PROP. II. THEOR. II.

The Superficies of every Liquid that is conſiſtant and

ſetled ſhall be of a Sphærical Figure, which Figure

ſhall have the ſame Center with the Earth.

ſetled ſhall be of a Sphærical Figure, which Figure

ſhall have the ſame Center with the Earth.

Let us ſuppoſe a Liquid that is of ſuch a conſiſtance as that it

is not moved, and that its Superficies be cut by a Plane along

by the Center of the Earth, and let the Center of the Earth

be the Point K: and let the Section of the Superficies be the Line

A B G D. I ſay that the Line A B G D is the Circumference of a

229[Figure 229]

Circle, and that the Center

thereof is the Point K And

if it be poſſible that it may

not be the Circumference

of a Circle, the Right

Lines drawn ^{*} by the Point

K to the ſaid Line A B G D

ſhall not be equal. There

fore let a Right-Line be

taken greater than ſome of thoſe produced from the Point K unto

the ſaid Line A B G D, and leſſer than ſome other; and upon the

Point K let a Circle be deſcribed at the length of that Line,

Now the Circumference of this Circle ſhall fall part without the

ſaid Line A B G D, and part within: it having been preſuppoſed

that its Semidiameter is greater than ſome of thoſe Lines that may

be drawn from the ſaid Point K unto the ſaid Line A B G D, and

leſſer than ſome other. Let the Circumference of the deſcribed

Circle be R B G H, and from B to K draw the Right-Line B K: and

drawn alſo the two Lines K R, and K E L which make a Right

Angle in the Point K: and upon the Center K deſcribe the Circum

ference X O P in the Plane and in the Liquid. The parts, there

fore, of the Liquid that are ^{*} according to the Circumference

X O P, for the reaſons alledged upon the firſt Suppoſition, are equi

jacent, or equipoſited, and contiguous to each other; and both

theſe parts are preſt or thruſt, according to the ſecond part of the

Suppoſition, by the Liquor which is above them. And becauſe the

two Angles E K B and B K R are ſuppoſed equal [by the 26. of 3.

of Euclid,] the two Circumferences or Arches B E and B R ſhall

be equal (foraſmuch as R B G H was a Circle deſcribed for ſatis

faction of the Oponent, and K its Center:) And in like manner

the whole Triangle B E K ſhall be equal to the whole Triangle

B R K. And becauſe alſo the Triangle O P K for the ſame reaſon

is not moved, and that its Superficies be cut by a Plane along

by the Center of the Earth, and let the Center of the Earth

be the Point K: and let the Section of the Superficies be the Line

A B G D. I ſay that the Line A B G D is the Circumference of a

229[Figure 229]

Circle, and that the Center

thereof is the Point K And

if it be poſſible that it may

not be the Circumference

of a Circle, the Right

Lines drawn ^{*} by the Point

K to the ſaid Line A B G D

ſhall not be equal. There

fore let a Right-Line be

taken greater than ſome of thoſe produced from the Point K unto

the ſaid Line A B G D, and leſſer than ſome other; and upon the

Point K let a Circle be deſcribed at the length of that Line,

Now the Circumference of this Circle ſhall fall part without the

ſaid Line A B G D, and part within: it having been preſuppoſed

that its Semidiameter is greater than ſome of thoſe Lines that may

be drawn from the ſaid Point K unto the ſaid Line A B G D, and

leſſer than ſome other. Let the Circumference of the deſcribed

Circle be R B G H, and from B to K draw the Right-Line B K: and

drawn alſo the two Lines K R, and K E L which make a Right

Angle in the Point K: and upon the Center K deſcribe the Circum

ference X O P in the Plane and in the Liquid. The parts, there

fore, of the Liquid that are ^{*} according to the Circumference

X O P, for the reaſons alledged upon the firſt Suppoſition, are equi

jacent, or equipoſited, and contiguous to each other; and both

theſe parts are preſt or thruſt, according to the ſecond part of the

Suppoſition, by the Liquor which is above them. And becauſe the

two Angles E K B and B K R are ſuppoſed equal [by the 26. of 3.

of Euclid,] the two Circumferences or Arches B E and B R ſhall

be equal (foraſmuch as R B G H was a Circle deſcribed for ſatis

faction of the Oponent, and K its Center:) And in like manner

the whole Triangle B E K ſhall be equal to the whole Triangle

B R K. And becauſe alſo the Triangle O P K for the ſame reaſon