1X, leſſer than T: Which is manifeſted, ſince we underſtand the
Fulciment, one while under the Line B C, and another while under
C A, and the Diſtances of the Forces to be alike in both Caſes, to
wit, the length B D. But in the firſt Caſe, the Diſtance of the Re
ſiſtance from the Fulciment, which is the half of the Line C A, is
greater than the Diſtance in the other Caſe, which is the half of B
C: Therefore the Force of the Weight T, muſt of neceſſity be grea
ter than X, as much as the half of the breadth C A is greater than
half the thichneſſe B C, the firſt ſerving for the Counter-Leaver of
C A, and the ſecond of C B to overcome the ſame Reſiſtance, that
is the quantity of the Fibres, or ſtrings of the whole Baſe A B.
Conclude we therefore, that the ſaid Priſm or Ruler, which is
broader than it is thick, reſiſteth, bresking more the edge-waies
than the flat-waies, according to the Proportion of the breadth to
the thickneſs.
Fulciment, one while under the Line B C, and another while under
C A, and the Diſtances of the Forces to be alike in both Caſes, to
wit, the length B D. But in the firſt Caſe, the Diſtance of the Re
ſiſtance from the Fulciment, which is the half of the Line C A, is
greater than the Diſtance in the other Caſe, which is the half of B
C: Therefore the Force of the Weight T, muſt of neceſſity be grea
ter than X, as much as the half of the breadth C A is greater than
half the thichneſſe B C, the firſt ſerving for the Counter-Leaver of
C A, and the ſecond of C B to overcome the ſame Reſiſtance, that
is the quantity of the Fibres, or ſtrings of the whole Baſe A B.
Conclude we therefore, that the ſaid Priſm or Ruler, which is
broader than it is thick, reſiſteth, bresking more the edge-waies
than the flat-waies, according to the Proportion of the breadth to
the thickneſs.
It is requiſite that we begin in the next place
PROPOSITION III.
To find according to what proportion the encreaſe of the
Moment of the proper Gravity is made in a Priſm
or Cylinder, in relation to the proper Reſiſtance
againſt Fraction, whilſt that being parallel to the
Horizon, it is made longer and longer: Which Mo
ment I find to encreaſe ſucceſsively in duplicate Pro
portion to that of the prolongation.
Moment of the proper Gravity is made in a Priſm
or Cylinder, in relation to the proper Reſiſtance
againſt Fraction, whilſt that being parallel to the
Horizon, it is made longer and longer: Which Mo
ment I find to encreaſe ſucceſsively in duplicate Pro
portion to that of the prolongation.
For demonſtration whereof, deſcribe the Priſm or Cylin
der A D, firmly faſtned in the Wall at the end A, and let
it be equidiſtant from the Horizon, and let the ſame be
underſtood to be prolonged as far as E, adding thereto the part
B E. It is manifeſt, that the prolongation of the Leaver A B
to C encreaſeth, by it ſelf alone, that is taken abſolutely, the
Moment of the Force preſſing againſt the Reſiſtance of the
Separation and Rupture to be made in A, according to the pro
portion of C A to B A: but, moreover, the Weight of the Solid
affixed B E, encreaſeth the Moment of the preſſing Gravity of
the Weight of the Solid A B, according to the Proportion of
the Priſm A E to the Priſm A B; which proportion is the ſame
as that of the length A C, to the length A B: Therefore it is clear
der A D, firmly faſtned in the Wall at the end A, and let
it be equidiſtant from the Horizon, and let the ſame be
underſtood to be prolonged as far as E, adding thereto the part
B E. It is manifeſt, that the prolongation of the Leaver A B
to C encreaſeth, by it ſelf alone, that is taken abſolutely, the
Moment of the Force preſſing againſt the Reſiſtance of the
Separation and Rupture to be made in A, according to the pro
portion of C A to B A: but, moreover, the Weight of the Solid
affixed B E, encreaſeth the Moment of the preſſing Gravity of
the Weight of the Solid A B, according to the Proportion of
the Priſm A E to the Priſm A B; which proportion is the ſame
as that of the length A C, to the length A B: Therefore it is clear