1Again, by dividing, I D ſhall be to D Z, as one to two: But Z D was to D A, that is, to D L,
as two to five: Therefore, ex equali, and Converting, L D is to D I, as five to one: and, by
Converſion of Proportion, D L is to D I, as five to four: But D Z was to D L, as two to
five: Therefore, again, ex equali, D Z is to L I, as two to four: Therefort L I is double
of D Z: Which was to be demonſtrated.
as two to five: Therefore, ex equali, and Converting, L D is to D I, as five to one: and, by
Converſion of Proportion, D L is to D I, as five to four: But D Z was to D L, as two to
five: Therefore, again, ex equali, D Z is to L I, as two to four: Therefort L I is double
of D Z: Which was to be demonſtrated.
P
Q
And, A D is to D I, as five to one.] This we have but juſt now demon
ſtrated.
ſtrated.
R
For it hath been demonſtrated, above, that the Portion whoſe
Axis is greater than Seſquialter of the Semi-parameter, if it have
not leſſer proportion in Gravity to the Liquid, &c.] He hath demonstra
ted this in the fourth Propoſition of this Book.
Axis is greater than Seſquialter of the Semi-parameter, if it have
not leſſer proportion in Gravity to the Liquid, &c.] He hath demonstra
ted this in the fourth Propoſition of this Book.
CONCLVSION II.
If the Portion have leſſer proportion in Gravity to the
Liquid, than the Square S B hath to the Square
B D, but greater than the Square X O hath to the
Square B D, being demitted into the Liquid, ſo in
clined, as that its Baſe touch not the Liquid, it ſhall
continue inclined, ſo, as that its Baſe ſhall not in the
leaſt touch the Surface of the Liquid, and its Axis
ſhall make an Angle with the Liquids Surface, greater
than the Angle X.
A
Therfore repeating the firſt figure, let the Portion have unto
the Liquid in Gravitie a proportion greater than the Square
X O hath to the ſquare B D, but leſſer than the Square made of
the Exceſſe by which the Axis is greater than Seſquialter of the Semi
280[Figure 280]
Parameter, that is, of S B, hath to
the Square B D: and as the Portion
is to the Liquid in Gravity, ſo let
the Square made of the Line ψ be
to the Square B D: ψ ſhall be great
er than X O, but leſſer than the
Exceſſe by which the Axis is grea
ter than Seſquialter of the Semi
parameter, that is, than S B. Let
a Right Line M N be applyed to
fall between the Conick-Sections
A M Q L and A X D, [parallel to
B D falling betwixt O X and B D,] and equall to the Line ψ: and let
it cut the remaining Conick Section A H I in the point H, and the
Right Line R G in V. It ſhall be demonſtrated that M H is double to
H N, like as it was demonſtrated that O G is double to G X.
the Liquid in Gravitie a proportion greater than the Square
X O hath to the ſquare B D, but leſſer than the Square made of
the Exceſſe by which the Axis is greater than Seſquialter of the Semi
280[Figure 280]Parameter, that is, of S B, hath to
the Square B D: and as the Portion
is to the Liquid in Gravity, ſo let
the Square made of the Line ψ be
to the Square B D: ψ ſhall be great
er than X O, but leſſer than the
Exceſſe by which the Axis is grea
ter than Seſquialter of the Semi
parameter, that is, than S B. Let
a Right Line M N be applyed to
fall between the Conick-Sections
A M Q L and A X D, [parallel to
B D falling betwixt O X and B D,] and equall to the Line ψ: and let
it cut the remaining Conick Section A H I in the point H, and the
Right Line R G in V. It ſhall be demonſtrated that M H is double to
H N, like as it was demonſtrated that O G is double to G X.
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