1the Exceſs by which it exceedeth the Square F Q: And, therefore, by Converſion of Proportion,
the whole Portion is to the part thereof above the Liquid, as the Square B D is to the Square,
F que for the Square B D is ſo much greater than the Exceſs by which it exceedeth the Squar,
F Q as is the ſaid Square F que
the whole Portion is to the part thereof above the Liquid, as the Square B D is to the Square,
F que for the Square B D is ſo much greater than the Exceſs by which it exceedeth the Squar,
F Q as is the ſaid Square F que
E
F
For the parts towards L ſhall move downwards, and thoſe to
wards A upwards.] We thus carrect theſe words, for in Tartaglia's Tranſlation it
is falſly, as I conceive, read Quoniam quæ ex parte L ad ſuperiora ferentur, becauſe
the Line thàt paſſeth thorow Z falls perpendicularly on the parts towards L, and that thorow
G falleth perpendicularly on the parts towards A: Whereupon the Centre Z, together with thoſe
parts which are towards L ſhall move downwards; and the Centre G, together with the parts
which are towards A upwards.
wards A upwards.] We thus carrect theſe words, for in Tartaglia's Tranſlation it
is falſly, as I conceive, read Quoniam quæ ex parte L ad ſuperiora ferentur, becauſe
the Line thàt paſſeth thorow Z falls perpendicularly on the parts towards L, and that thorow
G falleth perpendicularly on the parts towards A: Whereupon the Centre Z, together with thoſe
parts which are towards L ſhall move downwards; and the Centre G, together with the parts
which are towards A upwards.
G
It ſhall in like manner be demonſtrated that the Portion ſhall not
reſt, but incline untill that its Axis do make an Angle with the
Surface of the Liquid, equall to the Angle B.] This may be eaſily demon
ſtratred, as nell from what hath been ſaid in the precedent Propoſition, as alſo from the two
latter Figures, by us inſerted
reſt, but incline untill that its Axis do make an Angle with the
Surface of the Liquid, equall to the Angle B.] This may be eaſily demon
ſtratred, as nell from what hath been ſaid in the precedent Propoſition, as alſo from the two
latter Figures, by us inſerted
PROP. X. THEOR. X.
The Right Portion of a Rightangled Conoid, lighter
than the Liquid, when it ſhall have its Axis greater
than to be unto the Semiparameter, in proportion as
fifteen to four, being demitted into the Liquid, ſo as
than the Liquid, when it ſhall have its Axis greater
than to be unto the Semiparameter, in proportion as
fifteen to four, being demitted into the Liquid, ſo as
that its Baſe touch not the ſame, it ſhall ſometimes
ſtand perpendicular; ſometimes inclined; and ſome
times ſo inclined, as that its Baſe touch the Surface
of the Liquid in one Point only, and that in two Po-
ſitions; ſometimes ſo that its Baſe be more ſubmer-
ged in the Liquid; and ſometimes ſo as that it doth
not in the leaſt touch the Surface of the Liquid;
according to the proportion that it hath to the Liquid
in Gravity. Every one of which Caſes ſhall be anon
demonſtrated.
A
B
C
D
E
Let there be a Portion, as hath been ſaid; and it being cut
thorow its Axis, by a Plane erect unto the Superficies of the
Liquid, let the Section be A P O L, the Section of a Right
angled Cone; and the Axis of the Portion and Diameter of the
Section B D: and let B D be cut in the Point K, ſo as that B K
be double of K D; and in C, ſo as that B D may have the ſame
proportion to K C, as fifteen to four: It is manifeſt, therefore,
that K C is greater than the Semi-parameter: Let the
thorow its Axis, by a Plane erect unto the Superficies of the
Liquid, let the Section be A P O L, the Section of a Right
angled Cone; and the Axis of the Portion and Diameter of the
Section B D: and let B D be cut in the Point K, ſo as that B K
be double of K D; and in C, ſo as that B D may have the ſame
proportion to K C, as fifteen to four: It is manifeſt, therefore,
that K C is greater than the Semi-parameter: Let the
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