1
59[Figure 59]
B D in λ; and from the Point O, and parallel to
A λ, draw O X; and let it touch the Section in O,
as in the first Figure: And the (d) Angle at X,
ſhall be equall alſo to the angle λ: But the angle at Y
is equall to the Angle at γ; and the (e) Angle
A Γ D greater than the Angle A λ D, which falleth
without it: Therefore the Angle at Y ſhall be great
er than that at X. And becauſe now the Portion
turneth about, ſo, as that the Baſe doth not touch
the Liquid, the Axis ſhall make an Angle with its
Surface greater than the Angle G; that is, than the
Angle Y: And, for that reaſon, much greater than
the Angle X.
59[Figure 59]B D in λ; and from the Point O, and parallel to
A λ, draw O X; and let it touch the Section in O,
as in the first Figure: And the (d) Angle at X,
ſhall be equall alſo to the angle λ: But the angle at Y
is equall to the Angle at γ; and the (e) Angle
A Γ D greater than the Angle A λ D, which falleth
without it: Therefore the Angle at Y ſhall be great
er than that at X. And becauſe now the Portion
turneth about, ſo, as that the Baſe doth not touch
the Liquid, the Axis ſhall make an Angle with its
Surface greater than the Angle G; that is, than the
Angle Y: And, for that reaſon, much greater than
the Angle X.
(d) By 29 of the
firſt.
firſt.
(e) By 16. of the
firſt.
firſt.
CONCLUSION III.
If the Portion have the ſame proportion in Gravity to the
Liquid, that the Square X O hath to the Square
BD, being demitted into the Liquid, ſo inclined, as that
its Baſe touch not the Liquid, it ſhall ſtand and
continue inclined, ſo, as that its Baſe touch the Sur
face of the Liquid, in one Point only, and its Axis ſhall
make an Angle with the Liquids Surface equall to the
Angle X. And, if the Portion have the ſame proportion
in Gravity to the Liquid, that the Square P F hath
to the Square B D, being demitted into the Liquid,
& ſet ſo inclined, as that its Baſe touch not the Liquid,
it ſhall ſtand inclined, ſo, as that its Baſe touch the
Surface of the Liquid in one Point only, & its Axis ſhall
make an Angle with it, equall to the Angle Φ.
Liquid, that the Square X O hath to the Square
BD, being demitted into the Liquid, ſo inclined, as that
its Baſe touch not the Liquid, it ſhall ſtand and
continue inclined, ſo, as that its Baſe touch the Sur
face of the Liquid, in one Point only, and its Axis ſhall
make an Angle with the Liquids Surface equall to the
Angle X. And, if the Portion have the ſame proportion
in Gravity to the Liquid, that the Square P F hath
to the Square B D, being demitted into the Liquid,
& ſet ſo inclined, as that its Baſe touch not the Liquid,
it ſhall ſtand inclined, ſo, as that its Baſe touch the
Surface of the Liquid in one Point only, & its Axis ſhall
make an Angle with it, equall to the Angle Φ.
Let the Portion have the ſame proportion in Gravity to tho
Liquid that the Square XO hath to the Square B D; and let
it be demitted into the Liquid ſo inclined, as that its Baſe touch
60[Figure 60]
not the Liquid. And cutting it by
a Plane thorow the Axis, erect unto
the Surface of the Liquid, let the
Section of the Solid, be the Section
of a Right-angled Cone, A P M L;
let the Section of the Surface of the
Liquid be I M; and the Axis of the
Portion and Diameter of the Section
B D; and let B D be divided as be
fore; and draw PN parallel to IM
Liquid that the Square XO hath to the Square B D; and let
it be demitted into the Liquid ſo inclined, as that its Baſe touch
60[Figure 60]not the Liquid. And cutting it by
a Plane thorow the Axis, erect unto
the Surface of the Liquid, let the
Section of the Solid, be the Section
of a Right-angled Cone, A P M L;
let the Section of the Surface of the
Liquid be I M; and the Axis of the
Portion and Diameter of the Section
B D; and let B D be divided as be
fore; and draw PN parallel to IM