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

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1nue, but will return to be according to the
240[Figure 240]
It is manifeſt that the Gen­
tre of the Sphære is in the Line F T.
again, foraſmuch as the Portion of a Sphære
may be greater or leſſer than an Hemiſ­
phære, and may alſo be an Hemiſphære, let
the Centre of the Sphære in the Hemiſ­
phære be the Point T, & in the leſſer Por­
tion the Point P, and in the Greater the

Point R.
And ſpeaking firſt of that greater
Portion which hath its Baſe within the
Liquid, thorow R and L, the Earths Cen­
241[Figure 241]
tre, draw the line RL.
The Portion that is
above the Liquid, hath its Axis in the Per­
pendicular paſſing thorow R; and by
what hath been ſaid before, its Centre of
Gravity ſhall be in the Line N R; let it
be the Point R: But the Centre of Gra­
vity of the whole Portion is in the line F
T, betwixt R and F; let it be X: The re­
mainder therefore of that Figure, which is
within the Liquid ſhall have its Centre in
the Right Line R X prolonged in the part
242[Figure 242]
towards X, taken ſo, that the part pro­
longed may have the ſame Proportion to
X R, that the Gravity of the Portion that
is above the Liquid hath to the Gravity
of the Figure that is within the Liquid.
Let O be the Centre of that ſame Figure:
and thorow O draw the Perpendicular L
Now the Gravity of the Portion that
is above the Liquid ſhall preſs according
to the Right Line R L downwards; and
the Gravity of the Figure that is in the
Liquid according to the Right Line O L upwards: There the Figure
ſhall not continue; but the parts of it towards H ſhall move down­
wards, and thoſe towards E upwards: &
243[Figure 243]
this ſhall ever be, ſo long as F T is accord­
ing to the Perpendicular.
The Portion that is above the Liquid

hath its Axis in the Perpendicular paſſing
thorow K.] For draw B C cutting the Line N K in
M; and let N K out the Circumference A B C D in G. In
the ſame manner as before me will demonſtrate, that the Axis

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