PROPOSITION I.
A Solid Priſm or Cylinder of Glaſſe, Steel, Wood, or
other Frangible Matter, that being ſuſpended length
waies, will ſuſtain a very great Weight hanged
Thereat, will, Sidewaies, (as we ſaid even now) be
broken in pieces by a far leſſer Weight, according as
its length ſhall exceed its thickneſs.
other Frangible Matter, that being ſuſpended length
waies, will ſuſtain a very great Weight hanged
Thereat, will, Sidewaies, (as we ſaid even now) be
broken in pieces by a far leſſer Weight, according as
its length ſhall exceed its thickneſs.
Wherefore let us deſcribe the Solid Priſm A B C D,
fixed into a Wall by the Part A B, and in the
other extream ſuppoſe the Force of the Weight E;
(alwaies underſtanding the Wall to be erect to the Horizon,
and the Priſm or Cylinder faſtened in the Wall at Right-An
gles) it is manifeſt, that being to break, it will be broken in the place
B, where the Mortace in the Wall ſerveth for Fulciment, and B C
for the part of the Leaver in which lieth the force, and the thick
neſſe of the Solid B A is the other part of the Leaver, in which
lieth the Reſiſtance, which conſiſteth in the unfaſtening, or divi
ding, that is to be made of the part of the Solid B D, that is with
out the Wall from that which is within: and by what hath been
declared, the Moment
65[Figure 65]
of the Force placed in
C, is to the Moment of
the Reſiſtance that lieth
in the thickneſſe of the
Priſm, that is, in the
Connection of the Baſe
B A, with the parts con
tiguous to it, as the
length C B is to the half
of B A: And therefore
the abſolute Reſiſtance
againſt Fraction that is
in the Priſm B D,
(which abſolute Reſi
ſtance is that which is
made by drawing it
downwards, for at that
time the motion of the Mover is the ſame with that of the Body
Moved) againſt the fracture to be made by help of the Leaver
fixed into a Wall by the Part A B, and in the
other extream ſuppoſe the Force of the Weight E;
(alwaies underſtanding the Wall to be erect to the Horizon,
and the Priſm or Cylinder faſtened in the Wall at Right-An
gles) it is manifeſt, that being to break, it will be broken in the place
B, where the Mortace in the Wall ſerveth for Fulciment, and B C
for the part of the Leaver in which lieth the force, and the thick
neſſe of the Solid B A is the other part of the Leaver, in which
lieth the Reſiſtance, which conſiſteth in the unfaſtening, or divi
ding, that is to be made of the part of the Solid B D, that is with
out the Wall from that which is within: and by what hath been
declared, the Moment
65[Figure 65]of the Force placed in
C, is to the Moment of
the Reſiſtance that lieth
in the thickneſſe of the
Priſm, that is, in the
Connection of the Baſe
B A, with the parts con
tiguous to it, as the
length C B is to the half
of B A: And therefore
the abſolute Reſiſtance
againſt Fraction that is
in the Priſm B D,
(which abſolute Reſi
ſtance is that which is
made by drawing it
downwards, for at that
time the motion of the Mover is the ſame with that of the Body
Moved) againſt the fracture to be made by help of the Leaver