1that the two augmentations of the Lengths and of the Gravities
being put together, the Moment compounded of both is in double
66[Figure 66]
proportion to ei
ther of them. We
conclude there
fore, That the Mo
ments of the For
ces of Priſmes and
Cylinders of equal
thickneſſe, but of
unequal length, are
to one another in
duplicate proporti
on to that of their
Lengths; that is,
are as the Squares of
their Lengths.
being put together, the Moment compounded of both is in double
66[Figure 66]proportion to ei
ther of them. We
conclude there
fore, That the Mo
ments of the For
ces of Priſmes and
Cylinders of equal
thickneſſe, but of
unequal length, are
to one another in
duplicate proporti
on to that of their
Lengths; that is,
are as the Squares of
their Lengths.
We will ſhew, in
the ſecond place,
according to what proportion the Reſiſtance of Fraction in Priſmes
and Cylinders encreaſeth, when they continue of the ſame length,
and encreaſe in thickneſs. And here I ſay, that
the ſecond place,
according to what proportion the Reſiſtance of Fraction in Priſmes
and Cylinders encreaſeth, when they continue of the ſame length,
and encreaſe in thickneſs. And here I ſay, that
PROPOSITION IV.
In Priſmes and Cylinders of equal length, but unequal
thickneſs, the Reſiſtance againſt Fraction encreaſeth
in a proportion iriple to the Diameters of their
Thickneſſes, that is, of their Baſes.
thickneſs, the Reſiſtance againſt Fraction encreaſeth
in a proportion iriple to the Diameters of their
Thickneſſes, that is, of their Baſes.
Let the two Cylinders be theſe A and B, [as in Fig. 5.]
whoſe equal lengths are D G, and F H, the unequal Baſes
the Circles, whoſe Diameters are C D, and E F. I ſay,
that the Reſiſtance of the Cylinder B is to the Reſiſtance of the
Cylinder A againſt Fraction, in a proportion triple to that which
the Diameter F E hath to the Diameter D C. For if we conſider
the abſolute and ſimple Reſiſtance that reſides in the Baſes, that
is, in the Circles E F, and D C to breaking, offering them vio
lence by pulling them end-waies, without all doubt, the Reſiſtance
of the Cylinder B, is ſo much greater than that of the Cylinder A,
by how much the Circle E F is greater than C D; for the Fibres,
Filaments, or tenacious parts, which hold together the Parts of the
Solid, are ſo many the more. But if we conſider, that in offering
whoſe equal lengths are D G, and F H, the unequal Baſes
the Circles, whoſe Diameters are C D, and E F. I ſay,
that the Reſiſtance of the Cylinder B is to the Reſiſtance of the
Cylinder A againſt Fraction, in a proportion triple to that which
the Diameter F E hath to the Diameter D C. For if we conſider
the abſolute and ſimple Reſiſtance that reſides in the Baſes, that
is, in the Circles E F, and D C to breaking, offering them vio
lence by pulling them end-waies, without all doubt, the Reſiſtance
of the Cylinder B, is ſo much greater than that of the Cylinder A,
by how much the Circle E F is greater than C D; for the Fibres,
Filaments, or tenacious parts, which hold together the Parts of the
Solid, are ſo many the more. But if we conſider, that in offering