Potential and Real Levers; a Body Falling Through Water
A hung weight's changing load, an infinite series of cord-triangles, and constant descent through water.
Folio 5v continues the analysis of a weight hung from cords, distinguishing 'potential' from 'real' levers and counter-levers and tracing how the weight d (of 2) loses heaviness to a cord as it swings from the perpendicular b toward a: a half at b, a third at m, three quarters at n, and all at a. Folio 10r generalises the cord-triangle, showing that as the upright is divided into 7/8, 3/4, 5/8 and 1/2 of its hypotenuse the load on the two cords grows without bound, so the weight would become infinite were the cords unbreakable. A closing note observes that a heavy body sinking through water falls at constant speed, because water neither opens a path nor makes a wave downward as air does. Both leaves carry pulley, cord and semicircle diagrams lettered a through s.
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Natural weight borne only by the perpendicular cords
The natural, simple weight is sustained only by those cords where the lever has ended, that is, those that descend perpendicular and parallel over the weight they carry, as shown in the first figure a.
Potential lever versus real counter-lever
In the second figure the lever is generated in the space c b (that is a b, born at b and ending at the right angle a). This lever is 'potential', while the counter-lever b s is 'real'.
Force at e and the true quantity of a weight
In the third demonstration all the force put at e to pull the potential lever c b resists the descent of the real counter-lever c d; lacking a real lever, the whole power of e answers at c. Before working, one must find the true quantity of the weight, which changes at every degree of motion out of its perpendicular.
A weight loses heaviness as it swings off the perpendicular
The weight d, under the middle of line a c at b, has lost half its heaviness to cord c d; under m it had lost a third, under n three quarters, and at a it will have lost all of it. Reckoned along line b d it keeps its full gravity of 2; reckoned along d s it loses half.
Upright-to-hypotenuse ratio and an infinite series
A weight at the middle of a level cord makes a triangle whose upright stands to its hypotenuse as the central weight stands to the load felt at the attachments. As successive uprights measure 7/8, 3/4, 5/8, then half of the hypotenuse, the load multiplies, so infinite weight would fall on the cords if they did not break.
A body falls through water at constant speed
A heavy body descending through water always keeps one same velocity, because water does not open the way to the moving body as air does, nor can it make a wave downward. Penetrating a medium of equal resistance, the body must move at equal speed.