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the Angles at F and ω are equall; as alſo, that S B and B C, and

S R and C R are equall to one another: And, therefore, N X and

G Y are alſo equall; and X T and Y I. And ſince G H is double

to H I, N X ſhall be leſſer than double of X T. Let N M therefore

be double to M T; and drawing a Line from M to K, prolong it

unto E. Now the Centre of Gravity of the whole ſhall be the

Point K; of the part which is in the Liquid the Point M; and

that of the part which is above the Liquid in the Line prolonged

as ſuppoſe in E. Therefore, by what was even now demonſtrated

it is manifeſt that the Portion ſhall not ſtay thus, but ſhall incline, ſo

as that its Baſe do in no wiſe touch the Surface of the Liquid

And that the Portion will ſtand, ſo, as to make an Angle with the

Surface of the Liquid leſſer than

[Figure 75]

the Angle φ, ſhall thus be demon

ſtrated. Let it, if poſſible, ſtand,

ſo, as that it do not make an Angle

leſſer than the Angle φ; and diſpoſe

all things elſe in the ſame manner a

before; as is done in the preſet

Figure. We are to demonſtrat

in the ſame method, that N T is e-

quall to ψ; and by the ſame reaſor

equall alſo to G I. And ſince that in

the Triangles P φ C and N F S, the Angle F is not leſſer than the

Angle φ, B F ſhall not be greater than B C: And, therefore, neither

ſhall S R be leſſer than C R; nor N X than P Y: But ſince P F is

greater than N T, let P F be Seſquialter of P Y: N T ſhall be leſſer

than Seſquialter of N X: And, therefore, N X ſhall be greate

than double of X T. Let N M be double of M T; and drawing

Line from M to K prolong it. It is manifeſt, now, by what hath

been ſaid, that the Portion ſhall not continue in this poſition, but ſhall

turn about, ſo, as that its Axis do make an Angle with the Surface

of the Liquid, leſſer than the Angle φ.