A load on a slope and the common center of gravity
Resolving a weight's force on an incline, and reciprocal rules for the center of gravity of two joined weights
This mechanics sheet studies how a heavy body resting on a sloping site splits its weight into two different aspects, showing itself more powerful toward whichever motion it more hinders. Further notes state that a body can press on its support with more than its natural weight, that resistance is weaker the farther it lies from the fixed point, and that the heavier part guides the motion. The last two blocks give reciprocal center-of-gravity rules: given the weights and positions the common center is fixed (weights 4 and 2 at a and b divide the span so that a, twice as heavy, sits twice as near the center c), and conversely, given the center and positions each weight is determined. Diagrams show a weight held on an incline, a pulley carrying two weights, and balances with numbered loads.
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A load on a slope divides its weight
A heavy body held fast on a sloping site distinguishes its weight into two different aspects, resolving the single load into two directed components.
Pulley with two weights, one on an incline
A load suspended over a sloping site divides its power into two parts attending to two different aspects, showing itself more powerful toward that which more hinders one of the motions; the figure is marked 4 and 2.
Bearing more than the natural weight; weaker resistance
A weight can give its support more than its own natural weight; the body showing itself heavier is the one with weaker resistance, and that resistance is weaker the more remote it is from its fixed point. The heavier part makes itself the guide of the motion of bodies.
Center of gravity of two joined weights
Given the weights and positions of heavy bodies, their common center is fixed. With weights 4 and 2 at positions a and b, the center c cuts the span a b nearer to a than to b in proportion to their weights; a, being twice as heavy, lies twice as near c.
Deriving each weight from the common center
Conversely, given the center of the union and the positions, each weight is determined: with center b and the joined weights d e along a c, since a is twice as near the center as c, a is twice as heavy. The heavier body draws nearer the central line.