On gravity and the cord: levers, counter-levers and angles
A triangle cut unequally by its axis, and how lever ratio and pendant angle set the load felt by a cord
Headed 'On gravity and the cord', the page proves geometrically that a section cut unequally distant from a triangle's base is divided into unequal parts by the triangle's axis, using the definition of the circle. A series of analogous figures then relates the mechanics: if a lever is double its counter-lever the cord feels half the weight, and the potential lever shrinks as the angle of the two real pendants grows more obtuse. Closing rules restate that obtuse real angles carry their potential angle outside, while a right real angle makes the two angles one; a run of small triangular diagrams down the right margin, lettered a, b, c, d, e, f, o, r, illustrates each case, and the folio ends 'Turn the page.'
On this page
A triangle section divided unequally by its axis
A cut a e made unequally distant from base a b of triangle a b c is divided into unequal parts by the axis d c, proved from the definition of the circle. The circle d r f exhibits the difference r o between the two parts.
A lever double its counter-lever halves the load on the cord
If the lever a d were double its counter-lever a b, the cord d e would feel half the weight f; this holds only when the lever d a lies in the site of equality, which requires the pendants a n and e n supporting weight f to be equidistant.
The potential lever shrinks as the pendant angle grows obtuse
The potential lever a b is smaller than the arm of its potential counter-lever a c in proportion as the angle of the two real pendants a d p becomes more obtuse.
Obtuse angles carry the potential angle outside; right angles unite them
Every obtuse real angle has its potential angle outside itself, as obtuse angle a b c has potential angle a d b on its outer side. And if the real angle is right, the potential and real angles are one and the same, as angle a b c shows.