|
❉ Blog post 20 on diagrams in the arts and sciences delves in to Leonardo Da Vinci's life long obsession with diagram making. From documenting ideas and observations, to elaborate mechanical instructions, blueprints for buildings and sketches for paintings, the diagram was the creative engine that drove his endless pursuit of knowledge and understanding.  1) Glimpse into the left side of a human skull, about 1651 © Royal Collection Trust / Her Majesty Queen Elizabeth II (CC BY-NC-SA 4.0) The surviving notebooks of early Renaissance artist and polymath Leonardo da Vinci (1452-1519) reveal a masterful fluency in his use of diagrams. Indeed, during certain periods, his distinctive mirror-written notes and diagrammatic sketches were his medium of choice for observing and analysing the world, rather than drawing and painting. However as we'll see, all of these modes of exploration and expression were intimately connected, especially so in the case of his complex preparatory diagrams that underlie some of his major paintings. Geometry was fundamental to Leonardo’s process of understanding both the visible forms of nature and the hidden mechanisms and forces underlying natural phenomena. His vision of the interplay of these rules of geometry was transformative and dynamic rather than static, as if he observed nature as a process of geometry in action. He was however not merely content to record how something worked, but also strove to find out why it worked the way it did, and it was this insatiable curiosity that transformed a technician into a scientist. (1) In the words of the great da Vinci scholar Martin Kemp, for Leonardo, the "...muscles of the human body worked immaculately according to the laws that governed levers. The flow of the blood in the vessels and of the air in the bronchial tubes in the lungs was governed by the geometrical rules that applied to all branching systems. A flying bird was designed in perfect conformity with the geometry of airflow.” (2) (See figures 2-5)
Leonardo studied anatomy and the proportions of the human body throughout his career, and applied this deep understanding in drawings such as The Vitruvian Man (c.1490) (figure 6). This diagrammatic sketch was Leonardo's attempt to answer an ancient puzzle set 1500 before his time by the first century Roman architect and engineer Marcus Vitruvius Pollio (c. 75–25 BCE). In his book De Architectura, Vitruvius founds his theory of architecture on the proportions of the human body, which he considered nature’s greatest work. The challenge was to show how the human figure can be positioned within a circle and a square with the navel at the centre. Ancient thinkers had long invested the circle and the square with symbolic powers, with the circle representing the cosmic and the divine, and the square the earthly and the secular. Leonardo's elegant solution was to position his figure so that the navel aligned with the centre of the circle, but then to position the square off-centre in alignment with the base of the circle. (figure 6)  6) The Vitruvian Man, c. 1490 Pen and ink with wash over metalpoint on paper, 34.6 cm × 25.5 cm Interestingly, a number of other artists from around the same period also attempted solutions to the Vitruvian puzzle, and some comparative examples are included below that highlight the refined technical elegance of Leonardo's draftsmanship and his exceptional knowledge of anatomy. One drawing in particular, made by Leonardo's close friend Giacomo Andrea Da Ferrara, actually predates that of Leonardo's, and its rediscovery in a lost manuscript in Ferrara, Italy in 1986, lead some art historians to question whether or not Leonardo's drawing was actually of copy of his friend's solution. (3) (See figure 9)  7) Perspective study for the adoration of the Magi, c. 1481 Ink on paper, 16.3 x 29 cm, Florence, Galleria degli Uffizi Leonardo’s preparatory study for the adoration of the Magi is one of his most remarkable sketches. (figure 7) The immaculately depicted geometry of the tiled floor and the static architecture of the temple interior highlight the turbulent graphic images of the figures and animals depicted within it. British art historian Kenneth Clark described the drawing as "a carefully measured courtyard invaded by a retinue of ghosts". Clark considered it one of Leonardo's most revealing drawings, and the earliest evidence of his scientific attainments in perspective, which to his mind provided "a scaffold for the artist's imagination." (4) Likewise, Martin Kemp considers the sketch an exemplar of the paradoxical combination of contained measure and unconstrained improvisation characteristic of many of Leonardo’s drawings. (5) The reduction of complex natural forms to their underlying geometrical relations was, however, more of an intuitive process for Leonardo than one relying upon the techniques of mathematics. Kemp has suggested that this preference may have been two-fold, both in Leonardo’s own limited abilities at mathematics and algebra but also as an intellectual preference for a more fluid model of a dynamic world based on the beauty of proportions, interrelations and first-hand experience of the world. Leonardo referred to geometry as “the science of continuous quantity’” whereas he referred to numbers and mathematics as dealing with “discontinuous quantities” with little correspondence to the nature of actual physical forms. (6) In his essay for the book accompanying the 2006 exhibition 'Leonardo da Vinci: Experience, Experiment and Design' at the Victoria and Albert museum in London, Kemp discusses Leonardo’s use of disegno as a means to think visually. Disegno was a common term used by Renaissance draughtsmen and is normally translated in English as either drawing (in a fine art context) or design (in the context of applied arts). Leonardo’s use of disegno allowed him to integrate the subjective imaginative faculty or fantasia with the intellect, which in turn achieved expression in the Renaissance concept of science (scientia). Misura was the term used to describe the measuring of proportions, the construction of perspective systems and rules of light and shade, and was regarded by Leonardo as the fundamentally scientific aspect of expression in painting. (7) In works such as the Perspective study for the adoration of the Magi (figure 6), we can see this process at work in the way he combines the fluid, creative, subjective process of disegno with the logic, rigor and measurement of misura. Kemp uses the following quote from Leonardo to support his claim that disegno was considered as the supreme tool that served the eye as a means of investigation and exposition. When Leonardo praises how the eye commands the hand, Kemp suggests that he was essentially making claims about the power of disegno: "Now do you not see that the eye embraces the beauty of the world? The eye is commander of astronomy; it makes cosmography; it guides and rectifies all the human arts; it conducts man to various regions of the world; it is the prince of mathematics; it’s sciences are most certain; it has measured the height and size of the stars; it has disclosed the elements and their distributions; it’s made predictions of future events by means of the course of the stars; it has generated architecture, perspective and divine painting. Oh excellent above all other things created by God… And it triumphs over nature, in that the constituent parts of nature are finite, but the works that the eye commands of the hands are infinite." (8)  8) Codex Arundel, circa 1480 - 1518 (See below for a link to a digitised version) However, it's immediately notable that the systems Leonardo is praising, all relate to the power of diagrams, diagramming, and diagrammatic thought processes, and this becomes even clearer if we consider the examples he refers to: astronomy and celestial charts, the theory and practice of the systems of proportions governing artistic beauty, cosmography (9), cartography and navigation, mathematics including trigonometry and geometry, the analysis of dynamic and static systems in the behavior of earth, water, air and fire, architectural plans, elevations, sections and systems of perspective and the ‘divine’ science of painting with its ‘roots in nature’. Drawing and thinking through diagrams was for da Vinci a natural, almost instinctual means to develop his ideas, communicate them with others and construct a science of painting. However, as with other artists of the Renaissance, Leonardo inherited the tradition for diagramming from Medieval diagrammers before him, as I covered in previously blog posts: Diagrams from the Dark Ages, and Cosmic Diagrams from Alchemical Laboratory. Leonardo's online Codex:Leonardo's Codex Arundel consists of 570 images of dense cryptic notes surrounding technical diagrams. The 283 page manuscript was digitized in 2007 as a joint project between the British Library and Microsoft called “Turning the Pages 2.0,” and can be accessed by clicking here. The Alternative Vitruvian Men: |
 10) Fra Giovanni Giocondo, 1511  12) Cesare di Lorenzo Cesariano |  11) Francesco Giorgi, 1525  13) Francesco di Giorgio Martini, 1470 |
 14) Cesare de Lorenzo Cesariano, 1521 |  15) Mariano di Jacopo (Taccola), c. 1382-1453 |
References and Notes:
1) Kenneth Clark, (1973). Leonardo Da Vinci, Penguin Books, UK, pg 39
2) Martin Kemp, (2007). Leonardo da Vinci: Experience, Experiment and Design. London: V&A Publications. pg 14
3) Claudio Sgarbi, (2012). At the Origin of Leonardo’s Ideal Man. DISEGNARECON, 5(9),
pg 177–186. https://doi.org/10.6092/issn.1828-5961/3166
4) Kenneth Clark, (1973). Leonardo Da Vinci, Penguin Books, UK, pg 39
5) Da Vinci, Leonardo, quoted in: Kemp, M. (2007) Leonardo da Vinci: Experience, Experiment and Design. London: V&A Publications. pg 96
6) Ibid. pg 23
7) Ibid. pg 18
8) Ibid. pg 96
9)Cosmography was considered a science between the fifteenth and seventeenth centuries,
attempting to map the general features of the cosmos or universe, describing both heaven
and earth (but without encroaching upon geography or astronomy).
1) Kenneth Clark, (1973). Leonardo Da Vinci, Penguin Books, UK, pg 39
2) Martin Kemp, (2007). Leonardo da Vinci: Experience, Experiment and Design. London: V&A Publications. pg 14
3) Claudio Sgarbi, (2012). At the Origin of Leonardo’s Ideal Man. DISEGNARECON, 5(9),
pg 177–186. https://doi.org/10.6092/issn.1828-5961/3166
4) Kenneth Clark, (1973). Leonardo Da Vinci, Penguin Books, UK, pg 39
5) Da Vinci, Leonardo, quoted in: Kemp, M. (2007) Leonardo da Vinci: Experience, Experiment and Design. London: V&A Publications. pg 96
6) Ibid. pg 23
7) Ibid. pg 18
8) Ibid. pg 96
9)Cosmography was considered a science between the fifteenth and seventeenth centuries,
attempting to map the general features of the cosmos or universe, describing both heaven
and earth (but without encroaching upon geography or astronomy).
0 Comments
❉ This is the eighth in a series of blogs that discuss diagrams and the diagrammatic format, especially in relation to fine art. I recently completed my PhD on this subject at Kyoto city University of the Arts, Japan's oldest Art School.
Feel free to leave comments or to contact me directly if you'd like any more information on life as an artist in Japan, what a PhD in Fine Art involves, applying for the Japanese Government Monbusho Scholarship program (MEXT), or to talk about diagrams and diagrammatic art in general.
Feel free to leave comments or to contact me directly if you'd like any more information on life as an artist in Japan, what a PhD in Fine Art involves, applying for the Japanese Government Monbusho Scholarship program (MEXT), or to talk about diagrams and diagrammatic art in general.
Sol Lewitt, Diagram and certificate for wall drawing #49, A Wall Divided Vertically into Fifteen Equal Parts, Each with a Different Line Direction and Colour, and All Combinations, 1970, Ink on paper
Towards the end of the 1960s, the American artist Sol LeWitt made a series of groundbreaking works that exist primarily as concepts. These concepts are established by precise sets of diagrammatic instructions that specify which combinations of lines, shapes, colours and dimensions should be used in order to recreate LeWitt's art works in reality.
When the diagrammatic instructions are purchased, an accompanying certificate validates the authenticity of the artwork and grants the owner permission to reconstruct the work in a location of their choice.
By attributing absolute priority to concept LeWitt gave a Platonic dimension to these artworks, in that he insisted that they exist in essence as ideas in a purely abstract, immaterial way. In the words of LeWitt himself, “the Idea becomes a machine that makes the art.” (1)
Radically, LeWitt proposed that in order for an artist to deepen their artistic practice, they should aim to remove their individual subjective decisions and taste from the creative act itself. Again, in the words of LeWitt:
"If the artist wishes to explore his idea thoroughly, then arbitrary or chance decisions would be kept to a minimum, while caprice, taste and other whimsies would be eliminated from the making of the art… To work with a plan that is preset is one way of avoiding subjectivity… This eliminates the arbitrary, the capricious, and the subjective as much as possible." (2)
When the diagrammatic instructions are purchased, an accompanying certificate validates the authenticity of the artwork and grants the owner permission to reconstruct the work in a location of their choice.
By attributing absolute priority to concept LeWitt gave a Platonic dimension to these artworks, in that he insisted that they exist in essence as ideas in a purely abstract, immaterial way. In the words of LeWitt himself, “the Idea becomes a machine that makes the art.” (1)
Radically, LeWitt proposed that in order for an artist to deepen their artistic practice, they should aim to remove their individual subjective decisions and taste from the creative act itself. Again, in the words of LeWitt:
"If the artist wishes to explore his idea thoroughly, then arbitrary or chance decisions would be kept to a minimum, while caprice, taste and other whimsies would be eliminated from the making of the art… To work with a plan that is preset is one way of avoiding subjectivity… This eliminates the arbitrary, the capricious, and the subjective as much as possible." (2)
Figure 1: Sol LeWitt, “Wall Drawing 85.” June 1971. Colored pencil. LeWitt Collection, Chester, Connecticut.
First Installation: LeWitt residence, New York (Art © 2011 The LeWitt Estate /Artists Rights Society, New York)
First Installation: LeWitt residence, New York (Art © 2011 The LeWitt Estate /Artists Rights Society, New York)
As a young graduate of Medical Biochemistry, the precise and methodical drawings of Sol LeWitt were the first conceptual art works I discovered, and I felt an immediate connection with the process, result and underlying philosophy.
Lewitt's stance epitomises what I would now call that of the "Romantic Objective", in that his artistic practice successfully combines the idealistic goals of objectivity with poetic irrationality. (A much more detailed explanation can be found in Chapter 4.1 and 4.2 of my PhD thesis "Romantic Objectivism: Diagrammatic thought in Contemporary Art", which is available for download from the research page of this website.)
Looking at the first five propositions from LeWitt’s Sentences on Conceptual Art helps clarify his position, and how he conceives the role that intuition and logic play as devices with in his work:
1. Conceptual artists are mystics rather than rationalists. They leap to conclusions that logic cannot reach.
2. Rational judgements repeat rational judgements.
3. Irrational judgements lead to new experiences.
4. Formal art is essentially rational.
5. Irrational thoughts should be followed absolutely and logically. (3)
The diagrammatic format is central to LeWitt's practice and he used diagrams both to store his artistic concepts and then later translate and transcribe them into reality.
Imperfections that arise naturally during the process of recreating the works by hand, add a range of tones and textures to the images and, over time, Lewitt found ways to incorporate even this into the nature of the work, as shown in the time lapse video below.
The video was made during the installation of his wall drawing #797 at the Blanton museum of Art, in which minor imperfections become amplified due to repetition, adding to the unique character of the final work.
Lewitt's stance epitomises what I would now call that of the "Romantic Objective", in that his artistic practice successfully combines the idealistic goals of objectivity with poetic irrationality. (A much more detailed explanation can be found in Chapter 4.1 and 4.2 of my PhD thesis "Romantic Objectivism: Diagrammatic thought in Contemporary Art", which is available for download from the research page of this website.)
Looking at the first five propositions from LeWitt’s Sentences on Conceptual Art helps clarify his position, and how he conceives the role that intuition and logic play as devices with in his work:
1. Conceptual artists are mystics rather than rationalists. They leap to conclusions that logic cannot reach.
2. Rational judgements repeat rational judgements.
3. Irrational judgements lead to new experiences.
4. Formal art is essentially rational.
5. Irrational thoughts should be followed absolutely and logically. (3)
The diagrammatic format is central to LeWitt's practice and he used diagrams both to store his artistic concepts and then later translate and transcribe them into reality.
Imperfections that arise naturally during the process of recreating the works by hand, add a range of tones and textures to the images and, over time, Lewitt found ways to incorporate even this into the nature of the work, as shown in the time lapse video below.
The video was made during the installation of his wall drawing #797 at the Blanton museum of Art, in which minor imperfections become amplified due to repetition, adding to the unique character of the final work.
Figure 2: Sol Lewitt, Wall Drawing #797
Black, red, yellow, and blue marker on wall Installation view, Feb. 2014
Blanton Museum of Art LeWitt Collection, Chester, Connecticut
© 2014 Estate of Sol LeWitt/Artist Rights Society (ARS)
Black, red, yellow, and blue marker on wall Installation view, Feb. 2014
Blanton Museum of Art LeWitt Collection, Chester, Connecticut
© 2014 Estate of Sol LeWitt/Artist Rights Society (ARS)
Germano Celant discusses this 'noise' added by humans during the process of making / transcribing LeWitt’s work in terms of entropy, a scientific term for measuring the level of disorder within a system:
" ...entropy of communication is reduced to the ideal state… in which the visual element is the exact result of a conceptual process [and] permits the extreme purification of the idea or concept, to the point at which it is presented for what it is, a rational and objective entity that does not admit those subjective or empathetic conditions that are part of the usual aesthetic operation. " (4)
Celant’s comments are idealistic in terms of the extent to which it is possible to strip an artwork entirely of its subjective nature, and are more suited to the early 'monosemic' works of the French conceptual artist Bener Venet, as we will see in a future post.
LeWitt's idealistic goal of objective image making lead him inevitably to the specialised visual language of mathematical geometry in his Location series, in which Platonic-type geometric forms are presented accompanied by labyrinthine poetic-instructional texts.
In order for the diagrams of geometry to function, a number of assumptions must first be made so that they can be said to represent the underlying mathematics. For example, a point of ink on paper is taken to represent a conceptual mathematical point of zero dimensions, and an ink line is understood as representing a perfect one-dimensional line of zero width.
Such paradoxical ambiguities are simply overlooked during the reading of such images, and the American Philosopher and Semiologist Charles Sanders Peirce referred to such inconvenient physical qualities as "accidental characters that have no significance”. (5)
" ...entropy of communication is reduced to the ideal state… in which the visual element is the exact result of a conceptual process [and] permits the extreme purification of the idea or concept, to the point at which it is presented for what it is, a rational and objective entity that does not admit those subjective or empathetic conditions that are part of the usual aesthetic operation. " (4)
Celant’s comments are idealistic in terms of the extent to which it is possible to strip an artwork entirely of its subjective nature, and are more suited to the early 'monosemic' works of the French conceptual artist Bener Venet, as we will see in a future post.
LeWitt's idealistic goal of objective image making lead him inevitably to the specialised visual language of mathematical geometry in his Location series, in which Platonic-type geometric forms are presented accompanied by labyrinthine poetic-instructional texts.
In order for the diagrams of geometry to function, a number of assumptions must first be made so that they can be said to represent the underlying mathematics. For example, a point of ink on paper is taken to represent a conceptual mathematical point of zero dimensions, and an ink line is understood as representing a perfect one-dimensional line of zero width.
Such paradoxical ambiguities are simply overlooked during the reading of such images, and the American Philosopher and Semiologist Charles Sanders Peirce referred to such inconvenient physical qualities as "accidental characters that have no significance”. (5)
Figure 3: Sol LeWitt, Location of a circle, from the series:
The location of six geometric figures (circle, square, triangle, rectangle, parallelogram and trapezoid).
1974, Set of six etchings, Edition of 25 10 AP.
The location of six geometric figures (circle, square, triangle, rectangle, parallelogram and trapezoid).
1974, Set of six etchings, Edition of 25 10 AP.
Sol LeWitt uses the high-fidelity, low-entropy notation of geometry, but contrasts it with a convoluted textual description of, or instructions for, each of his six geometric diagrams. He also chose to write the texts using everyday language rather than the efficient and specialised symbols of mathematics, and the result is a single sentence, hundreds of words long and almost impossible to mentally reconstruct.
 |  |  |
 |  |  |
Figure 4: Sol LeWitt, The location of six geometric figures
(circle, square, triangle, rectangle, parallelogram and trapezoid).
1974, Set of six etchings, Edition of 25 10 AP.
(circle, square, triangle, rectangle, parallelogram and trapezoid).
1974, Set of six etchings, Edition of 25 10 AP.
The texts accompanying each geometric image become almost religious mantras, where meaning is lost within the sounds of the words themselves. This fascinating juxtaposition of text and pure notation results in a poetic resonance that is "Romantic-Objective" as well as diagrammatic in nature:
Location of a Circle:
A circle whose radius is equal to half the distance between two points, the first point is found where two lines would cross if the first line were drawn from a point halfway between a point halfway between the center of the square and the upper right corner and the midpoint of the topside to a point halfway between a point halfway between the center of the square and the midpoint of the right side and a point halfway between the midpoint of the right side and the lower right corner, the second line of the first set is drawn from a point halfway between a point halfway between the center of the square and a point halfway between the midpoint and the left side and the upper left corner and the midpoint of the left side to a point halfway between a point halfway between the center of the square and the upper right corner and a point halfway between the midpoint of the right side and the upper right corner; the second point is found where two lines would cross if the first line is drawn from a point halfway between a point halfway between the center of the square and the midpoint of the bottom side and a point halfway between the center of the square and the lower left corner to a point halfway between the end of the first line of the first set and the end of the second line of the first set, the second line of the second set is drawn from a point halfway between the point where the first two lines have crossed and a point halfway between the start of the first line of the first set and a point halfway between the midpoint of the left side and the upper left corner to a point halfway between the end of the first line of the second set and the midpoint of the bottom side; all whose center is located equidistant to three points, the first of which is located at the center of the square, the second point is located at a point halfway between a point halfway between the center of the square and the upper left corner, the third point is located halfway between the start of the first line of the first set and the end of the first line of the second set.
A circle whose radius is equal to half the distance between two points, the first point is found where two lines would cross if the first line were drawn from a point halfway between a point halfway between the center of the square and the upper right corner and the midpoint of the topside to a point halfway between a point halfway between the center of the square and the midpoint of the right side and a point halfway between the midpoint of the right side and the lower right corner, the second line of the first set is drawn from a point halfway between a point halfway between the center of the square and a point halfway between the midpoint and the left side and the upper left corner and the midpoint of the left side to a point halfway between a point halfway between the center of the square and the upper right corner and a point halfway between the midpoint of the right side and the upper right corner; the second point is found where two lines would cross if the first line is drawn from a point halfway between a point halfway between the center of the square and the midpoint of the bottom side and a point halfway between the center of the square and the lower left corner to a point halfway between the end of the first line of the first set and the end of the second line of the first set, the second line of the second set is drawn from a point halfway between the point where the first two lines have crossed and a point halfway between the start of the first line of the first set and a point halfway between the midpoint of the left side and the upper left corner to a point halfway between the end of the first line of the second set and the midpoint of the bottom side; all whose center is located equidistant to three points, the first of which is located at the center of the square, the second point is located at a point halfway between a point halfway between the center of the square and the upper left corner, the third point is located halfway between the start of the first line of the first set and the end of the first line of the second set.
Nicholas Baume describes the location of six geometric figures (also produced as wall drawings) as one of LeWitt’s most disciplined and exacting works, and yet also his most absurd and wryly funny, suggesting that the text is a “form of abstract verbal play” for LeWitt. (6)
Importantly, LeWitt himself once remarked that he considered his Location series his “poetry”. (7)
Importantly, LeWitt himself once remarked that he considered his Location series his “poetry”. (7)
It is worth noting at this point that a strikingly similar example of pure geometric notation juxtaposed with its dense description in text can be found over half a century earlier the notebooks of Leonardo da Vinci, circa 1448 :
Figure 6: Leonardo da Vinci, Profile of a Man, plant, geometric figures etc.
(also known as the ‘Theme Sheet’) (detail)
c. 1448, pen and ink, Windsor Castle, The Royal Collection.
(also known as the ‘Theme Sheet’) (detail)
c. 1448, pen and ink, Windsor Castle, The Royal Collection.
Accompanying text: ( Located in the bottom left hand corner of image above )
" The triangle abc is similar to a third of the large triangle dbf because it is made up of two equal parts, that is abe and bec, and the large triangle is made up of 6 parts, and each of these parts is equal to each of the said 2, and the 6 parts are these: dec and ced and so on, in similar parts. And if the triangle abc had its sides similar to its axis, cb, the triangle dbf would receive in itself 4 of these triangles, whereas at present it receives 3; thus to see the difference from one of the triangles which are ¼ of the large one and one of those which are ⅓, have the large triangle divided in to twelfths, and say that it is 12 twelfths. Then say that the triangle which is a ⅓ of it is 4 of these twelfths and the triangle that is a ¼ of this large one contains three of these twelfths, so that the difference between 4 and 3 is one twelfth, whence we can say that the smaller is ¾ of the larger. "
" The triangle abc is similar to a third of the large triangle dbf because it is made up of two equal parts, that is abe and bec, and the large triangle is made up of 6 parts, and each of these parts is equal to each of the said 2, and the 6 parts are these: dec and ced and so on, in similar parts. And if the triangle abc had its sides similar to its axis, cb, the triangle dbf would receive in itself 4 of these triangles, whereas at present it receives 3; thus to see the difference from one of the triangles which are ¼ of the large one and one of those which are ⅓, have the large triangle divided in to twelfths, and say that it is 12 twelfths. Then say that the triangle which is a ⅓ of it is 4 of these twelfths and the triangle that is a ¼ of this large one contains three of these twelfths, so that the difference between 4 and 3 is one twelfth, whence we can say that the smaller is ¾ of the larger. "
The following selection of geometry diagrams are taken from the beautifully designed German book "der Geometrie descriptive" c.1865, by Leopold Mossbrugger. Fig.a in image 3, presents the various line types employed during the construction of these ideal types of mathematical forms, and the diagrammatic systems used to bring them into being as two dimensional lithographs upon the page.
This particular copy was purchased from an antiquarian bookstore in Prague, the capital the Czech Republic, in 2002
.
Figures 7-27: Selected images from "der Geometrie descriptive"
by Leopold Mossbrugger, c.1865
by Leopold Mossbrugger, c.1865
References:
1) LeWitt, S. (1967) Paragraphs on Conceptual Art. Art Forum. June, 1967
2) Ibid
3) LeWitt, S. (1969) Sentences on Conceptual Art. In: Art and Language, No. 11. (May 1969) p. 11
4) Celant, G. (2009) (First published:1988) The Sol LeWitt Orchestra. In: Sol LeWitt: 100 views. Eds. Markonish, D. and Cross, S. MASS MoCa in association with Harvard University Press, p. 27.
5) de Waal, C. (2013 ) Peirce: A guide for the perplexed, London: Bloomsbury Academic. p.88.
6) Baume, N. (2001) Sol LeWitt: Open cubes. Exhibition Catalogue. Hartford: Atheneum Museum of Art.
7) Lewitt, S. quoted in: LeWitt and Miller Keller, A. Excerpts from a Correspondence, 1981 – 1983. In: Suzanne Singer, ed., Sol LeWitt wall drawings, 1968 – 1984. Amsterdam: Stedelijk Museum, Eindhoven: Van Abbemuseum, Hartford: Wadford Atheneum, 1984. p. 18-25.
Dr. Michael Whittle
British artist and researcher
working between Kyoto
and Hong Kong
Posts:
Categories
All
Alchemical Art
Anatomy
Arakawa And Gins
Architecture
Contemporary Art
Duchamp
Genetics
Geology
Geometry
JMW Turner
Leonardo Da Vinci
Literature
Mathematics
Medieval Art
Musicology
Perspective
Physics
Romanticism
Sol LeWitt
Surrealism
Archives
June 2022
June 2021
August 2020
October 2019
August 2018
January 2018
November 2017
October 2017
April 2017
November 2016
October 2016
September 2016
June 2016
May 2016
April 2016
March 2016