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112. [[image: diagram of a line A C B pivoting at C with weights hanging off it labeled A G, D H, E I, and B F.]] This being supposed let us consider the balance A C B turning upon its support C, charged at ye end B, with a weight F making an equilibrium with ye 3 equal weights G H I, ye distance B C is to C E as 12 to 1, C D is double to C E, and C A double to C D: Now if ye weight G is 12 pound there must be a weight in F of 4 pounds to sustain it, since ye distance B C is ye triple of C A, there needs but 2 pound in F, to sustain ye weight H, and 1 pound to sustain ye weight I, and by that means a weight of 7 pounds will make an equilibrium with these 3 weights each of 12 pounds in G H & C I: If therefore we add a small weight in F ye three weights will be elevated; and althô they are elevated inequally each shall be acted by a weight of 12 pounds according to their distance from C, but it is not ye same in a solid that is broken transversly: And to feel it: [[image: diagram of two parallel lines A E B C (fulcrum) F on a rectangle A C (fulcrum) Q P. Suspended from N at F is a weight R. Let us suppose F C to be 12 foot C A four, C E 2, and C B one foot and that ye solid A D C N be joyned to ye stable solid A C P Q, by ye three equal and equally strong cords D I, G L, H M a little streched wch pass a cross by small holes in ye solid A C P Q and are knit together on ye [[strikethrough]] side [[/strikethrough]] other side as is seen in ye figure. Moreover let us suppose that to ye end each cord may be broken, it must be extended 2 lines and that a weight R suspended in F of 4 pounds may be strong enough to reduce ye cord I D to that extension of 2 lines, and that adding a very little weight it ought to break, it is evident that there must be 2 pounds to extend ye cord L G along 2 lines, and only 1 pound to extend after ye same manner ye cord H M, if ye center of ye motion is in C: But because that when ye cord D I ie extended 2 lines ye cord G L is extended but one line and ye cord H M but 1/2 line, when we draw them all together, it follows by ye second supposition that a weight of about 1 pound shall then make an equilibrium with ye tension of ye cord G L wch is but 1 line, and that there needs but 4 ounces to make an equilibrium with ye cord H M althô ye total resistance of ye last be 1 pound: and by consequent to reduce these 3 cords into that estate, it is sufficient that ye weight K be 5 1/4 pounds, and that if there is added a very small weight, ye cord D I will be broken and almost in a moment ye 2 others, since they resist much less than ye 3 together.
Transcription Notes:
mandc: Reviewed, amended image descriptions and changed J's to I's and other letter designations.
Image: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&viewMode=images&mode=imagepath&pn=283&ww=0.1262&wh=0.1825&wx=0.5374&wy=0.7076