1
293[Figure 293]
ſhall be equall to the Angle at φ; and the Line B S
equall to the Line B C; and S R to C R: Where
fore, M H ſhall be likewiſe equall to P Y. There
fore, having drawn HK and prolonged it; the
Centre of Gravity of the whole Portion ſhall be
K; of that which is in the Liquid H; and of
that which is above it, the Centre ſhall be in
the Line prolonged: let it be in ω. There
fore, along that ſame Line K H, which is per
pendicular to the Surface of the Liquid, ſhall
the part which is within the Liquid move up
wards, and that which is above the Liquld
downwards: And, for this cauſe, the Portion,
ſhall be no longer moved, but ſhall ſtay, and
reſt, ſo, as that its Baſe do touch the Liquids Surface in but one Point; and its Axis
maketh an Angle therewith equall to the Angle φ; And, this is that which we were to
demonſtrate.
293[Figure 293]ſhall be equall to the Angle at φ; and the Line B S
equall to the Line B C; and S R to C R: Where
fore, M H ſhall be likewiſe equall to P Y. There
fore, having drawn HK and prolonged it; the
Centre of Gravity of the whole Portion ſhall be
K; of that which is in the Liquid H; and of
that which is above it, the Centre ſhall be in
the Line prolonged: let it be in ω. There
fore, along that ſame Line K H, which is per
pendicular to the Surface of the Liquid, ſhall
the part which is within the Liquid move up
wards, and that which is above the Liquld
downwards: And, for this cauſe, the Portion,
ſhall be no longer moved, but ſhall ſtay, and
reſt, ſo, as that its Baſe do touch the Liquids Surface in but one Point; and its Axis
maketh an Angle therewith equall to the Angle φ; And, this is that which we were to
demonſtrate.
F
(g) By 9 of t
fifth.
fifth.
CONCLVSION IV.
If the Portion have greater proportion in Gravity
to the Liquid, than the Square F P to the Square
B D, but leſſer than that of the Square X O to the
Square B D, being demitted into the Liquid,
and inclined, ſo, as that its Baſe touch not the
Liquid, it ſhall ſtand and reſt, ſo, as that its Baſe
ſhall be more ſubmerged in the Liquid.
to the Liquid, than the Square F P to the Square
B D, but leſſer than that of the Square X O to the
Square B D, being demitted into the Liquid,
and inclined, ſo, as that its Baſe touch not the
Liquid, it ſhall ſtand and reſt, ſo, as that its Baſe
ſhall be more ſubmerged in the Liquid.
Again, let the Portion have greater proportion in
Gravity to the Liquid, than the Square F P to the
Square B D, but leſſer than that of the Square X O to
the Square B D; and as the Portion is in Gravity to the Liquid,
ſo let the Square made of the Line ψ be to the Square B D. Ψ
ſhall be greater than F P, and leſſer than X O. Apply, therefore,
the right Line I V to fall betwixt the Portions A V Q L and A X D;
and let it be equall to ψ, and parallel to B D; and let it meet
the Remaining Section in Y: V Y ſhall alſo be proved double
to Y I, like as it hath been demonſtrated, that O G is double off
G X. And, draw from V, the Line V ω, touching the Section
A V Q L in V; and drawing a Line from A to I, prolong it unto
que We prove in the ſame manner, that the Line A I is equall
to I que and that A Q is parallel to V ω. It is to be demonſtrated,
that the Portion being demitted into the Liquid, and ſo inclined,
as that its Baſe touch not the Liquid, ſhall ſtand, ſo, that its Baſe
ſhall be more ſubmerged in the Liquid, than to touch it Surface in
Gravity to the Liquid, than the Square F P to the
Square B D, but leſſer than that of the Square X O to
the Square B D; and as the Portion is in Gravity to the Liquid,
ſo let the Square made of the Line ψ be to the Square B D. Ψ
ſhall be greater than F P, and leſſer than X O. Apply, therefore,
the right Line I V to fall betwixt the Portions A V Q L and A X D;
and let it be equall to ψ, and parallel to B D; and let it meet
the Remaining Section in Y: V Y ſhall alſo be proved double
to Y I, like as it hath been demonſtrated, that O G is double off
G X. And, draw from V, the Line V ω, touching the Section
A V Q L in V; and drawing a Line from A to I, prolong it unto
que We prove in the ſame manner, that the Line A I is equall
to I que and that A Q is parallel to V ω. It is to be demonſtrated,
that the Portion being demitted into the Liquid, and ſo inclined,
as that its Baſe touch not the Liquid, ſhall ſtand, ſo, that its Baſe
ſhall be more ſubmerged in the Liquid, than to touch it Surface in