Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1the Weight to be at one extream, and the Force at the other, and
the Fulciment placed in ſome point between the extreams: but we
may make uſe of the Leaver another way, yet, placing, as we ſee,
the Fulciment in the extream A, the Force in the other extream C,
and ſuppoſing the Weight D to hang by ſome point in the midſt,

as here we ſee by the point B, in
this example it's manifeſt, that if
the Weight did hang at a point
Equi-diſtant from the two ex­
treams A and C, as at the point F,
the labour of ſuſtaining it would
be equally divided betwixt the
two points A and C, ſo that half
the Weight would be felt by the
Force C, the other half being ſu­
ſtained by the Fulciment A: but if the Grave Body ſhall be hanged
at another place, as at B, we ſhall ſhew that the Force in C is ſuffi­
cient to ſuſtain the Weight in B, as it hath the ſame proportion
to it, that the Diſtance, A B hath to the Diſtance A C.
For De­
monſtration of which, let us imagine the Line B A to be continued
right out unto G, and let the Diſtance B A be equall to A G, and
let the Weight hanging at G, be ſuppoſed equall to D: It is ma­
nifeſt, that by reaſon of the equality of the Weights D and E, and
of the Diſtances G A and A B, the Moment of the Weight E
ſhall equalize the Moment of the Weight D, and is ſufficient to
ſuſtain it: Therefore whatever Force ſhall have Moment equall to
that of the Weight E, and that ſhall be able to ſuſtain it, ſhall be
ſufficient likewiſe to ſuſtain the Weight D: But for ſuſtaining the
Weight E, let there be placed in the point C ſuch a Force, whoſe
Moment hath that proportion to the Weight E, that the Diſtance
G A hath to the Diſtance A C, it ſhall be ſufficient to ſuſtain it:
Therefore the ſame Force ſhall likewiſe be able to ſuſtain the
Weight D, whoſe Moment is equall to the of E: But look what
Proportion the Line G A hath to the Line A C; and A B alſo hath
the ſame to the ſaid A C, G A having been ſuppoſed equall to A B:
And becauſe the Weights E and D are equall, each of them ſhall
have the ſame proportion to the Force placed in C: Therefore the
Force in C is concluded to equall the Moment of the Weight D,
as often as it hath unto it the ſame proportion that the Diſtance B A
hath to the Diſtance C A.
And by moving the Weight, with the
Leaver uſed in this manner, it is gathered in this alſo, as well as in
the other Inſtruments, that what is gained in Force is loſt in Velo­
city: for the Force C raiſing the Leaver, and transferring it to A I,
the Weight is moved the Space B H, which is as much leſſer than
the Space C I paſſed by the Force, as the Diſtance A B is leſſer