1
264[Figure 264]
wards according to that ſame Perpendicular
which paſſeth thorow B; and the Portion
which is within the Liquid ſhall move up
wards acording to that paſſing thorow G:
From whence it is manifeſt that the Solid
ſhall turn about in ſuch manner, as that
its Baſe ſhall in no wiſe touch the Surface
of the Liquid; for that now when it touch
eth but in one Point only, it moveth down
wards on the part towards L. And though
N O ſhould not cut ω K, yet ſhall the ſame hold true.
264[Figure 264]wards according to that ſame Perpendicular
which paſſeth thorow B; and the Portion
which is within the Liquid ſhall move up
wards acording to that paſſing thorow G:
From whence it is manifeſt that the Solid
ſhall turn about in ſuch manner, as that
its Baſe ſhall in no wiſe touch the Surface
of the Liquid; for that now when it touch
eth but in one Point only, it moveth down
wards on the part towards L. And though
N O ſhould not cut ω K, yet ſhall the ſame hold true.
(a) By 10 of the
fifth.
fifth.
PROP. VIII. THE OR. VIII.
The Right Portion of a Rightangled Conoid, when it
ſhall have its Axis greater than ſeſquialter of the Se
mi-parameter, but leſſe than to be unto the ſaid Semi
parameter, in proportion as fifteen to fower, if it
have a leſſer proportion in Gravity to the Liquid, than
the Square made of the Exceſſe by which the Axis is
greater than Seſquialter of the Semi-parameter hath
to the Square made of the Axis, being demitted into
the Liquid, ſo as that its Baſe touch not the Liquid,
it ſhall neither return to Perpendicularity, nor conti
nue inclined, ſave only when the Axis makes an
Angle with the Surface of the Liquid, equall to that
which we ſhall preſently ſpeak of.
ſhall have its Axis greater than ſeſquialter of the Se
mi-parameter, but leſſe than to be unto the ſaid Semi
parameter, in proportion as fifteen to fower, if it
have a leſſer proportion in Gravity to the Liquid, than
the Square made of the Exceſſe by which the Axis is
greater than Seſquialter of the Semi-parameter hath
to the Square made of the Axis, being demitted into
the Liquid, ſo as that its Baſe touch not the Liquid,
it ſhall neither return to Perpendicularity, nor conti
nue inclined, ſave only when the Axis makes an
Angle with the Surface of the Liquid, equall to that
which we ſhall preſently ſpeak of.
Let there be a Portion as hath been ſaid; and let B D be equall
to the Axis: and let B K be double to K D; and R K equall
to the Semi-parameter: and let C B be Seſquialter of B R:
C D ſhall be alſo Sefquialter of K R. And as the Portion is to the
Liquid in Gravity, ſo let the Square F Q be to the Square D B;
and let F be double to Q: It is manifeſt, therefore, that F Q hath
to D B, leſs proportion than C B hath to B D; For C B is the
Exceſs by which the Axis is greater than Seſquialter of the Semi
parameter: And, therefore, F Q is leſs than B C; and, for the
ſame reaſon, F is leſs than B R. Let R ψ be equall to F; and draw
ψ E perpendicular to B D; which let be in power or contence the
half of that which the Lines K R and ψ B containeth; and
draw a Line from B to E: It is to be demonſtrated, that the
to the Axis: and let B K be double to K D; and R K equall
to the Semi-parameter: and let C B be Seſquialter of B R:
C D ſhall be alſo Sefquialter of K R. And as the Portion is to the
Liquid in Gravity, ſo let the Square F Q be to the Square D B;
and let F be double to Q: It is manifeſt, therefore, that F Q hath
to D B, leſs proportion than C B hath to B D; For C B is the
Exceſs by which the Axis is greater than Seſquialter of the Semi
parameter: And, therefore, F Q is leſs than B C; and, for the
ſame reaſon, F is leſs than B R. Let R ψ be equall to F; and draw
ψ E perpendicular to B D; which let be in power or contence the
half of that which the Lines K R and ψ B containeth; and
draw a Line from B to E: It is to be demonſtrated, that the