II.

Book II. Mechanic Pommer 49

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2

PROC POS. XVI.A Theorem.

len toro Povers conſiſting at the ends of 4 Leaver, ſiſtain a* weight hung on it, that ahich is neereſt to the weight ſuſt aintthe greater part F the Weight , and that which is further, the leſſerpart proport ionaliy to the diſtances reci procally.

Fig. 38. There are two powers A and B conſiſting at theends of the Leaver, and ſuſtaining the ſame weight C; J ſay,the Power A ſuſtains a greater part of the weight than B; thatis, if the weiglit C be 60 pounds and B& the double of AC; 1ſay, the power A ſuſlains 4b pounds, of the weight, and thepower B ſuſtains only 20 pounds: Or that the powers mayfuſtain the weight C, the power in B muſt be equal to aweigt of 20 pounds, and the Power in A equal to 40pounds.

Ibe Demonſtration. The Power A in reſpect of the Power Bis as the Prop, therefore that they may be in equilibro, it oughtto be as, A C, the diſtance of the weight from the Prop A, toAB the diſtance of the power from the ſame Prop, ſo thepower B to the weight C reciprocally(by the firſt of this) butA C is by ſuppoſition a third part of the line A B, thereforethere is required in Ba power equal to a third part of theweight, to wit, of 20 pounds; In like manner, becauſe with re-ſpect to the power A, as the power B hath by means of theProp, ſo will be the diſtance CB of the weight from the Prop,to AB che diſtance of the power from the ſame, as the powerA to the weight C reciprocally,(by the firſt of this) but CBis ſuppoſed to contain two third parts of the whole line A B,therefore alſo the Power A will be equal to 3 parts of theweight C, to wit, of forty pounds: Which was to be de-monſtrated. a— 1

H Corollary