Early Middle Ages


Theory of linear perspective



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Theory of linear perspective representation of 3-dimensional objects based on existence of a single vanishing point to which all parallel lines in a plane, other than the plane of the canvas, converge. Understanding of the relation between the actual length of an object and its length in the picture depending on its distance behind the plane of the canvas.


1415 Florentine artist and architect Filippo Brunelleschi (1377–1446) discovered the laws of perspective;

1434 the first general treatise Della Pictura on the laws of perspective by Florentine architect Leone Alberti (1404–1472) who worked also on maps (geometrical mapping) and had a book on cryptography.

Piero della Francesca (1420-1492) Florentine artist, among “many math books” the survived ones: Abacus treatise, Short book on the five regular solids and On perspective for painting.





Piero della Francesca




1450 Nicholas of Cusa studies geometry and logic. He studied the infinitely large and the infinitely small, considered the circle as the limit of regular polygons. Claimed the orbits of planets to be elliptic.

1470 Chuquet writes Triparty en la science des nombres, the first French algebra book. Zero and negative exponents are considered. Rationals/irrationals are discussed. Theory of equations: allowed negative coefficients. Introduced words “billion”, “trillion”, “quadrillion”.

1472 Peurbach publishes Theoricae Novae Planetarum (New Theory of the Planets). He uses Ptolemy's epicycle theory of the planets but believes they are controlled by the sun.

1474 Regiomontanus (Johannes Muller) Ephemerides, astronomical tables for the years 1475 to 1506 AD, and proposes a method for calculating longitude by using the moon. 1475 De triangulis planis et sphaericis (Concerning Plane and Spherical Triangles), studies spherical trigonometry to apply it to astronomy.









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