Seeing through
Dürer explained the Latin word perspectiva as Durchsehung, “seeing through”: a picture is what you see through a window, fixed on the glass.
43 / ANTIQUITY TO THE RENAISSANCE
Albrecht Dürer
A string runs from a hook in the wall, standing for the eye, to a corner of a chest. Where it passes through a glass frame is where that corner belongs in the drawing.
Explore the mathematics ↓
01 / PERSPECTIVE
Where on the glass does each point belong?
Use Dürer’s string machine to mark the corners of a chest on a glass.
Then move the chest to find out why far edges shrink, and why edges running away from you meet at one point.
=
=
THE IDEAWith the glass 3 units from the eye, a point at distance Z is drawn at 3 ÷ Z of its offset: across = 3X ÷ Z, up = 3Y ÷ Z. Far edges shrink, and parallel edges running straight away from the eye all meet at the point straight ahead of it.
The person behind the ideas
- Published Underweysung der Messung, a geometry book for artists, in 1525.
- Visited Bologna to learn the mathematics of art, and read Euclid, Vitruvius, Alberti and Pacioli.
- Published a book on fortification in 1527; his Treatise on Proportion appeared after his death in 1528.
More of the mathematics
Geometry for makers
The same book teaches constructions of curves, polygons and letters, and its last part covers the Platonic and Archimedean solids, shadows and perspective.