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

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1
B
For the declaration of this Propoſition, let a Solid Magnitude
that hath the Figure of a portion of a Sphære, as hath been ſaid,
be imagined to be de­

mitted into the Liquid; and
alſo, let a Plain be ſuppoſed
to be produced thorow the
Axis of that portion, and
thorow the Center of the
Earth: and let the Section
of the Surface of the Liquid
be the Circumference A B
C D, and of the Figure, the
Circumference E F H, & let
E H be a right line, and F T
the Axis of the Portion.
If now
it were poſſible, for ſatisfact­
it be ſuppoſed that the ſaid Axis were not according to the (a) Per­

pendicular; we are then to demonſtrate, that the Figure will not
continue as it was conſtituted by the Adverſary, but that it will re­
turn, as hath been ſaid, unto its former poſition, that is, that the
Axis F T ſhall be according to the Perpendicular.
It is manifeſt, by
the Corollary of the 1. of 3. Euclide, that the Center of the Sphære
is in the Line F T, foraſmuch as that is the Axis of that Figure.
And in regard that the Por­

tion of a Sphære, may be
greater or leſſer than an He­
miſphære, and may alſo be
an Hemiſphære, let the Cen­
tre of the Sphære, in the He­
miſphære, be the Point T,
and in the leſſer Portion the
Point P, and in the greater,
the Point K, and let the Cen­
tre of the Earth be the Point
L.
And ſpeaking, firſt, of
that greater Portion which
hath its Baſe out of, or a­
bove, the Liquid, thorew the Points K and L, draw the Line KL
cutting the Circumference E F H in the Point N, Now, becauſe

every Portion of a Sphære, hath its Axis in the Line, that from the
Centre of the Sphære is drawn perpendicular unto its Baſe, and hath
its Centre of Gravity in the Axis; therefore that Portion of the Fi­
gure which is within the Liquid, which is compounded of two