[The Vitruvian Man: an anatomical drawing for proportions by Leonardo Da Vinci]
The aim of the study was to find out and to analyse the text by Vitruvius which inspired the famous drawing by Leonardo da Vinci (circa 1490) kept in the Galleria dell'Accademia, in Venezia, Italy: the man inscribed in one circle and in one square. The book "de Architectura" by Vitruvius Marcus Pollio was printed several times since the Renaissance when both the roman architecture of antiquity and this text became very popular. From a French translation by Claude Perrault in 1864, it became easy to find a French translation with the original text in Latin (Paris, 2003, Les Belles Lettres, French text by Pierre Gros). The drawing by Leonardo da Vinci illustrates with great accuracy and fidelity the quotation of Vitruvius (with the exception of two of the 12 main relationships). The genius of Leonardo da Vinci was to keep only one trunk, head and neck for two pairs of limbs: scapular and pelvic; to make the circle tangent to the lower edge of the square; to adjust a few features of the quotation for the equilibrium of the whole figure; and of course to bring his incredible skill as a drawer (one of the best of his century). The drawing was made on a sheet of paper 344x245mm, in black ink which became dark brown with time; several lines complete the figure above and below; a short caption and a horizontal scale appear just under the drawing. The celebrity of the drawing, a symbol of the Renaissance, of the equilibrium of man and mankind, of the universality of the artists and intellectuals of the time (Humanism) made it iconic and it has been constantly reproduced and adapted especially for advertisement and logos, not only in the medical field.
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Best practice advice for capturing human anatomy
Drawing the human body without some knowledge of anatomy is like playing a board game without the rule book and some key pieces missing: It’s frustrating and confusing. After you learn all the rules and get good at the game, you can change the rules. But that’s because you understand the dynamics of the game and you can change things to improve it.
Being confident with anatomy makes drawing easier and more fun! In this workshop, I’ll give you some advice to guide your anatomy studies, so you can learn how to draw people accurately, and with confidence.
01. Think first, then draw
Anatomy is very specific and the difference between a drawing that’s 'right' and a drawing that’s 'wrong' can be subtle. If your drawings are scribble-like and you don’t commit to any one line, your brain is busy just processing the image, so it won’t notice anatomical mistakes. If you’re studying anatomy, you should have a good foundation in basic drawing skills already, and you should use it.
02. Ignore gesture at your peril
Gesture lies at the heart of every figure drawing. Anatomy should be a new layer, and a new way to express gesture… not a replacement for it. The anatomical forms should be designed to follow and reveal the gesture.
03. Memorise the simple forms
The human body is organic. It’s full of curves, bumps and mushy-looking things. But your drawings shouldn’t look mushy. You can try to copy exactly what you see, but if the understanding and accuracy isn’t there, then it will show.
A better approach is to learn to break down the body into simple forms. This is why I teach the simple form for all areas of the body. Simple forms are simple enough that you can actually memorise them, and pull them out of your pocket whenever you need to.
04. Pay attention to the skeleton
It’s easy to tell when an artist doesn’t know the skeleton, even if you’re just looking at their fully fleshed figures. The muscles won’t aim to the right place. The skeleton is complicated, but there’s much less variation in the forms of the skeleton than the forms of the muscles and body fat. Knowing the skeleton makes it easier to construct the body, understand how it works, and put the muscles on top of it correctly. Take the time to learn it and your drawings will benefit for the rest of your career.
05. Review and correct
After you finish a drawing, take a critical look at it to see where you can improve. You can ask a friend, mentor or online community for help. Then, actually follow through on what you notice, and make corrections to your drawings. It’s not enough for your eyes to see what went wrong – your hands have to fix it. You can do this to yesterday’s homework, or even drawings you made months or years ago.
06. Don’t just read about it
Reading or listening to an explanation of anatomy may be enough for you to intellectually understand it, but that doesn’t mean you can draw it. We’re artists. We have a bigger job to do than just understand anatomy. You have to learn to draw it so it’s believable and interesting. And the only way to do that is to draw. Draw a lot!
07. Steer clear of snowmen
Don’t draw symmetrical bulges everywhere. That makes your drawing look stiff and boring. The contours tend to zigzag down the body, creating a dynamic flow. Furthermore, muscles usually work in pairs: when one side flexes the other is resting.
08. Don’t include every detail
Remember: not every bone, tendon and muscle has to be accented in every drawing. Indeed, anatomical details in the wrong spots can make a drawing look stiff and fake. Pick and choose details that support the overall picture, and let those be enough. In general, you’ll probably choose details that are at or near the focal point, and that flow with the gesture or composition.
09. Be patient
Learning anatomy is a slow process. Take your time on every drawing and with every area of the body. You can’t learn everything in your first pass. You’ll have to come back to review and add to your understand of all the parts every few years for the rest of your career. Don’t expect to be a master immediately. Never stop learning.
10. Be goal-oriented in your practice
There’s a lot to anatomy to study and lots of aspects of it to study. For example, if you’re practising gesture, the anatomy needs context. Make the forms work with the pose and focus on making the anatomy dynamic. If you’re studying form, use cross contour lines and shading to add dimension. Focus on constructing the body parts using simple forms and avoid organic forms you don’t understand. Pick a goal and focus on it. Make sure you’re getting the most out of your practice time.
11. Try different exercises
Anatomy tracings, drawing from life, drawing from photos, drawing from your imagination, drawing from other drawings (master copies), sculpture… Not only is this fun, but it helps your brain process information in different ways, and fills in gaps in your knowledge.
12. Get to grips with the language
There’s lots of memorisation with anatomy, and it can be overwhelming if you’re hearing all these terms for the first time. Terms like medial and lateral, abduction and adduction, origin and insertion, subcutaneous and so on. Consider making flashcards or other old-school study methods to help memorise the bulk of the terminology babble.
When you can speak about anatomy fluently, you can think about anatomy fluently, which means you’re going to have an easier time when you’re drawing. This is the least important part of anatomy for artists, but it sure is helpful. You’ll feel a lot better when you know the terms. And of course, you’ll leave your fellow spellers in the dust on Scrabble nights!
This article was originally published in ImagineFX, the world's best-selling magazine for digital artists. Subscribe now.
Anatomy Drawing With Figurosity
In this tutorial we’ll be doing an anatomy drawing of the male figure using Figurosity.
Click here to visit Figurosity: https://figurosity.com/
Drawing the human figure accurately can be incredibly challenging. In fact, oftentimes it can seem like such an overwhelming task that we completely avoid it or give up on it entirely.
Luckily we don’t have to tackle it all at once. The good news is the human figure can be backward engineered, broken down to its basic foundations and rebuilt from the ground up.
Funnily enough it’s the foundations of the human figure that allow us to draw it convincingly. It’s not the design of our characters or intricate details and decorative trinkets we draw in on top that counts. It’s their underlying skeleton, cloaked in the surrounding muscle structure which holds all of that other stuff up.
That’s what we’ll be studying in today’s figure drawing tutorial, starting with the basic mannequin model which we’ll use to establish the placement, proportions and pose of the male figure.
The mannequin model is built using a series of simplistic, primitive forms that represent the key parts of the human body – the head, torso and the limbs.
Because these building blocks are so basic, we’re able to easily think about and construct our figures from any angle, in any pose, from observation or imagination. The mannequin model is essentially a prototype dummy model used to compose our characters and give them the best chance of success right from the get go.
Since the mannequin model is so basic, we have a greater flexibility to explore and experiment with a variety of poses and views that our characters could be potentially presented in. Very rapidly we’re able to scribble down a rough and rudimentary figure that can be adjusted or revised in seconds. This speeds up our process, and allows us to reach the most optimal outcome for our characters in a minimal amount of time.
Once we’ve established the foundations of our figure drawing with the mannequin model, we’re then ready to begin drawing the anatomy in on top. The human body consists of a complex system of muscles that’s near impossible to remember all at once. The best approach we can take here is to focus on each key area of the body and take note of the main muscle groups found within it.
By learning the muscle groups that reside in each part of the human body separately, we’re able to keep things manageable and thoroughly address the topic with a deeper attention to detail than we’d otherwise be able to achieve tackling the muscle structure of the entire figure all at once. We want to go less broad with our learning at first, and focus on the depth of knowledge we’d like to attain instead.
We do that through anatomy drawings like the one you’re about to see demonstrated in this tutorial.
As you watch, notice how I attend to each part of the figure individually, placing in the main muscle groups one section at a time until I’ve covered it in its entirety. As I draw each muscle in, I’m only focused on the muscle groups within that specific area. I forget about the rest of the figure, pin pointing my attention on the portion I’m working on instead of stretching it out across the entire character.
This reinforces my learning experience and allows me to take in more information due the heightened level of focus I’m exercising from one point to the next. As a result, I’m more easily able to remember the muscle groups I’m learning about throughout the study. I’m able to execute the anatomy drawing with a greater amount of accuracy, as well as catch mistakes quicker when they happen.
Throughout this tutorial one of the key themes we’ll be concentrating on for both the mannequin model and muscle structure of the male human figure is ‘form’. We want to think of both of these components as having depth to them so that we can in turn give our character’s more dimension.
To help you out with this, I’ll show you how I use cross contours to overlay a wire-frame that runs along the surface form of the mannequin model and muscles throughout the figure. This allows us to click our thinking over into a three dimensional mindset so that we can construct our characters with that additional level of depth and dimension by default.
I hope that you get loads of value out of watching this tutorial, and that you put the insights you’re about to learn to good use.
Thanks for watching, and until next time – keep on practicing, and keep on creating!
Software Used: Manga Studio
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Drawing male anatomy
Learn from Anatomy to Improve Your Poses
The key to improving is to do our best and put our heart into what we do. Anatomy is not an easy subject, but I hope that this article can be a quick guide for you and get you in the mood to keep learning. Let’s start with the building blocks of the human figure:
The spine is the body’s support, also allowing motion in the torso. Its vertical shape differentiates humans from other species. It is not a straight line, but a curve. Its shape makes the pelvis and the rib cage tilt slightly. Let’s divide it up into three parts to see it better:
- Cervical spine — supports and provides mobility to the head
- Dorsal or thoracic spine — supports the ribs.
- Lumbar spine — a little before the pelvis, connected to the sacrum.
In the neck, the cervical spine (1) is located just behind the jaw (2). There are a variety of muscles that operate the movement of the head. The most visible one has a very, very long name (sternocleidomastoid!), but you can easily recognize it by its V shape, parting from the ear to the center of the clavicles (3). In the center of these muscles is the Adam’s apple, which is more prominent in men (4).
The dorsal spine is the part that connects to the arms. You can draw it in many ways, I like to give it an ovoid shape that resembles the shape of the ribs (1).
The sternum (2) closes this structure in the front, creating, with the spine, an imaginary line that divides the body into two. Use them as a guide!
The clavicles (3) are like a bicycle handlebar, you can think of them as a shoulder support. Every time the arms move, they will change direction.
In the back, you will find the scapulae or shoulder blades. They are triangle shaped and help move the arms. The shape of the back changes following the movements of these bones.
The pelvis is located at the end of the torso, connected to the lumbar spine from the sacrum (1). On both sides you can see the ilium (2); and in the front, the pubis (3).
As these are somewhat irregular bones, I like to simplify them by drawing a pair of discs for the ilium, and the sacrum as an inverted triangle.
The ilium (1) will guide you to draw the angles of the hip. On the back, these two dimples at the end of the spine, before reaching the buttocks, will help us identify the sacrum (2).
Note that female hips are generally wider than male hips — one of the main differences.
Limbs can move in many ways, but knowing their limitations will save us from drawing unrealistic poses (or bone-breaking poses, ouch!).
In the upper part of the arm (A) there is the humerus, a long and strong bone that connects to the elbow and articulates the forearm (B).
In the forearm you will find the radius (1) and the ulna (2). These bones cross to allow the rotation of the wrist. Some artists draw part of the forearm as a box to define its volume (3).
Can you see a tiny lump just behind your wrist? (4) It is part of the ulna. You can use it as a reference point to locate the orientation of the arm.
In Fig. A we have the leg bones:
The femur (1) in the thigh; the knee (2) in the middle of the leg; the fibula (3) and the tibia (4) in the calf area.
The legs should support the body and give it the balance it needs, but there is a detail that sometimes escapes us: the legs do not have completely vertical line. In order to achieve balance, there must be rhythm. Notice the slight inclination in the femur from the hip to the knee, and the curves (fig. B) that create the contour of the leg (side view).
Other interesting details about the leg:
Between the hip bone and the femur, there is a space that can be seen as an indentation in the skin, mainly in men who have less muscle mass in that area.
In figure C, we have the ankle. Its bones are placed at different heights, with the fibula on the outer side (*) being lower.
Figure D is a back view of the knee. On the outer side (*) the muscles do not generate too much change in the contour, but on the inner side a small lump is created (I have also pointed this out in figure A).
According to some academic standards, 7 or 8 heads is the ideal height of an adult. However, each person has different proportions according to their physical characteristics. If you compare people of different heights you will notice that individually they maintain proportions according to their own body.
To prove this, let us look at the following example: two adults, a man and a woman. Although the female figure is shorter, her body is divided into 7 heads (which fits within the standard) and the male figure is only a third of a head taller
In the example I have also included the figure of a child. Take into account that, at early ages, the body has not developed completely, so their measures are a little undefined. This one is about 5 heads high.
Aside from this, artists do change their characters’ proportions totally out of these “ideal” ones, to emphasize their unique characteristics or to enhance their drawing styles. (But this is not an excuse to ignore the fundamentals!)
A trick! I like comparing elements of the same length, just to make sure that everything is well proportioned as I draw. For example, the hands are about the size of the face; the feet are as long as the forearm.
Another piece of data that I find fascinating is the fact that, if you extend your arms, they are side to side the same length as your height!
Finally, four points which will help us to get better at drawing day by day.
- Observation: Study how people walk, their poses, the different types of bodies… Create a reference gallery in your mind and, if possible, take pictures!
- Think in 3D: To understand a figure/shape, the best thing is to analyze it from different perspectives.
- Research: Read about body parts, bones, muscles, functions, etc. From an artist’s point of view is fine, you do not need to become a doctor! We are interested in those anatomy parts which affect the shapes and movements of the body.
- Draw, draw, draw! Practice drawing the whole figure and detailed studies of some especially difficult parts.
Thank you very much for reading!
If you like, you can check out my social networks and my portfolio to see some of my work.
Bring Energy and Life to Your Poses!
Drawing by Leonardo da Vinci, made around 1490
The Vitruvian Man (Italian: L'uomo vitruviano[ˈlwɔːmo vitruˈvjaːno]; originally known as Le proporzioni del corpo umano secondo Vitruvio, lit. 'The proportions of the human body according to Vitruvius') is a drawing made by the ItalianpolymathLeonardo da Vinci in about 1490. It is accompanied by notes based on the work of the Roman architect Vitruvius. The drawing, which is in ink on paper, depicts a man in two superimposed positions with his arms and legs apart and inscribed in a circle and square.
The drawing represents Leonardo's concept of the ideal human body proportions. Its inscription in a square and a circle comes from a description by the ancient Roman architect Vitruvius in Book III of his treatise De architectura. Yet, as has been demonstrated, Leonardo did not represent Vitruvius's proportions of the limbs but rather included those he found himself after measuring male models in Milan. While the drawing is named after Vitruvius, some scholars today question the appropriateness of such a title, given that it was first used in the 1490s.
First published in reproduction in 1810, the drawing did not attain its present fame until further reproduced in the later 19th century, and it is not clear that it influenced artistic practice in Leonardo's day or later. It is kept in the Gabinetto dei disegni e delle stampe of the Gallerie dell'Accademia, in Venice, Italy, under reference 228. Like most works on paper, it is displayed to the public only occasionally, so it is not part of the normal exhibition of the museum. The work was recently on display at the Louvre's exhibit of Leonardo's work, from 24 October 2019 to 24 February 2020 as part of an agreement between France and Italy.
Subject and title
Leonardo's image demonstrates the blend of mathematics and art during the Renaissance and demonstrates his deep understanding of proportion. In addition, the picture represents a cornerstone of his attempts to relate man to nature. Encyclopædia Britannica online states, "Leonardo envisaged the great picture chart of the human body he had produced through his anatomical drawings and Vitruvian Man as a cosmografia del minor mondo (cosmography of the microcosm). He believed the workings of the human body to be an analogy for the workings of the universe."
According to Leonardo's accompanying text, written in mirror writing, it was made as a study of the proportions of the (male) human body as described in Vitruvius's De architectura 3.1.2–3, which reads:
For the human body is so designed by nature that the face, from the chin to the top of the forehead and the lowest roots of the hair, is a tenth part of the whole height; the open hand from the wrist to the tip of the middle finger is just the same; the head from the chin to the crown is an eighth, and with the neck and shoulder from the top of the breast to the lowest roots of the hair is a sixth; from the middle of the breast to the summit of the crown is a fourth. If we take the height of the face itself, the distance from the bottom of the chin to the under side of the nostrils is one third of it; the nose from the under side of the nostrils to a line between the eyebrows is the same; from there to the lowest roots of the hair is also a third, comprising the forehead. The length of the foot is one sixth of the height of the body; of the forearm, one fourth; and the breadth of the breast is also one fourth. The other members, too, have their own symmetrical proportions, and it was by employing them that the famous painters and sculptors of antiquity attained to great and endless renown. Similarly, in the members of a temple there ought to be the greatest harmony in the symmetrical relations of the different parts to the general magnitude of the whole. Then again, in the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centred at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square.
— Ten Books on Architecture, Vitruvius
While Leonardo shows direct knowledge of the work of Vitruvius, his drawing does not follow the description of the ancient text. In drawing the circle and square he observes that the square cannot have the same centre as the circle, but is centered at the groin. This adjustment is the innovative part of Leonardo's drawing and what distinguishes it from earlier illustrations. He also departs from Vitruvius by drawing the arms raised to a position in which the fingertips are level with the top of the head, rather than Vitruvius's much lower angle, in which the arms form lines passing through the navel.
It may be noticed by examining the drawing that the combination of arm and leg positions creates sixteen different poses. The pose with the arms straight out and the feet together is seen to be inscribed in the superimposed square. On the other hand, the spread-eagle pose is seen to be inscribed in the superimposed circle.
Leonardo's collaboration with Luca Pacioli, the author of Divina proportione (Divine Proportion) have led some to speculate that he incorporated the golden ratio in Vitruvian Man, but this is not supported by any of Leonardo's writings, and its proportions do not match the golden ratio precisely.Vitruvian Man is likely to have been drawn before Leonardo met Pacioli.
Inspiration and possible collaboration
Many artists attempted to design figures which would satisfy Vitruvius' claim that a human could fit into both a circle and a square, with the earliest known being by Francesco di Giorgio Martini in the 1480s. Leonardo may have been influenced by the work of his friend Giacomo Andrea, an architect and expert on Vitruvius, with whom Leonardo records as having dined in 1490. Leonardo also directly references "Andrea's Vitruvius". Andrea's drawing features erasure marks indicating its unique creation. As with Leonardo's Vitruvian Man, Andrea's circle is centered on the navel, but only one pose is included.
Translation of the text
The text is in two parts, above and below the image.[a][b] The upper part paraphrases Vitruvius:
Vetruvio, architect, puts in his work on architecture that the measurements of man are in nature distributed in this manner: that is a palm is four fingers, a foot is four palms, a cubit is six palms, four cubits make a man, a pace is four cubits, a man is 24 palms and these measurements are in his buildings. If you open your legs enough that your head is lowered by one-fourteenth of your height and raise your hands enough that your extended fingers touch the line of the top of your head, know that the centre of the extended limbs will be the navel, and the space between the legs will be an equilateral triangle.
The lower section of text gives these proportions:
The length of the outspread arms is equal to the height of a man; from the hairline to the bottom of the chin is one-tenth of the height of a man; from below the chin to the top of the head is one-eighth of the height of a man; from above the chest to the top of the head is one-sixth of the height of a man; from above the chest to the hairline is one-seventh of the height of a man. The maximum width of the shoulders is a quarter of the height of a man; from the breasts to the top of the head is a quarter of the height of a man; the distance from the elbow to the tip of the hand is a quarter of the height of a man; the distance from the elbow to the armpit is one-eighth of the height of a man; the length of the hand is one-tenth of the height of a man; the root of the penis is at half the height of a man; the foot is one-seventh of the height of a man; from below the foot to below the knee is a quarter of the height of a man; from below the knee to the root of the penis is a quarter of the height of a man; the distances from below the chin to the nose and the eyebrows and the hairline are equal to the ears and to one-third of the face.
The points determining these proportions are marked with lines on the drawing. Below the drawing is a single line equal to a side of the square and divided into four cubits, of which the outer two are divided into six palms each, two of which have the mirror-text annotation "palmi"; the outermost two palms are divided into four fingers each, and are each annotated "diti".
The drawing was purchased from Gaudenzio de' Pagave by Giuseppe Bossi, who described, discussed and illustrated it in his monograph on Leonardo's The Last Supper, Del Cenacolo di Leonardo da Vinci (1810). The following year he excerpted the section of his monograph concerned with the Vitruvian Man and published it as Delle opinioni di Leonardo da Vinci intorno alla simmetria de' Corpi Umani (1811), with a dedication to his friend Antonio Canova.
After Bossi's death in 1815 the Vitruvian Man was acquired in 1822, along with a number of his drawings, by the Gallerie dell'Accademia in Venice, Italy, and has remained there since. After the Louvre requested the drawing for a major exhibition of Leonardo's works to open on 24 October 2019, the Italia Nostra argued that the drawing was too fragile to be transported. At a hearing on 16 October 2019, a judge ruled that the group had not proven that the work was too fragile to travel, but set a maximum amount of light for the drawing to be exposed to as well as a subsequent rest period to offset its overall exposure to light. Italy's Minister for Cultural Affairs tweeted that "Now a great cultural operation can start between Italy and France on the two exhibitions about Leonardo in France and Raphael in Rome."
- ^Above the image:
Vetruvio, architecto, mecte nella sua op(er)a d'architectura, chelle misure dell'omo sono dalla natura
disstribuite inquessto modo cioè che 4 diti fa 1 palmo, et 4 palmi fa 1 pie, 6 palmi fa un chubito, 4
cubiti fa 1 homo, he 4 chubiti fa 1 passo, he 24 palmi fa 1 homo ecqueste misure son ne' sua edifiti.
Settu ap(r)i ta(n)to le ga(m)be chettu chali da chapo 1/14 di tua altez(z)a e ap(r)i e alza tanto le b(r)acia che cholle lunge dita tu tochi la linia della
somita del chapo, sappi che 'l cie(n)tro delle stremita delle
ap(er)te me(m)bra fia il bellicho. Ello spatio chessi truova infralle ga(m)be fia tria(n)golo equilatero
- ^Below the image:
Tanto ap(r)e l'omo nele b(r)accia, qua(n)to ella sua alteza.
Dal nasscimento de chapegli al fine di sotto del mento è il decimo dell'altez(z)a del(l)'uomo. Dal di socto del mento alla som(m)i-
tà del chapo he l'octavo dell'altez(z)a dell'omo. Dal di sop(r)a del pecto alla som(m)ità del chapo fia il sexto dell'omo. Dal di so-
p(r)a del pecto al nasscime(n)to de chapegli fia la sectima parte di tucto l'omo. Dalle tette al di sop(r)a del chapo fia
la quarta parte dell'omo. La mag(g)iore larg(h)ez(z)a delle spalli chontiene insè [la oct] la quarta parte dell'omo. Dal go-
mito alla punta della mano fia la quarta parte dell'omo, da esso gomito al termine della isspalla fia la octava
parte d'esso omo; tucta la mano fia la decima parte dell'omo. Il menb(r)o birile nasscie nel mez(z)o dell'omo. Il
piè fia la sectima parte dell'omo. Dal di socto del piè al di socto del ginochio fia la quarta parte dell'omo.
Dal di socto del ginochio al nasscime(n)to del memb(r)o fia la quarta parte dell'omo. Le parti chessi truovano infra
il me(n)to e 'l naso e 'l nasscime(n)to de chapegli e quel de cigli ciasscuno spatio p(er)se essimile alloreche è 'l terzo del volto
- ^The Secret Language of the Renaissance – Richard Stemp
- ^ abLugli, Emanuele. "In cerca della perfezione: nuovi elementi per l'Uomo vitruviano di Leonardo Da Vinci" [In Search of Perfection: New Elements for Leonardo Da Vinci's Vitruvian Man]. Leonardo e Vitruvio: Oltre Il Cerchio e Il Quadrato, ed. By Francesca Borgo (in Italian).
- ^"The Vitruvian man". Leonardodavinci.stanford.edu. Retrieved 20 August 2010.
- ^"Da Vinci's Code". Witcombe.sbc.edu. Retrieved 20 August 2010.
- ^"Leonardo da Vinci's Unexamined Life as a Painter". Aleteia. 1 December 2019. Retrieved 1 December 2019.
- ^"Louvre exhibit has most da Vinci paintings ever assembled". The Atlantic. 1 December 2019. Retrieved 1 December 2019.
- ^Heydenreich, Ludwig Heinrich (30 April 2017). "Leonardo da Vinci". Encyclopædia Britannica. Encyclopædia Britannica, inc. Retrieved 24 June 2017.
- ^"Leonardo: The Man Who Saved Science". Secrets of the Dead. Season 16. Episode 5. 5 April 2017. PBS.
- ^Vitruvius. "I, "On Symmetry: In Temples And In The Human Body"". Ten Books on Architecture, Book III. Translated by Morris Hicky Morgan. Harvard University Press. Retrieved 15 October 2020 – via Gutenberg.org.
- ^"The Vitruvian Man – Leonardo Da Vinci". About.com. Archived from the original on 12 April 2014. Retrieved 20 November 2018.
- ^ abc"Leonardo: The Man Who Saved Science". Secrets of the Dead. Season 16. Episode 5. 5 April 2017. 52 minutes in. PBS.
- ^Leonardo da Vinci's Polyhedra, by George W. Hart
- ^Livio, Mario (1 November 2002). "The golden ratio and aesthetics". Plus Magazine. Retrieved 26 November 2018.
- ^Keith Devlin (May 2007). "The Myth That Will Not Go Away". Retrieved 26 September 2013.
- ^Donald E. Simanek. "Fibonacci Flim-Flam". Archived from the original on 17 March 2016. Retrieved 27 November 2018.
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I can go slower if you feel motion sick. I do not feel sick. Not at all. - Ariel mumbled. And then what.