Leonardo Da Vinci

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LEONARDO di ser PIERO DA VINCI (1452-1519), Italy

Any person with a wide ranging interest and profound knowledge of many different disciplines is described as a Polymath, but there have been none from his time to this, who can match Leonardo!

Painter; Architect; Inventor; Scientist; Mathematician; Engineer; Writer; Botanist; Musician; Sculptor; Mechanic; Geologist; Cartographer; Town Planner and Anatomist.


Da Vinci is probably best known for his painting of Mona Lisa which hangs in the Louvre in Paris.

This is probably the most controversial painting in its 500 year history. Debate has raged endlessly about her lack of eyebrows (thought to be the fashion at the time), the enigmatic smile and the identity of the model. There is a school of thought that the model was actually a male.

He paid meticulous attention to detail in all his work, as demonstrated by the perfect representation of the plants in his painting of the Virgin of the Rocks.

Many of his botanical sketches, accompanied by detailed notes, are in the Royal Library at Windsor


Although painted on a wall, The Last Supper is an atypical fresco as Leonardo experimented by sealing the wall then treating his work as if he were painting on wood. To this day, despite extensive restoration, efforts are still being made to maintain the integrity of this masterpiece. Leonardo’s love of mathematics is conveyed by the perfection of the perspective and the balance of each group of three. The intricacies of the fine details displayed in the lacework on the cloth, the clarity of the glassware, the soft glow of the pewter are remarkable.

There is also controversy surrounding the interpretation of this work. Debate centres on whether it portrays the consecration of the bread and the wine, or whether it shows the reaction to Christ’s pronouncement of betrayal is ongoing. Some scholars feel that through the sheer brilliance of Leonardo’s interpretation, it is both.


In the following two examples, one of a plant and the other of a dog’s head, we find how Leonardo applied mathematical equations and geometry to everyday things. For example: Leonardo claimed “that each year when the branches of plants have concluded their maturation, when added together, the sum total of their cross-section is equal to the cross-section of the trunk.” This is illustrated by the image where you can also see his peculiar style of writing everything backwards.

He also discovered “that the distance from the tip of the dog’s snout to its brow is exactly equal to the distance from its brow to its ear, and that the lowest point of snout is on a line with the lowest point of the ear.”


Maths and Anatomy

A Roman architect named Vitruvius, who lived circa 1 BCE, was the first to propose the theory that a human body could fit inside both a circle and a square. He associated the circle as being symbolic with the divine and the square with secular aspects.

Leonardo, in his famous drawing expanded on this theory by using his knowledge of maths and anatomy to illustrate perfect proportions. The Vitruvian Man shows how the human body can be fitted perfectly within both a circle and a square. This drawing is now more commonly associated with health practices wishing to epitomise the fully balanced body.


The sheer brilliance of this man led him in many different directions. His vision of how a town should be planned demonstrated how the logics of mathematics could be applied to engineering projects, while he used the eye of the artist to combine beauty with practicality.

Had the town he planned in 1516 been built, it would have advanced the world at that time to an almost modern day standards of heating, communication and hygiene

His plan, for which he adapted the principle of Archimedes Screw, featured fresh water inlets as well as waste disposal and all homes had running hot and cold water.

He created machines to improve ventilation and even had pipes running through the walls of the buildings for heating and cooling the rooms. He designed automatic opening doors and to quote from The Last Years by Ton Pascal: The heavy main doors of each building, opened and closed automatically when approached, using sophisticated balance and pressure points on a crank mechanism system, only now put to use with the advent of computers.

Included in his plan were schools and centres for recreation. He paid attention to open spaces, avenues were lined with trees, artwork was displayed on corners and numerous fountains added to the ambience of a city that would be interactive with its residents and allow its residents to be interactive within it.


This is one of many inventions that Leonardo recorded in his Portfolios.

His design for a flying machine was based on his observation of birds in flight, and the ‘bat’ wings bear testimony to this. Everything about the design was carefully calculated allowing for balanced body weight and various cranks for levitation and direction. The only flaw was that manpower alone could never have got the craft off the ground!

However, the man’s mind did not stop working at this point. He figured out that there should be some sort of safety device in flight, and designed a parachute.

This parachute was recently tested (although the jumper also wore a backup ‘chute). It descended perfectly, the only issue being that it could not be steered or adjusted to accommodate the prevailing conditions.


This extract form online Britannica, written by Ludwig Heinrich Heydenreich, presents a lesson from the Master himself.

“In defining painting as a science, Leonardo also emphasizes its mathematical basis. In the notebooks he explains that the 10 optical functions of the eye (“darkness, light, body and colour, shape and location, distance and closeness, motion and rest”) are all essential components of painting. He addresses these functions through detailed discourses on perspective that include explanations of perspectival systems based on geometry, proportion, and the modulation of light and shade. He differentiates between types of perspective, including the conventional form based on a single vanishing point, the use of multiple vanishing points, and aerial perspective. In addition to these orthodox systems, he explores—via words and geometric and analytic drawings—the concepts of wide-angle vision, lateral recession, and atmospheric perspective, through which the blurring of clarity and progressive lightening of tone is used to create the illusion of deep spatial recession. He further offers practical advice—again through words and sketches—about how to paint optical effects such as light, shadow, distance, atmosphere, smoke, and water, as well as how to portray aspects of human anatomy, such as human proportion and facial expressions.”

Visit the “Leonardo Links” page where you will find a select choice of sites which will give you further insight into this amazing man.