THE UNIQUE CASE of the VITRUVIAN PRINCIPLE a Thesis
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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. -
Simple Rules for Incorporating Design Art Into Penrose and Fractal Tiles
Bridges 2012: Mathematics, Music, Art, Architecture, Culture Simple Rules for Incorporating Design Art into Penrose and Fractal Tiles San Le SLFFEA.com [email protected] Abstract Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable M.C. Escher-like image that works esthetically as well as functionally requires resolving incongruencies at a tile’s edge while constrained by its shape. Escher was the most well known practitioner in this style of mathematical visualization, but there are significant mathematical objects to which he never applied his artistry including Penrose Tilings and fractals. In this paper, we show that the rules of creating a traditional tile extend to these objects as well. To illustrate the versatility of tiling art, images were created with multiple figures and negative space leading to patterns distinct from the work of others. 1 1 Introduction M.C. Escher was the most prominent artist working with tessellations and space filling. Forty years after his death, his creations are still foremost in people’s minds in the field of tiling art. One of the reasons Escher continues to hold such a monopoly in this specialty are the unique challenges that come with creating Escher type designs inside a tessellation[15]. When an image is drawn into a tile and extends to the tile’s edge, it introduces incongruencies which are resolved by continuously aligning and refining the image. This is particularly true when the image consists of the lizards, fish, angels, etc. which populated Escher’s tilings because they do not have the 4-fold rotational symmetry that would make it possible to arbitrarily rotate the image ± 90, 180 degrees and have all the pieces fit[9]. -
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). -
Leonardo Universal
Leonardo Universal DE DIVINA PROPORTIONE Pacioli, legendary mathematician, introduced the linear perspective and the mixture of colors, representing the human body and its proportions and extrapolating this knowledge to architecture. Luca Pacioli demonstrating one of Euclid’s theorems (Jacobo de’Barbari, 1495) D e Divina Proportione is a holy expression commonly outstanding work and icon of the Italian Renaissance. used in the past to refer to what we nowadays call Leonardo, who was deeply interested in nature and art the golden section, which is the mathematic module mathematics, worked with Pacioli, the author of the through which any amount can be divided in two text, and was a determined spreader of perspectives uneven parts, so that the ratio between the smallest and proportions, including Phi in many of his works, part and the largest one is the same as that between such as The Last Supper, created at the same time as the largest and the full amount. It is divine for its the illustrations of the present manuscript, the Mona being unique, and triune, as it links three elements. Lisa, whose face hides a perfect golden rectangle and The fusion of art and science, and the completion of the Uomo Vitruviano, a deep study on the human 60 full-page illustrations by the preeminent genius figure where da Vinci proves that all the main body of the time, Leonardo da Vinci, make it the most parts were related to the golden ratio. Luca Pacioli credits that Leonardo da Vinci made the illustrations of the geometric bodies with quill, ink and watercolor. -
Art and Anatomy: the Vitruvian Teen
Curriculum Units by Fellows of the Yale-New Haven Teachers Institute 2006 Volume VI: Anatomy and Art: How We See and Understand Art and Anatomy: The Vitruvian Teen Curriculum Unit 06.06.01 by Wendy Decter, M.D. Justification Ultimately, learning becomes interdisciplinary as we mature and have opportunities for varied experiences. As adults and teachers it is our responsibility to facilitate growth and provide opportunity for different experiences. Meaningful interpretation and integration of experience must be modeled for our students as well. In grade school children build reading, writing, computational and analytical skills in a step by step fashion usually with one teacher each year. The next teacher uses the previous years' accomplishments as building blocks. Gradually vocabulary expands and students read more complex books. Perspective expands as we start to learn about countries and cultures other than our own, and examine the physical world around us. A sense of community and of the value of education is a necessary ingredient, both in school and at home. Throughout the grades, our students' required readings are set in the historical setting that is being explored from a social standpoint. Our students are acquiring the computational skills needed in their current scientific studies. They move from learning about their town, to their state, to their country and finally to their world and beyond. In middle school and high school courses and the school day becomes compartmentalized. English, now dubbed Language Arts, Social Studies, Science, Math, Art, and Foreign Language are separate departments with differentiated courses taught by many teachers in many ways. -
Decoding the Last Supper
HOUSE OF TRUTH | TOTUUDEN TALO Decoding the Last Supper The Great Year and Men as Gods House of Truth | www.houseoftruth.education 21.6.2013 Table of Contents Introduction ....................................................................................................................................................... 2 The Last Supper and the Great Year .................................................................................................................. 3 36 engravings on the roof ............................................................................................................................. 4 Elements of the Last Supper .......................................................................................................................... 5 Hands of Christ .............................................................................................................................................. 6 The Lesser Conclusion ................................................................................................................................... 7 Men as Gods in the Last Supper ........................................................................................................................ 8 Roman trio of gods ........................................................................................................................................ 9 Evidence number 153 ................................................................................................................................. -
This Kinetic World: Rethinking the Grid (Neo-Baroque Calls)
PERFORMANCE PHILOSOPHY THIS KINETIC WORLD: RETHINKING THE GRID (NEO-BAROQUE CALLS) LARA D. NIELSEN IE UNIVERSITY—MADRID Distance is not a safety zone but a field of tension. Theodor Adorno, Minima Moralia (2005, 127) Changing course and moving to Spain got me thinking about the grid again. I thought I’d left it, but I was heading right back into it. Truth is, there’s no getting out of it. Some things are for real. It is in Spain that the city grid (la cuadrícula) renewed its license, so to speak, on modernity. Ruins of 2nd century BCE cities like Baelo Claudia, for instance, a Roman municipality doing trade with the Maghreb, imprint the grid’s heterogeneous and syncretic leave (complete with basilica, forum, amphitheatre, temples of Juno, Minerva and the Egyptian Isis). The Alhambra in Granada was built over Roman ruins, its fine interior courts and muqarnas (geometrical, or honeycomb vaulting) the signature of Moorish architecture and design. On the exterior, the grand scale of its organic layout piles quadrangular additions across the mountain ridge in a manner reminiscent of ramshackle medieval cities throughout the Mediterranean, with passages going this way and that. Thus it is noteworthy that among the first known cuadrículas implemented in early modern Spain was a military encampment built in Santa Fe de Granada, in 1491, by Catholic armies forcing out the Muslim Emirate of Granada in the Reconquista. For the Romans as for the Emirates and the Spanish, city grid regimes are conditioned by contact with its “others.” PERFORMANCE PHILOSOPHY VOL 3, NO 1 (2017):285–309 DOI: https://doi.org/10.21476/PP.2017.31127 ISSN 2057–7176 For some 200 years, Granada was the last Emirate standing in Iberia. -
Francis Bacon's Challenge to the Figurative
FIGURE AND FLESH: FRANCIS BACON’S CHALLENGE TO THE FIGURATIVE TRADITION IN WESTERN ART A THESIS SUBMITTED TO THE DEPARTMENT OF GRAPHIC DESIGN AND THE INSTITUTE OF FINE ARTS ¡ ¢ £ ¤ ¥ ¦ § ¨ © § ¦ ¨ IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FINE ARTS By Müge Telci May, 2002 I certify that I have read this thesis and in my opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Fine Arts. _________________________________________________ Assist. Prof. Dr. Mahmut Mutman (Thesis Supervisor) I certify that I have read this thesis and in my opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Fine Arts. __________________________________________________ Assoc. Prof. Dr. Emel Aközer I certify that I have read this thesis and in my opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Fine Arts. ____________________________________________________ Assist. Prof. Dr. Asuman Suner I certify that I have read this thesis and in my opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Fine Arts. _____________________________________________________ Zafer Aracagök Aproved by the Institute of Fine Arts ______________________________________________________ Prof. Dr. Bülent Özgüç Director of the Institute Of Fine Arts ii ABSTRACT FIGURE AND FLESH: FRANCIS BACON’S CHALLENGE TO FIGURATIVE TRADITION IN WESTERN ART Müge Telci M.F.A in Graphical Arts Supervisor: Assist. Prof. Dr. Mahmut Mutman June, 2002 When figuring the body is at stake within the Western tradition of art, figuration comes up as a question of framing and controlling the mass of body (flesh, bones, body liquids etc…). -
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. -
Vitruvian Man
Activity 1A: Ratio Calculations: Vitruvian Man Students complete a table of ideal human proportions based on Leonardo da Vinci’s iconic drawing of Vitruvian Man. Students use the ratios to calculate dimensions of body features for different-sized individuals with Vitruvian Man’s proportions. Students measure dimensions of head and height for humans and animated characters and calculate their head : height ratios. Understandings • The relationships between body parts can be expressed mathematically using ratios. • Human body ratios vary. • A person’s or character’s appearance can be altered by varying his or her body ratios. Materials Needed • Optional: Printed or digital images of animated characters with varying body proportions (see Advance Preparation) • Handout 1: Unit Overview • Assessment Checklist: Character Design • Handout 2: Vitruvian Man Proportions • Optional: Proportion Matters slide presentation (see Advance Preparation) • Handout 3: Calculating Vitruvian Man Measurements • Handout 4: Human Head : Height Ratios • Rulers • Images of people and animated characters from Appendix A: Head : Height Proportion Images (one per student) (see Advance Preparation) • Handout 5: Journal Assignment DIGITAL/MEDIA/ARTS: MATHEMATICS 8 PROPORTION MATTERS © Education Development Center, Inc. 2011 1. Optional: Show students animated characters with varying proportions. Display the images of animated characters. Ask students: • What do you notice about the differences in the sizes of these characters’ heads in relation to their bodies? What about the sizes of their facial characteristics, such as eyes and mouths? • What effect do you think these visual properties have on your perception of the character? 2. Introduce the concept of proportion. Tell students that in this unit they will look at how body and facial proportions can be quantified mathematically. -
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.