1away a pretty big part towards the end with a notable alleviation
of the weight; which in Beams of great Rooms would be commo
dious, and of no ſmall proſit. And it would be pretty, to find what
Figure that Solid ought to have, that it might have equal Reſi
ſtance in all its parts; ſo as that it were not with more eaſe to be
broken by a weight that ſhould preſſe it in the midſt, than in any
other place.
of the weight; which in Beams of great Rooms would be commo
dious, and of no ſmall proſit. And it would be pretty, to find what
Figure that Solid ought to have, that it might have equal Reſi
ſtance in all its parts; ſo as that it were not with more eaſe to be
broken by a weight that ſhould preſſe it in the midſt, than in any
other place.
SALV. I was juſt about to tell you a thing very notable and
pleaſant to this purpoſe. I will aſſume a brief Scheme for the bet
ter explanation of my meaning. This Figure D B is a Priſm, whoſe
Reſiſtance againſt Fraction in the term A D by a Force preſſing
at the term B, is leſſe than the Reſiſtance that would be found in
the place C I, by how much the length C B is leſſer than B A; as
hath already been demon
ſtrated. Now ſuppoſe the
68[Figure 68]
ſaid Priſme to be ſawed
Diagonally according to the
Line FB, ſo that the oppo
ſite Surfaces may be two
Triangles, one of which to
wards us is F A B. This So
lid obtains a quality contrary to the Priſme, to wit, that it leſſe re
ſiſteth Fraction by the Force placed in B at the term C than at A,
by as much the Length C B is leſſe than B A; Which we will ea
ſily prove: For imagining the Section C N O parallel to the other
A F D, the Line F A ſhall be to C N in the Triangle F A B in the
ſame proportion, as the Line A B is to B C: and therefore if we
ſuppoſe the Fulciment of the two Leavers to be in the Points A
and C, whoſe Diſtances are B A, A F, B C, and C N, theſe, I ſay,
ſhall be like: and therefore that Moment which the Force placed
at B hath at the Diſtance B A above the Reſiſtance placed at the
Diſtance A F, the ſaid Force at B ſhall have at the Diſtance BC
above the ſame Reſiſtance, were it placed at the Diſtance C N:
But the Reſiſtance to be overcome at the Fulciment C, being pla
ced at the Diſtance C N, from the Force in B is leſſer than the
Reſiſtance in A ſo much as the Rectangle C O is leſſe than the
Rectangle A D; that is, ſo much as the Line C N is leſs than A F;
that is, C B than B A: Therefore the Reſiſtance of the part O C B
againſt Fraction in C is ſo much leſs than the Reſiſtance of the
whole D A O againſt Fracture in O, as the Length C B is leſs than
A B. We have therefore from the Beam or Priſme D B, taken
away a part, that is half, cutting it Diagonally, and left the Wedge
or triangular Priſm F B A; and they are two Solids of contrary
Qualities, namely, that more reſiſts the more it is ſhortned, and this
in ſhortning loſeth its toughneſs as faſt. Now this being granted,
pleaſant to this purpoſe. I will aſſume a brief Scheme for the bet
ter explanation of my meaning. This Figure D B is a Priſm, whoſe
Reſiſtance againſt Fraction in the term A D by a Force preſſing
at the term B, is leſſe than the Reſiſtance that would be found in
the place C I, by how much the length C B is leſſer than B A; as
hath already been demon
ſtrated. Now ſuppoſe the
68[Figure 68]ſaid Priſme to be ſawed
Diagonally according to the
Line FB, ſo that the oppo
ſite Surfaces may be two
Triangles, one of which to
wards us is F A B. This So
lid obtains a quality contrary to the Priſme, to wit, that it leſſe re
ſiſteth Fraction by the Force placed in B at the term C than at A,
by as much the Length C B is leſſe than B A; Which we will ea
ſily prove: For imagining the Section C N O parallel to the other
A F D, the Line F A ſhall be to C N in the Triangle F A B in the
ſame proportion, as the Line A B is to B C: and therefore if we
ſuppoſe the Fulciment of the two Leavers to be in the Points A
and C, whoſe Diſtances are B A, A F, B C, and C N, theſe, I ſay,
ſhall be like: and therefore that Moment which the Force placed
at B hath at the Diſtance B A above the Reſiſtance placed at the
Diſtance A F, the ſaid Force at B ſhall have at the Diſtance BC
above the ſame Reſiſtance, were it placed at the Diſtance C N:
But the Reſiſtance to be overcome at the Fulciment C, being pla
ced at the Diſtance C N, from the Force in B is leſſer than the
Reſiſtance in A ſo much as the Rectangle C O is leſſe than the
Rectangle A D; that is, ſo much as the Line C N is leſs than A F;
that is, C B than B A: Therefore the Reſiſtance of the part O C B
againſt Fraction in C is ſo much leſs than the Reſiſtance of the
whole D A O againſt Fracture in O, as the Length C B is leſs than
A B. We have therefore from the Beam or Priſme D B, taken
away a part, that is half, cutting it Diagonally, and left the Wedge
or triangular Priſm F B A; and they are two Solids of contrary
Qualities, namely, that more reſiſts the more it is ſhortned, and this
in ſhortning loſeth its toughneſs as faſt. Now this being granted,