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A Segment of a Circle being given to describe<lb/><gap/> of which it is the Segment<lb/>-----<p><head>Prop XXX Prob.</head>To bisect a given circumference, that is to divide<lb/>it into two equal parts.</p>-----<p><head>Prop XXXV Theor.</head>If two straight lines within a circle cut one another,<lb/>the rectangle contained by the Segments of one<lb/>of them is equal to the rectangle contained by<lb/>the segments of the other.</p><pb/>In equal circles, equal angles stand upon equal<lb/>circumferences, whether they be at the centers<lb/>or circumferences.<lb/>-----<p><head>Prop XXXI Theor.</head>In a circle, the angle in a semicircle is a right<lb/>angle, but the angle in a segment greater then<lb/>a semicircle, is less than a right angle; and<lb/>the angle in a segment less than a semicircle<lb/>is greater than a right angle.</p>-----<p><head>Prop XXXVI Theor</head>If from any point without a circle two straight<lb/>lines be drawn, one of which cuts the circle. and<lb/>the other touches it; the rectangle contained by the<lb/>whole lines which cuts the circle, and the part<lb/>of it without the circle shall be equal to the<lb/>Square of the line which touches it</p><pb/>In equal circles, the angles<lb/>equal circumferences, are equ<lb/>whether they be at the cen<lb/>rences<lb/>-----<p><head>Prop XXXII Th</head>If a straight line touches a cir<lb/>of contact a straight line be dra<lb/>the angle made by this line with<lb/>the circle, shall be equal to<lb/>are in the alternate segment</p>-----<p><head>Prop XXXVII</head>If from a point without a ci<lb/>two straight lines, one of whi<lb/>and the other meets it; if the<lb/>whole line which cuts the<lb/>of it without the circle be eq<lb/>the line which meets it, the<lb/>shall touch the circle. —</p><pb/><head>Book the</head><p><head>Prop I Prob</head>In a given Circle to place a straight<lb/>line, equal to a given Straight line,<lb/>not greater than the Diameter of<lb/>the Circle</p>-----<p><head>Prop VII Prob</head>To describe a Square about a<lb/>given Circle</p>-----<p><head>Prop XIII Prob</head>To inscribe a circle in a given<lb/>equilateral & equiangular pentagon.</p><pb/><head>Prop II Prob.</head>In a given Circle to inscribe a triangle<lb/>equiangular to <add>a</add> given triangle.<lb/>-----<p><head>Prop VIII Prob.</head>To inscribe a circle in a given<lb/>Square</p>-----<p><head>Prop XIV Prob.</head>To inscribe a Circle about a given<lb/>equilateral & equiangular pentagon</p><pb/><head>Prop III Prob</head>About a given Circle to describe a<lb/>triangle equiangular to a given<lb/>triangle<lb/>-----<p><head>Prop IX Prob.</head>To describe a Circle about a given<lb/>Square.</p>-----<p><head>Prop XV Prob</head>To inscribe an equilateral &<lb/>equiangular hexagon in a given Circle.</p> | |||
A Segment of a Circle being given to describe
of which it is the Segment
-----
Prop XXX Prob.To bisect a given circumference, that is to divide
it into two equal parts.
-----
Prop XXXV Theor.If two straight lines within a circle cut one another,
the rectangle contained by the Segments of one
of them is equal to the rectangle contained by
the segments of the other.
---page break---
In equal circles, equal angles stand upon equal
circumferences, whether they be at the centers
or circumferences.
-----
Prop XXXI Theor.In a circle, the angle in a semicircle is a right
angle, but the angle in a segment greater then
a semicircle, is less than a right angle; and
the angle in a segment less than a semicircle
is greater than a right angle.
-----
Prop XXXVI TheorIf from any point without a circle two straight
lines be drawn, one of which cuts the circle. and
the other touches it; the rectangle contained by the
whole lines which cuts the circle, and the part
of it without the circle shall be equal to the
Square of the line which touches it
---page break---
In equal circles, the angles
equal circumferences, are equ
whether they be at the cen
rences
-----
Prop XXXII ThIf a straight line touches a cir
of contact a straight line be dra
the angle made by this line with
the circle, shall be equal to
are in the alternate segment
-----
Prop XXXVIIIf from a point without a ci
two straight lines, one of whi
and the other meets it; if the
whole line which cuts the
of it without the circle be eq
the line which meets it, the
shall touch the circle. —
---page break---
Book the
Prop I ProbIn a given Circle to place a straight
line, equal to a given Straight line,
not greater than the Diameter of
the Circle
-----
Prop VII ProbTo describe a Square about a
given Circle
-----
Prop XIII ProbTo inscribe a circle in a given
equilateral & equiangular pentagon.
---page break---
Prop II Prob.In a given Circle to inscribe a triangle
equiangular to a given triangle.
-----
Prop VIII Prob.To inscribe a circle in a given
Square
-----
Prop XIV Prob.To inscribe a Circle about a given
equilateral & equiangular pentagon
---page break---
Prop III ProbAbout a given Circle to describe a
triangle equiangular to a given
triangle
-----
Prop IX Prob.To describe a Circle about a given
Square.
-----
Prop XV ProbTo inscribe an equilateral &
equiangular hexagon in a given Circle.
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Identifier: | JB/135/073/004"JB/" can not be assigned to a declared number type with value 135. |
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135 |
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073 |
the propositions of the third and fourth books of euclid as expressed by simson |
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004 |
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private material |
2 |
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recto |
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sir samuel bentham |
[[watermarks::[tall thin motif with prince of wales feathers] icv]] |
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46191 |
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