1B C, is as the Length B C to the half of A B in the Priſm, which
in the Cylinder is the Semidiameter of its Baſe. And this is our firſt
Propoſition. And obſerve, that what I have ſaid ought to be un
derſtood, when the Confideration of the proper Weight of the So
lid B D is removed: which Solid I have taken as weighing nothing.
But in caſe we would bring its Gravity to account, conjoyning it
with the Weight E, we ought to add to the Weight E the half of
the Weight of the Solid B D: ſo that the Weight B D being
v. gr. two pounds, and the Weight of E ten pounds, we are to
take the Weight E, as if it were eleven pounds.
in the Cylinder is the Semidiameter of its Baſe. And this is our firſt
Propoſition. And obſerve, that what I have ſaid ought to be un
derſtood, when the Confideration of the proper Weight of the So
lid B D is removed: which Solid I have taken as weighing nothing.
But in caſe we would bring its Gravity to account, conjoyning it
with the Weight E, we ought to add to the Weight E the half of
the Weight of the Solid B D: ſo that the Weight B D being
v. gr. two pounds, and the Weight of E ten pounds, we are to
take the Weight E, as if it were eleven pounds.
SIMP. And why not as if it were twelve?
SALV. The Weight E, Simplicius, hanging at the term C,
gravitates in reſpect of B C, with all its Moment of ten pounds,
whereas if only B D were pendent, it would weigh with its whole
Moment of two pounds; but, as you ſee, that Solid is diſtributed
thorow all the length B C, uniformly, ſo that its parts near to the
extream B, gravitate leſſe than the more remote: ſo that, in a word,
compenſating thoſe with theſe, the weight of the whole Priſm is
brought to operate under the Center of its Gravity, which anſwe
reth to the middle of the Leaver B C: But a Weight hanging at
the end C, hath a Moment double to that which it would have
hanging at the middle: And therefore the half of the Weight of
the Priſm ought to be added to the Weight E, when we would uſe
the Moment of both, as placed in the Term C.
gravitates in reſpect of B C, with all its Moment of ten pounds,
whereas if only B D were pendent, it would weigh with its whole
Moment of two pounds; but, as you ſee, that Solid is diſtributed
thorow all the length B C, uniformly, ſo that its parts near to the
extream B, gravitate leſſe than the more remote: ſo that, in a word,
compenſating thoſe with theſe, the weight of the whole Priſm is
brought to operate under the Center of its Gravity, which anſwe
reth to the middle of the Leaver B C: But a Weight hanging at
the end C, hath a Moment double to that which it would have
hanging at the middle: And therefore the half of the Weight of
the Priſm ought to be added to the Weight E, when we would uſe
the Moment of both, as placed in the Term C.
SIMP. I apprehend you very well, and, if I deceive not my ſelf,
me thinks, that the Power of both the Weights B D and E, ſo placed,
would have the ſame Moment, as if the whole Weight of B D, and
the double of E were hanged in the midſt of the Leaver B C.
me thinks, that the Power of both the Weights B D and E, ſo placed,
would have the ſame Moment, as if the whole Weight of B D, and
the double of E were hanged in the midſt of the Leaver B C.
SALV. It is exactly ſo, and you are to bear it in mind. Here we
may immediatly underſtand
may immediatly underſtand
PROPOSITION II.
How, and with what proportion, a Ruler, or Priſm,
more broad than thick, reſiſteth Fraction, better if it
be forced according to its breadth, than according to
its thickneſſe.
more broad than thick, reſiſteth Fraction, better if it
be forced according to its breadth, than according to
its thickneſſe.
For underſtanding of which, let a Priſm be ſuppoſed A D:
[as in Fig. 4.] whoſe breadth is A C, and its thickneſs much
leſſer C B: It is demanded, why we would attempt to break
it edge-waies, as in the firſt Figure it will reſiſt the great Weight
T, but placed flat-waies, as in the ſecond Figure, it will not reſiſt
[as in Fig. 4.] whoſe breadth is A C, and its thickneſs much
leſſer C B: It is demanded, why we would attempt to break
it edge-waies, as in the firſt Figure it will reſiſt the great Weight
T, but placed flat-waies, as in the ſecond Figure, it will not reſiſt