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