or use it for any other purpose other than for your personal non-commercial use. FSTC Limited has taken all reasonable care to ensure that pages published in this document and on the MuslimHeritage.com Web Site were accurate at the time of publication or last modification. Web sites are by nature experimental or constantly changing. Hence information published may be for test purposes only, may be out of date, or may be the personal opinion of the author. Readers should always verify information with the appropriate references before relying on it. -
Copying, Commonplaces, and Technical Knowledge: the Architect-Engineer As Reader
COPYING, COMMONPLACES, AND TECHNICAL KNOWLEDGE: THE ARCHITECT-ENGINEER AS READER Alexander Marr I Recent work on the history of technology has drawn attention to the importance of manuscripts and, in particular, drawings for the design, construction, comprehension, and use of machines in the Renaissance and Early Modern period.1 Documents such as the workshop drawings of Antonio da Sangallo or the extensive extant papers of Heinrich Schick- hardt are now finding a place alongside better-known printed works, such as the ‘theatres of machines’ by Ramelli, Besson, and Bachot.2 Yet com- paratively little is known about the book ownership and reading habits of those artisans involved in the processes of machine design, construc- tion, and implementation. The present essay seeks to shed new light on these subjects, through an examination of an important – but somewhat neglected – manuscript compilation of text and images on technical top- ics (ranging from practical mathematics to building), made in the early seventeenth century by the French architect-engineer Jacques Gentillâtre (1578–c. 1623).3 To date, this manuscript has been discussed exclusively within the context of the theory and practice of architecture, yet the diversity of subjects with which it is concerned (notably the numerous uses to which machines may be put) demands that the document be 1 See e.g. Lefèvre W. (ed.), Picturing Machines, 1400–1700 (Cambridge, MA-London: 2004). 2 See the useful table of ‘Prominent Sources of Early Modern Machine Design’ in Lefèvre, “Introduction to Part I”, in idem, Picturing Machines 13–15. An important addition to this table is Ambroise Bachot’s theatre of machines: Gouuernail (Melun: 1598). -
FACTS Standards
FACTS Standards INTERNATIONAL STANDARD GUIDE FRM-400 Addopted-1997 Using The Goldenmean For Proportional Divisions In Decorative Standards-1998 Matting Revised-1999 Revised-2000 FACTS publishes this document as a public service. Its use is voluntary, and all results obtained by its use must be entirely the responsibility of the user. This document is subject to revision, change and/or withdrawal at any time. © FACTS 2000 1.00 Design (defined) To plan out in systematic, usually graphic form: To create or contrive for a particular purpose or effect: To create or execute in an artistic or highly skilled manner. 1.01 Everything can be called a design, but to achieve good design the particular purpose must be clear. 1.02 When designing for the framing of artwork art the purpose is " create a surrounding to complement with out distraction". 1.03 When designing for wall decor the latitude is greater, the purpose may be to create a greater interest, make a color or size statement, brighten a drab corner or create something everyone will ask about. 1.04 The Golden Mean provides a formula for the pleasing division of space. 2.00 The Golden Mean (divine proportion) 2.01 In about 300 BC a mathematician by the name of Euclid established a formula that also occurs in nature, when applied to an area that area can be divided into visually balanced unequal proportions that were visually pleasing to the eye. 2.02 In the 1st century BC Vitruvius, a Roman architect of c.90-c.20 BC, wrote De Architectura or the "Ten Books" documenting Roman and Greek architectural history and building practices. -
De Allereerste Nederlandse Vertaling Van (De) 'Divina Proportione'
Grootveld, Roelo s, Huylebrouck De allereerste Nederlandse vertaling van (De) ‘Divina Proportione’, mét talloze kritische voetnoten. D. Huylebrouck: vertaling van ‘Divina Proportione’ Inleidende vraag (Boekenbeurs%): 15de eeuw: uitvinding boekdrukkunst) wat was het meest gedrukte en verspreide boek* De Bijbel Nog ‘bestsellers’ uit de 15 de eeuw* Euclides: ‘Elementen’. Luca Pacioli: - ‘Summa de arit metica, ...’ - ‘Goddelijke Ver ouding’. Terloops: wat is wereldwi,d het meest gedrukte en verspreide boek vandaag* De catalogus van Ikea. D. Huylebrouck: vertaling van ‘Divina Proportione’ Luca Pacioli (1445-1517), broeder en wiskundige. In 14,- ontmoette ij Leonardo da Vinci Ludovico (145. - 1519 ). Sforza Luca Leonardo (Hertog Pacioli maakte de Milaan illustraties: /ijn enige offici1le publicaties. -iniatuur uit het manuscript van Gen.ve D. Huylebrouck: vertaling van ‘Divina Proportione’ Twee manuscripten nu bewaard in Gen4ve en in 5ilaan (14,8). 7 een gedrukte versie (150,). Boek: succes door de tekeningen van Leonardo. D. Huylebrouck: vertaling van ‘Divina Proportione’ Boek Pacioli: versc illende ‘delen’, waarvan vertaald werden: Einde Divina Proportione 0egin De 1rchitectura Beide delen niet gesc eiden door een titelblad. 1) ‘Divina Proportione’ .) ‘De Arc itectura’ D. Huylebrouck: vertaling van ‘Divina Proportione’ ‘De Arc itectura’; Er is een /ogenaamd ‘3 de deel’; Libellus: niet in de vertaling. Pacioli /egt: deel 3 = Piero della Francesca, ik publiceerde et als een gedrukt wederdienst in… Geen plagiaat; … eindigt met ‘Finis’. Dus: be oort niet tot Pacioli’s tractaat. D. Huylebrouck: vertaling van ‘Divina Proportione’ Later werd (de titel van) et boek veel geciteerd door adepten van de ‘myt e van de gulden snede’ Door gebrek aan een goede vertaling? Duits: ‘De Leer van de Gulden Snede’. -
Leonardo's Vitruvian Man Drawing: a New Interpretation Looking at Leonardo's Geometric Constructions
Nexus Netw J (2015) 17:507–524 DOI 10.1007/s00004-015-0247-7 RESEARCH Leonardo’s Vitruvian Man Drawing: A New Interpretation Looking at Leonardo’s Geometric Constructions Vitor Murtinho1 Published online: 9 April 2015 Ó Kim Williams Books, Turin 2015 Abstract Generally speaking, today’s scientific community considers that the famous figure drawn by Leonardo da Vinci at the end of the fifteenth century was made using the Golden ratio. More specifically, the relationship established between the circle’s diameter and the side of the square is a consequence of the geometric relationship probably discovered by Euclid, but made famous by Luca Pacioli in his De Divina proportione. Aware of the close working relationship between Leonardo and Pacioli, namely in the writing of this last book, the theory that establishes a close relationship between these two figures, making use of this remarkable mathematical relationship, has gained credibility. In fact, the use of the Divina proporzione, despite being a very stimulating construction on an intellectual level, presents too great a margin of error, especially for such a competent geometrician as Leonardo da Vinci was. For that reason, the relationship between these two figures (square and circle) is grounded on a much simpler geometric relationship than the one found at the base of the definition, for instance, of Le Corbusier’s Modulor. Keywords Leonardo da Vinci Á Vitruvian man Á Vesica piscis Á Golden number Á Proportion Introduction No human investigation may claim to be a true science if it has not passed through mathematical demonstrations, and if you say that the sciences that begin and end in the mind exhibit truth, this cannot be allowed, but must be & Vitor Murtinho [email protected] 1 CES-Department of Architecture, University of Coimbra, Colegio das Artes, Largo D. -
Palladio and Vitruvius: Composition, Style, and Vocabulary of the Quattro Libri
LOUIS CELLAURO Palladio and Vitruvius: composition, style, and vocabulary of the Quattro Libri Abstract After a short preamble on the history of the text of Vitruvius during the Renaissance and Palladio’s encounter with it, this paper assesses the Vitruvian legacy in Palladio’s treatise, in focusing more particularly on its composition, style, and vocabulary and leaving other aspects of his Vitruvianism, such as his architectural theory and the five canonical orders, for consideration in subsequent publications. The discussion on composition concerns Palladio’s probable plans to complete ten books, as an explicit reference to Vitruvius’ treatise. As regards style, the article highlights Palladio’s intention to produce an illustrated treatise like those of Francesco di Giorgio Martini, Sebastiano Serlio, and Giacomo Barozzi da Vignola (whereas the treatise of Vitruvius was probably almost unillustrated), and Palladio’s Vitruvian stress on brevity. Palladio is shown to have preferred vernacular technical terminology to the Vitruvian Greco-Latin vocabulary, except in Book IV of the Quattro Libri in connection with ancient Roman temples. The composition, style, and vocabulary of the Quattro Libri are important issues which contribute to an assessment of the extent of Palladio’s adherence to the Vitruvian prototype in an age of imitation of classical literary models. Introduction The De architectura libri X (Ten Books on Architecture) of the 1st-Century BCE Roman architect and military engineer Marcus Vitruvius Pollio was a text used by Andrea Palladio (1508-1580) and many other Renaissance architects both as a guide to ancient architecture and as a source of modern design. Vitruvius is indeed of great significance for Renaissance architecture, as his treatise can be considered as a founding document establishing the ground rules of the discipline for generations after its first reception in the Trecento and early Quattrocento.1 His text offers a comprehensive overview of architectural practice and the education required to pursue it successfully. -
Vitruvian Man and Divine Proportion
Vitruvian Man and Divine Proportion Leonardo da Vinci’s Vitruvian Man taking a fixed module, in each case, both was originally an illustration for a book on for the parts of a building and for the the works of the Roman architect Marcus whole, by which the method of symmetry Vitruvius Pollio (first century BCE), who is put to practice. For without symmetry designed many of the most beautiful and proportion no temple can have a temples in Rome. In his ten-volume work, regular plan; that is, it must have an exact De Architectura, Vitruvius established the proportion worked out after the fashion guidelines for classic Roman architecture. of the members of a finely shaped human Describing how a temple should be body.’’ planned and built, Vitruvius wrote: In this passage is found the key to the “The planning of temples depends composition of ancient architecture, which upon symmetry: and the method of this was firmly revived in the Renaissance. architects must diligently apprehend. It Echoing the ancient Greeks, the human arises from proportion (which in Greek body was seen as symbolic of all Nature, is called analogia). Proportion consists of the microcosm reflecting the macrocosm. Page 1 Thus Nature, in the form of the human Nature as follows: that is that 4 fingers body, was to be the architect’s (or the make 1 palm, and 4 palms make 1 foot, 6 artist’s) guide. In this form of architecture palms make 1 cubit; 4 cubits make a man’s (or art, engineering, or planning, etc.) height. And 4 cubits make one pace and the science of geometry is employed by 24 palms make a man; and these measures means of small whole numbers to build he used in his buildings. -
The Thin White Line: Palladio, White Cities and the Adriatic Imagination
Chapter � The Thin White Line: Palladio, White Cities and the Adriatic Imagination Alina Payne Over the course of centuries, artists and architects have employed a variety of means to capture resonant archaeological sites in images, and those images have operated in various ways. Whether recording views, monuments, inscrip- tions, or measurements so as to pore over them when they came home and to share them with others, these draftsmen filled loose sheets, albums, sketch- books, and heavily illustrated treatises and disseminated visual information far and wide, from Europe to the margins of the known world, as far as Mexico and Goa. Not all the images they produced were factual and aimed at design and construction. Rather, they ranged from reportage (recording what there is) through nostalgic and even fantastic representations to analytical records that sought to look through the fragmentary appearance of ruined vestiges to the “essence” of the remains and reconstruct a plausible original form. Although this is a long and varied tradition and has not lacked attention at the hands of generations of scholars,1 it raises an issue fundamental for the larger questions that are posed in this essay: Were we to look at these images as images rather than architectural or topographical information, might they emerge as more than representations of buildings, details and sites, measured and dissected on the page? Might they also record something else, something more ineffable, such as the physical encounters with and aesthetic experience of these places, elliptical yet powerful for being less overt than the bits of carved stone painstakingly delineated? Furthermore, might in some cases the very material support of these images participate in translating this aesthetic 1 For Italian material the list is long. -
Research Library Acquisitions
G e tty Resea r ch I n st i t u t e RESEARCH LIBRARY ACQUISITIONS The Resea rch Library at the Getty Resea rch Inst i tu te builds its special co l l e c t i o n s a cco rding to four broad thematic ca te g o r i es: Histo r i o g ra p hy of Art, Arc h i te c tu re, and A rchaeology; the Modern Period; History of Collecting and Display; and Visual So u rces. Selected Special Collections Acquisitions Made between July 1, 2001, and June 30, 2002 Historiography of Art, Gaspard Monge (French, 1746–1818) Architecture, and Archaeology Géométrie descriptive, Paris, 1799 The first complete edition of the course lec- RARE BOOKS AND PERIODICALS tures on descriptive geometry of the French mathematician, professor, and administrator Chérubin d’Orléans (French, 1613–1697) who worked in the regime of Napoleon as La dioptrique ocu l a i re, ou la théorique, la head of the Institut d’Egypt in Cairo. p os i t i ve et la mechanique, de l’o cu l a i re 2564-354 d i o ptrique et to u t es ses es p è ces, Pa ri s , 1 6 7 1 An illustrated work on the science of perspec- ARCHIVES AND MANUSCRIPTS tive with diagrams of optical experiments and Italian manuscript dictionary of contemporary instruments.The author was a iconography, ca. 1575–1600 Capuchin priest (born Michèle Lasséré) who A manu s c ript dictionary of iconogr a p hy that became well known for his manufacture of was most likely produced in a literary and art i s - optical aids. -
At a Medieval Cathedral
A master mason could adeptly and repeatedly apply a few simple geometric operations and tools, such as the mason’s large compass, to A produce a myriad of sophisticated designs. Mathematical Look at a Medieval Hugh McCague York University Cathedral f you wish to design and build a cathedral, you’d better know some mathematics. The application of mathematics Ihas been central to the design and execution of art and architecture from the Classical era through the Middle Ages and still today. The renown of the Greek prescriptive sculptur- al instructions, the Canon of Polykleitos, attests to this. T h e celebrated Roman architectural and engineering manual, Vitruvius's De Architectura, also emphasized the importance of mathematics in fulfilling the purpose of building. Medieval stonemasonry was itself reverently known as the Art of Geometry. Our focus here will be on the mathematics known and used by medieval stonemasons, in particular in the con- struction of Durham Cathedral in Northeast England. One of the main applications of mathematics in medieval architecture was practical geometry. Practical geometry did not concern itself with axioms, deductions, theorems and proofs. Its approach was more empirical and time-tested. Generally, medieval masons including master masons would not have been able to read more abstract or speculative math- ematical treatises in Latin, even if they were allowed access to them in the libraries of bishops and monasteries. However, a master mason could adeptly and repeatedly apply a few simple geometric operations and tools, such as the mason’s larg e compass, to produce a myriad of sophisticated designs as attested to by extant late med- ieval design manuscripts, by full-scale working drawings still etched on some church floors and walls, and by the cathedrals themselves.