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23.

[[image: drawing of an inclined plane starting at the right point labeled G, sloping upward to the left to point F and down to base line corner H.  There is a pulley B at F. There is a cord D attached to a large weight C on the plane, and the cord passes over the pulley and is attached to a smaller weight A hanging from the pulley B.]]

Ye forces of these weights on their respective quantities of motion, we must multiply ye weight of ye bowl C D by ye length F H and that of ye bowl A by a length equal to F G since that bowl makes as much way in mounting on in descending as ye bowl C B, and that it goeth towards ye centre of ye earth. but if F G is triple to F H, and that ye weight C B is triple to ye weight A, there will be an equilibrium, betweeen these weights wch proceeds from ye causes explained in ye two first rules; but if there is added any small weight either to ye weight A, or to ye weight B, it will descend and make ye other mount up drawing ye pully and [[?(p esign)]] [[blank space]] After ye same manner may be explained ye equilibrium wch ought to happen when ye plain F G shall be more or less inclined by applying there ye same rules, wch one may call principalls of Experience or Laws of nature.

As if ye weights as A and B in ye following figure are upon planes differently inclined as C D, C F, D F, being supposed horizontal and C G perpendicular to B F it will needfull to make an equilibrium that ye weight B may be so ye weight A as ye line C F to ye line C D it is

[[image: drawing of a double sided inclined plane, slope on left steeper than slope on right, base line D G S F, peak at C supporting a pulley, a cord over the pulley attached to weight A on left slope and B on right slope.  There is a perpendicular line from C down to baseline G; a and another perpendicular line from 1/3 of the way down the right slope at H to the base line J]]

proved by ye same rules for if F H is taken equall to C D and that H J is drawn prallel to C G, it is manifest that while ye weight B should from F to H, ye weight A should go from [[strikethuough]] [[?]] [[/stikethrough]] C to D therefore C G should be ye measure of ye swiftness of ye weight a in reguard of ye centre of ye earth, and H J that of weight B going from F to H in ye same time; but as F C to F H so is C G to H J, and by ye third rule ye weight B ought to be ye weight A as C G to H J, disposed will stop one ye other.

The same thing will happen to two weights tyed to ye ends of ye spokes of a wheel that is to say to ye end that ye weight is situated at ye extremity of ye spoke K A may make an equilibrium with ye weights B, ye line A K being Horizontall and ye line B K elevated 60 degrees above A K F; It is necessary that ye weight B should be double to ye weight A; for ye line B F being drawen perpendicular to ye spoke K B untill it meets ye line A K G F, ye plane B F shall be elevated 30 degrees, and ye perpendicular B G shall not be above half of B F therefore ye motion of ye weight B advances F being made at ye beginning according to ye tangent B F will not be advanced towards ye centre of ye Earth but ye space B G ye half of B F whereas ye weight A will have its direction according to ye tangent M A H perpendicular to A K F wch is removed directly from ye centre, and by consequence will be disposed to go two times as swift

Transcription Notes:
mandc: it is difficult sometimes to tell the difference between B and D. Capital D sometimes has a loop at the top and often looks like a lower case "h" or cursive "b." Capital B usually looks more like a capital B than D does. Note that translator failed to designate point D (below ball C) on his diagram. Note also that translator often leaves a space after a word he apparently intends to back and fill in the proper English word. By interpretation the word might be: "axis" of C D, as interpreted in the Desaguliers translation p. 85. Link: https://transcription.si.edu/transcribe/8339/SIL-39088003881398_0027