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

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1of Direction A D H and A E I are Right Angles, we ſuppoſe that
theſe two Forces I and H weigh alike upon the Center A as if they
were nearer to the Center, at the equal Diſtances A B and A C,
and we alſo ſuppoſe the ſame if theſe very Forces were ſuſpended
both together in A, the Angles of Directions being ſtill Right
Angles.
PROPOSITION I.
Theſe Principles agreed upon, we will eaſily demonſtrate,
in Imitation of Archimedes, that upon a ſtraight Balance
the Forces, of which and of all their parts the Lines of Dire­
ction are parallel to one another, and perpendicular to the Balance,
ſhall couuterpoiſe and make an Equilibrium, when the ſaid Forces
ſhall be to one another in Reciprocal proportion of their Arms,
which we think to be ſo manifeſt to you, that we thence ſhall de­
rive the Demonſtration of this Univerſal Propoſition to which we
haſten.
PROPOS. II.
In every Balance or Leaver, if the proportion of the Forces is
reciprocal to that of the Perpendicular Lines drawn from the
Center or Point of the Fulciment unto the Lines of Direction
of the Forces, drawing the one againſt the other, they ſhall make
an Equilibrium, and drawing on one and the ſame ſide, they ſhall
have a like Effect, that is to ſay, that they ſhall have as much Force
the one as the other, to move the Balance.
In this Figure let the Center of the Balance be A, the Arm A B,
bigger than A C, and firſt let the Lines of Direction B D, and E C
be perpendicular to the Arms A B and A C, by which Lines the
Forces D and E (which may be made of Weights if one will) do
draw; and that there is the ſame rate

of the Force D to the Force E as there
is betwixt the Arm A C to the Arm
A B: the Forces drawing one againſt
the other, I ſay, that they will make an
Equilibrium upon the Balance C A B.
For let the Arm C A be prolonged
unto F, ſo as that AF may be equal to
A B: and let C A F be conſidered as a
ſtreight Balance, of which let the Center be A: and let there be
ſuppoſed two Forces G and H, of which and of all their parts the
Lines of Direction are parallel to the Line C E, and that the
Force G be equal to the Force D, and H to E, the one, to wit G,