## PROJECTIVE GEOMETRY

### Projective Geometry in the seventeenth century

To paint the world as they see it, painters developed a system of focused perspective inspiring new geometrical ideas. Euclidean geometry is tactile because it agrees with the sense of touch but not always with the sense of sight, it deals with lines that never meet but we never **see** parallel lines. The artist draws parallel lines that converge, introducing foreshortening and perspective to give the eye an illusion of reality.
This motivated mathematicians to search for theorems on the intersection of lines and curves.

**Desargues**

Girad Desargues (1596-1662) was the first major mathematician to explore the suggestions arising out of the work on perspective.

Desargues Theorem

**Pascal**

Pascal (1623-1662) proved a theorem in projective geometry at the age of 16.

Pascal Theorem

### Projective Geometry in the nineteenth century

**Brianchon**
Brianchon (1783-1864) worked during the early nineteenth century revival of projective geometry. He created a theorem that states that:

**If a hexagon is circumscribed about a circle the lines joining opposite vertices meet in one point**, this theorem applies to any conic section.

### Map making

To make a map we have to project figures from a sphere into a flat sheet. The principles involved are the same as those of perspective and projective geometry.
Gerard Mercator (1512-94) the Flemish cartographer developed the most famous method, the Mercartor's projection.

New Geometry, New Worlds

Golden Age of Greek Geometry

History of Mathematics Module

Links to other History of Mathematics sites

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These pages are maintained by M.I.Woodcock.