1the proportion of the whole Portion unto that part thereof which is above the Liquid ſhall not be
greater than that of the Square N O unto the Square M O: Which was to be demonſtrated.
greater than that of the Square N O unto the Square M O: Which was to be demonſtrated.
And hence it followeth that P F is not leſſe than O M, nor P B
than O H.] This followeth by the 10 and 14 of the fifth, and by the 22 of the ſixth of
Euclid, as hath been ſaid above.
B
A Line, therefore, drawn from Hat Right Angles unto N O ſhall
meet with P B betwixt P and B.] Why this ſo falleth out, we will ſhew in the
next.
meet with P B betwixt P and B.] Why this ſo falleth out, we will ſhew in the
next.
C
PROP. VI. THEOR. VI.
The Right Portion of a Rightangled Conoid lighter
than the Liquid, when it ſhall have its Axis greater
than ſeſquialter of the Semi-parameter, but leſſe than
to be unto the Semi-parameter in proportion as fifteen
to fower, being demitted into the Liquid ſo as that
its Baſe do touch the Liquid, it ſhall never stand ſo
enclined as that its Baſe toucheth the Liquid in one
Point only.
than the Liquid, when it ſhall have its Axis greater
than ſeſquialter of the Semi-parameter, but leſſe than
to be unto the Semi-parameter in proportion as fifteen
to fower, being demitted into the Liquid ſo as that
its Baſe do touch the Liquid, it ſhall never stand ſo
enclined as that its Baſe toucheth the Liquid in one
Point only.
Let there be a Portion, as was ſaid; and demit it into the Li
quid in ſuch faſhion as that its Baſe do touch the Liquid in
one only Point: It is to be demonſtrated that the ſaid Portion
ſhall not continue ſo, but ſhall turn about in ſuch manner as that
its Baſe do in no wiſe touch the Surface of the Liquid. For let it be
cut thorow its Axis by a Plane erect
255[Figure 255]
upon the Liquids Surface: and let
the Section of the Superficies of the
Portion be A P O L, the Section of
a Rightangled Cone; and the Sect
ion of the Surface of the Liquid be
A S; and the Axis of the Portion
and Diameter of the Section N O:
and let it be cut in F, ſo as that O
F be double to F N; and in ω ſo, as that N O may be to F ω in the
ſame proportion as fifteen to four; and at Right Angles to N O
draw ω Now becauſe N O hath greater proportion unto F ω than
unto the Semi-parameter, let the Semi-parameter be equall to F B:
and draw P C parallel unto A S, and touching the Section A P O L
in P; and P I parallel unto N O; and firſt let P I cut Kω in H. For
aſmuch, therefore, as in the Portion A P O L, contained betwixt
the Right Line and the Section of the Rightangled Cone, K ω is
parallel to A L, and P I parallel unto the Diameter, and cut by the
quid in ſuch faſhion as that its Baſe do touch the Liquid in
one only Point: It is to be demonſtrated that the ſaid Portion
ſhall not continue ſo, but ſhall turn about in ſuch manner as that
its Baſe do in no wiſe touch the Surface of the Liquid. For let it be
cut thorow its Axis by a Plane erect
255[Figure 255]upon the Liquids Surface: and let
the Section of the Superficies of the
Portion be A P O L, the Section of
a Rightangled Cone; and the Sect
ion of the Surface of the Liquid be
A S; and the Axis of the Portion
and Diameter of the Section N O:
and let it be cut in F, ſo as that O
F be double to F N; and in ω ſo, as that N O may be to F ω in the
ſame proportion as fifteen to four; and at Right Angles to N O
draw ω Now becauſe N O hath greater proportion unto F ω than
unto the Semi-parameter, let the Semi-parameter be equall to F B:
and draw P C parallel unto A S, and touching the Section A P O L
in P; and P I parallel unto N O; and firſt let P I cut Kω in H. For
aſmuch, therefore, as in the Portion A P O L, contained betwixt
the Right Line and the Section of the Rightangled Cone, K ω is
parallel to A L, and P I parallel unto the Diameter, and cut by the