Force and Accidental Weight: the Lever, the Spring, and Rectangles
The real lever at right angle, a spring fixed at one end, and geometric transformation of rectangles
Studies of 'force or accidental weight' combine mechanics with geometry. Marginal notes argue that a real lever reaches the first degree of its power when its arm meets it at a right angle, and that a spring fixed at one end is harder to move as the driver's junction departs from perpendicular. A drawn spring-and-crank and two pairs of rectangles accompany a problem: shortening the parallel a c to length b c without changing its thickness, and asking its new width. A large compass-drawn circle overlies the upper text.
On this page
The real lever is strongest at a right angle
The real lever is always in the first degree of its power when its arm stands at a right angle to it, proved by the rule that 'where the potential lever is generated, the real one lacks its power.' That power is greater or lesser as the lever extends to greater or lesser length.
A spring fixed at one end
A spring fixed at one extremity and movable at the other becomes harder to move the further the driver's junction with that end departs from a right angle. The difficulty grows together with the diminution of the potential lever it generates.
Building an equal quadrilateral from rectangles
Extend the diameter c o to n, at the height of p n, side of the right-angled figure p n c, then make a matching inverted right-angled figure n c t to complete the quadrilateral p n c t. Dividing it at the given height b c yields the line b S, so that quadrilateral b c s t equals the quadrilateral built on p c and a c.