Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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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.
(a) By 5. of the
firſt of this.
(b) By 11. of the
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.
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

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