1Therefore B and R are equall. And becauſe that of the Magni
tude FA the Gravity is B: Therefore of the Liquid Body N I the
Gravity is O R. As F A is to N I, ſo is B to O R, or, ſo is R to
O R: But as R is to O R, ſo is I to N I, and A to F A: Therefore
I is to N I, as F A to N I: And as I to N I ſo is (b) A to F A.
Therefore F A is to N I, as A is to F A: Which was to be demon
ſtrated.
tude FA the Gravity is B: Therefore of the Liquid Body N I the
Gravity is O R. As F A is to N I, ſo is B to O R, or, ſo is R to
O R: But as R is to O R, ſo is I to N I, and A to F A: Therefore
I is to N I, as F A to N I: And as I to N I ſo is (b) A to F A.
Therefore F A is to N I, as A is to F A: Which was to be demon
ſtrated.
(a) By 5. of the
firſt of this.
firſt of this.
(b) By 11. of the
fifth of Eucl.
fifth of Eucl.
PROP. II. THEOR. II.
A
^{*} The Right Portion of a Right angled Conoide, when it
ſhall have its Axis leſſe than ſeſquialter ejus quæ ad
Axem (or of its Semi-parameter) having any what
ever proportion to the Liquid in Gravity, being de
mitted into the Liquid ſo as that its Baſe touch not
the ſaid Liquid, and being ſet ſtooping, it ſhall not
remain ſtooping, but ſhall be restored to uprightneſſe.
I ſay that the ſaid Portion ſhall ſtand upright when
the Plane that cuts it ſhall be parallel unto the Sur
face of the Liquid.
ſhall have its Axis leſſe than ſeſquialter ejus quæ ad
Axem (or of its Semi-parameter) having any what
ever proportion to the Liquid in Gravity, being de
mitted into the Liquid ſo as that its Baſe touch not
the ſaid Liquid, and being ſet ſtooping, it ſhall not
remain ſtooping, but ſhall be restored to uprightneſſe.
I ſay that the ſaid Portion ſhall ſtand upright when
the Plane that cuts it ſhall be parallel unto the Sur
face of the Liquid.
Let there be a Portion of a Rightangled Conoid, as hath been
ſaid; and let it lye ſtooping or inclining: It is to be demon
ſtrated that it will not ſo continue but ſhall be reſtored to re
ctitude. For let it be cut through the Axis by a plane erect upon
the Surface of the Liquid, and let the Section of the Portion be
A PO L, the Section of a Rightangled Cone, and let the Axis
246[Figure 246]
of the Portion and Diameter of the
Section be N O: And let the Sect
ion of the Surface of the Liquid be
I S. If now the Portion be not
erect, then neither ſhall A L be Pa
rallel to I S: Wherefore N O will
not be at Right Angles with I S.
ſaid; and let it lye ſtooping or inclining: It is to be demon
ſtrated that it will not ſo continue but ſhall be reſtored to re
ctitude. For let it be cut through the Axis by a plane erect upon
the Surface of the Liquid, and let the Section of the Portion be
A PO L, the Section of a Rightangled Cone, and let the Axis
246[Figure 246]of the Portion and Diameter of the
Section be N O: And let the Sect
ion of the Surface of the Liquid be
I S. If now the Portion be not
erect, then neither ſhall A L be Pa
rallel to I S: Wherefore N O will
not be at Right Angles with I S.
Draw therefore K ω, touching the Section of the Cone I, in the
Point P [that is parallel to I S: and from the Point P unto I S
draw P F parallel unto O N, ^{*} which ſhall be the Diameter of the
Section I P O S, and the Axis of the Portion demerged in the Li
quid. In the next place take the Centres of Gravity: ^{*} and of
the Solid Magnitude A P O L, let the Centre of Gravity be R; and
of I P O S let the Centre be B: ^{*} and draw a Line from B to R
prolonged unto G; which let be the Centre of Gravity of the