Leonardo Da Vinci

In 1487, Leonardo participated in a competition to design a tiburio (lantern tower) for Milan’s cathedral, collaborating with architects Donato Bramante and Francesco di Giorgio. Though his proposal was ultimately rejected, their shared work on church design, proportion, and geometry led to deeper studies, including exploration of Vitruvius’s De Architectura, a Roman treatise linking human and architectural symmetry. Leonardo and his colleagues produced various drawings of the “Vitruvian Man,” but Leonardo’s version, created around 1490, was uniquely precise, blending anatomical observation with philosophical symbolism. His drawing depicts a nude man inside both a circle and square, visually linking the microcosm of man to the macrocosm of the universe. Vitruvian Man became a defining symbol of Renaissance humanism, reflecting Leonardo’s fusion of art, science, and geometry. The chapter also emphasizes the collaborative environment of the Milanese court, where such interdisciplinary breakthroughs were made possible.

In 1489, Leonardo da Vinci was officially commissioned to design a monumental equestrian statue honoring Ludovico Sforza’s father, Duke Francesco. Leonardo received a court residence, studio space, and a stipend, launching one of his most ambitious projects. The planned bronze statue—three times life-size—led Leonardo to pursue exhaustive anatomical studies of horses, culminating in a detailed clay model completed in 1493. Simultaneously, he developed complex and innovative casting techniques to execute the statue in a single pour, defying traditional multi-part methods. His detailed engineering sketches included systems of furnaces, molds, and materials. Despite his ingenuity, the project was never completed. War with France redirected the bronze to cannon-making, and invading troops destroyed Leonardo’s clay model in 1499. Though never realized, the horse monument demonstrated Leonardo’s fusion of art, anatomy, and engineering—and his tendency to dream big, even when fate intervened.

In the early 1490s, Leonardo da Vinci began to broaden his intellectual pursuits, teaching himself Latin and amassing a library that spanned science, poetry, anatomy, engineering, and philosophy. While he initially prized firsthand experience over classical scholarship, he came to embrace the complementary power of theory and experiment. He meticulously studied phenomena by observing, recording, and testing his ideas, often devising original tools and techniques to do so. He made profound analogies across disciplines—comparing trees to arteries, rivers to veins, and sound to light—to understand the natural world. His insatiable curiosity and observational prowess, especially regarding motion, helped him forge early versions of the scientific method. Leonardo’s legacy as a scientist stems not from formal education but from his relentless questioning, acute observation, and synthesis of art and inquiry, laying groundwork for a more empirical and interdisciplinary vision of knowledge.

Beginning in the 1490s, Leonardo da Vinci spent over two decades studying bird flight and developing designs for human-powered flying machines. His work merged artistic observation with mechanical innovation, producing more than 500 detailed sketches and 35,000 words on the subject. Initially inspired by theatrical stagecraft, Leonardo transitioned to serious engineering, studying anatomy, air pressure, fluid dynamics, and the principles of motion. He observed birds with intense precision and drafted early theories that anticipated Newton’s third law and Bernoulli’s principle. His Codex on the Flight of Birds explored gravity, aerodynamics, and the curved structure of wings. Though he never created a functional flying machine, he produced elegant gliders and flapping contraptions, testing them in private and over water. In his final years, he returned to creating mechanical birds for court amusement, echoing where his fascination with flight had begun.

Leonardo’s fascination with motion led him to study machines with the same detail he applied to anatomy. Unlike most contemporaries, he used exploded diagrams and layered drawings to understand how motion was transferred through parts like gears, levers, pulleys, and springs. He tackled engineering challenges such as regulating the speed of unwinding springs and maximizing human muscle output. He designed tools powered by water, gravity, or people—including needle grinders and waterwheels—and investigated the feasibility of perpetual motion. Through visual thought experiments, he concluded such machines were impossible, largely due to friction. He became one of the first to study friction methodically, devising instruments to measure it and even inventing ball bearings and friction-reducing alloys. His work helped establish a mechanistic worldview that foreshadowed Newtonian physics, rooted in the belief that the same physical laws govern machines, living bodies, and nature itself.

Leonardo developed a deep appreciation for mathematics, especially geometry, as a tool for understanding the natural world. Although he struggled with arithmetic and algebra, he excelled in visualizing shapes and using geometric analogies to explore scientific and artistic principles. With the help of mathematician Luca Pacioli, Leonardo learned Euclidean geometry and illustrated Pacioli’s On Divine Proportion, producing the only drawings he published during his lifetime. Fascinated by transformation of shapes, he explored the conservation of volume and pioneered ideas later formalized in topology. His relentless efforts to “square the circle” and solve other ancient mathematical puzzles became a lifelong obsession. Though he lacked the symbolic tools of later mathematicians, Leonardo’s visual experiments and thought processes foreshadowed key concepts in calculus and physics. To Leonardo, geometry wasn’t just a discipline—it was a path to discovering the harmonious patterns underlying nature and art.