1are light and of great Reſiſtance againſt bending and breaking.
For if a Wheat Straw that ſupports an Ear that is heavier than the
whole Stalk, were made of the ſame quantity of matter but were
maſſie or ſolid, it would be much leſſe repugnant to Fraction or
Flection. And with the ſame Reaſon Art hath obſerved, and Ex
perience confirmed, that an hollow Cane, or a Trunk of Wood
or Metal, is much more firm and tough than if being of the ſame
weight and length it were ſolid, which conſequently would be
more flender, and therefore Art hath contrived to make Lances hol
low within when they are deſired to be ſtrong and light. We will
ſhew therefore, that
For if a Wheat Straw that ſupports an Ear that is heavier than the
whole Stalk, were made of the ſame quantity of matter but were
maſſie or ſolid, it would be much leſſe repugnant to Fraction or
Flection. And with the ſame Reaſon Art hath obſerved, and Ex
perience confirmed, that an hollow Cane, or a Trunk of Wood
or Metal, is much more firm and tough than if being of the ſame
weight and length it were ſolid, which conſequently would be
more flender, and therefore Art hath contrived to make Lances hol
low within when they are deſired to be ſtrong and light. We will
ſhew therefore, that
PROPOSITION XV.
The Reſiſtances of two Cylinders, equall, and equally
long, one of which is Hollow, and the other Maſsie,
have to each other the ſame proportion, as their Dia
meters.
long, one of which is Hollow, and the other Maſsie,
have to each other the ſame proportion, as their Dia
meters.
Let the Cane or Hollow Cylinder be A E, [as in Fig. 17.]
and the Cylinder I N Maſſie, and equall in weight and length.
I ſay, the Reſiſtance of the Cane A E hath the ſame propor
tion to the Reſiſtance of the ſolid Cylinder, as the Diameter
A B hath to the Diameter I L. Which is very manifeſt; For the
Cane and the Cylinder I N being equal, and of equal lengths, the
Circle I L that is Baſe of the Cylinder ſhall be equal to the Ring
A B that is Baſe of the Cane A E, (I call the Superficies that re
maineth when a leſſer Circle is taken out of a greater that is Con
centrick with it a Ring:) and therefore their Abſolute Reſiſtan
ces ſhall be equal: but becauſe in breaking croſſe-waies we make
uſe in the Cylinder I N of the length L N for a Leaver, and of the
point L for a Fulciment, and of the Semidiameter or Diameter L I
for a Counter-Leaver; and in the Cane the part of the Leaver,
that is the Line B E is equal to L N; but the Counter-Leaver at
the Fulciment B is the Diameter or Semidiameter A B: It is mani
feſt therefore that the Reſiſtance of the Cane exceedeth that of
the Solid Cylinder as much as the Diameter A B exceeds the Dia
meter I L; Which is that that we ſought. Toughneſs therefore is ac
quired in the hollow Cane above the Toughneſs of the ſolid Cylin
der according to the proportion of the Diameters: provided al
waies that they be both of the ſame matter, weight, and length.
and the Cylinder I N Maſſie, and equall in weight and length.
I ſay, the Reſiſtance of the Cane A E hath the ſame propor
tion to the Reſiſtance of the ſolid Cylinder, as the Diameter
A B hath to the Diameter I L. Which is very manifeſt; For the
Cane and the Cylinder I N being equal, and of equal lengths, the
Circle I L that is Baſe of the Cylinder ſhall be equal to the Ring
A B that is Baſe of the Cane A E, (I call the Superficies that re
maineth when a leſſer Circle is taken out of a greater that is Con
centrick with it a Ring:) and therefore their Abſolute Reſiſtan
ces ſhall be equal: but becauſe in breaking croſſe-waies we make
uſe in the Cylinder I N of the length L N for a Leaver, and of the
point L for a Fulciment, and of the Semidiameter or Diameter L I
for a Counter-Leaver; and in the Cane the part of the Leaver,
that is the Line B E is equal to L N; but the Counter-Leaver at
the Fulciment B is the Diameter or Semidiameter A B: It is mani
feſt therefore that the Reſiſtance of the Cane exceedeth that of
the Solid Cylinder as much as the Diameter A B exceeds the Dia
meter I L; Which is that that we ſought. Toughneſs therefore is ac
quired in the hollow Cane above the Toughneſs of the ſolid Cylin
der according to the proportion of the Diameters: provided al
waies that they be both of the ſame matter, weight, and length.
It would be well, that in conſequence of this we try to inveſtigate
that which hapneth in other Caſes indifferently between all Canes
and ſolid Cylinders of equal length, although unequal in quantity
of weight, and more or leſs evacuated. And firſt we will demon
ſtrate, that
that which hapneth in other Caſes indifferently between all Canes
and ſolid Cylinders of equal length, although unequal in quantity
of weight, and more or leſs evacuated. And firſt we will demon
ſtrate, that