PROP. VII. THE OR. VII.
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 ſaid Semi-parameter in proportion
as fiſteen to fower, being demitted into the Liquid ſo
as that its Baſe be wholly within the Liquid, it ſhall
never ſtand ſo as that its Baſe do touch the Surface
of the Liquid, but ſo, that it be wholly within the
Liquid, and ſhall not in the leaſt touch its Surface.
than the Liquid, when it ſhall have its Axis greater
than Seſquialter of the Semi-parameter, but leſſe
than to be unto the ſaid Semi-parameter in proportion
as fiſteen to fower, being demitted into the Liquid ſo
as that its Baſe be wholly within the Liquid, it ſhall
never ſtand ſo as that its Baſe do touch the Surface
of the Liquid, but ſo, that it be wholly within the
Liquid, and ſhall not in the leaſt touch its Surface.
Let there be a Portion as hath been ſaid; and let it be de
mitted into the Liquid, as we have ſuppoſed, ſo as that its
Baſe do touch the Surface in one Point only: It is to be de
monſtrated that the ſame ſhall not ſo
263[Figure 263]
continue, 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 upon the Liquids Sur
face: and let the Section be A P O L,
the Section of a Rightangled
Cone; the Section of the Liquids
Surface S L; and the Axis of the
Portion and Diameter of the Section P F: and let P F be cut in
R, ſo, as that R P may be double to R F, and in ω ſo as that P F
may be to R ω as fifteen to fower: and draw ω K at Right Angles
mitted into the Liquid, as we have ſuppoſed, ſo as that its
Baſe do touch the Surface in one Point only: It is to be de
monſtrated that the ſame ſhall not ſo
263[Figure 263]continue, 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 upon the Liquids Sur
face: and let the Section be A P O L,
the Section of a Rightangled
Cone; the Section of the Liquids
Surface S L; and the Axis of the
Portion and Diameter of the Section P F: and let P F be cut in
R, ſo, as that R P may be double to R F, and in ω ſo as that P F
may be to R ω as fifteen to fower: and draw ω K at Right Angles
to P F: (a) R ω ſhall be leſſe than the Semi-parameter. There
fore let R H be ſuppoſed equall to the Semi-parameter: and
draw C O touching the Section in O and parallel unto S L; and
let N O be parallel unto P F; and firſt let N O cut K ω in the Point
I, as in the former Schemes: It ſhall be demonſtrated that N O is
to O I either ſeſquialter, or greater than ſeſquialter. Let O I be
leſſe than double to I N; and let O B be double to B N: and let
them be diſpoſed like as before. We might likewiſe demonſtrate
that if a Line be drawn thorow R and T it will make Right Angles
with the Line C O, and with the Surface of the Liquid: Where
fore Lines being drawn from the Points B and G parallels unto
R T, they alſo ſhall be Perpendiculars to the Surface of the Liquid:
The Portion therefore which is above the Liquid ſhall move