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22.

supposed perpendicular to an Horizontal line A C whereas if it had been elevated perpendicular by in ye same time unto a hight equal to A B it should have acted by all its weight, and should had a much greater force to elevate it.

       Rule 2

If two bodyes with [[?(resort)]] a spring of ye same matter dashing against one another horizontally and directly have their quantity of motion equal, that is to say if ye forces are recipricall to their bulk, as soon as they meet they will make an equilibrium, (it is supposed that ye bodys of ye same matter have their weight proportionalle to ye quantity of their matter) according to this rule, if a weight of two pounds going with swiftness of four degrees meet an other directly and horizontally of 4 pounds wch hath two degrees of swiftness, they shall stop one ye other and make an equalibrium; but if ye first of 2 pounds [[strikethrough]] it will away [[/strikethrough]] goeth 6 times as swift as an other of 10 pounds it will carry it along with it; for ye product of 2 by 6 wch is 12, is more than ye product of 10 and one.  From hence it easily proved that principall of ye mehanics, wch is not well proved y Archimedes Galileus, and many other Authors viz that whence in a balance ye weights and recipricall to their distance from ye centre of ye balance, they make an equilibrium

[[image: line drawing of a balance beam resting on a fulcrum or pivot point (A) showing the beam in two positions: 1. horizontal (B C), and 2. tipped downward on the left end (D), up on the right (E).  There is the representation of a ball or weight on the left end of the balance (B).  There is a smaller ball or weight at the right end (C) of the horizontal beam.]]

For let ye balance be B A C, A ye centre of ye motion, A C quadruple to A B; ye weight B quadruple to ye weight C, I say that one of ye weights will not carry away ye other; for let ye weight B if possible carry away ye other; but A cannot be moved with any swiftness that that may makeit descend thrô ye arc B D, that will  not make ye C go 4 times a swift thrô ye arc C E, since ye semidiameter A C is quadruple to ye semidiameter A B, and then ye gravitity at ye motion of these two bodies would be equal and a quantity of motion should thence force one that is equal to it, wch is impossible since they ought to make an equilibrium by ye 2d rule. for ye same reason ye weight C cannot descend, for then it can give to ye other weight a less quantity of motion than B being 30 pound and ye arm A B of a foot, one cannot sustain ye weight in put ye hand under, and that one shall easily sustain ye weight of one pound and 31 feet from ye point A if ye weight B is taken away for it has but ye weight of one pound though one must put it 100 feet distant from ye point A; and nevertheless if one put at ye same time ye small weight at 31 feet distance from ye point A, and ye large one foot, ye small will weigh down ye great,wch cannot happen but because it is disposed to give in descending a less quantity of motion to ye weight B than that which it takes, and that they both act and will all ye force of their weight by ye first rule, because they have ye same direction towards ye center of ye earth.

     Rule III

When two weights have not ye same direction towards the centre of ye earth and that they are so disposed that one cannot move without moving ye other as swift, one must not esteem the force of each by its simple quantity of motion, but by a respective quantity of motion which if found by multiplying each weight by its swiftness in reguard to its approach, or it remotion from ye centre of ye earth.  A is a weight hanged to ye pully B by E B A, wch sustains also ye bowl C D by means of two small cords joyned to [[?C ?D]] ossieu) [[blank space]] of ye bowl and to ye point E of ye cord A B E, H G is an Horizontal Line, H F is perpendicular; E B is parallel to ye inclined plain G F.  It is manifest that ye bowl is dispossed to go as swift as ye weight A Let ye weight A descend on ye bowl by descending make it mount upward, but when it hath passed thrô ye space F G in descending obliquely, it will not approach ye centre of ye earth but ye distance F H, considering all ye points of ye Line H G of two or three feet long as if it were equally distant from ye centre of ye earth, because that ye difference is insensable.  to ye end thefore to know

Transcription Notes:
Reviewed mandc: The phrase "If two bodyes with [[?(resort)]] a spring of ye same matter...." in another translation of this work reads as follows: "If two bodies without elasticity and of the same kind...." An inelastic body would have no "spring." http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/QERNH1MN/pageimg&start=11&pn=83&mode=imagepath Capital "D" in this middle English script sometimes looks like a lower case "h", sometimes a lower case cursive "b."