Leonardo da Vinci and the resolution of forces. Leonardo (1452–1519) asked himself how t...

Leonardo da Vinci and the resolution of forces. Leonardo (1452–1519) asked himself how the weight of a body, supported by two strings of different length, is apportioned between the two strings.

Three forces are acting at the point D: the tensions in the strings and the weight . Leonardo believed that

Was he right? (Source: Les Manuscrits de L´eonard de Vinci, published by Ravaisson-Mollien, Paris, 1890.) Hint: Resolve into a horizontal and a vertical component; do the same for holds. Express the ratios

in terms of α and β, using trigonometric functions, and compare the results.