xml:lang="en" lang="en" dir="ltr">

# ##### Views

Keep up to date with the latest news - subscribe to the Transcribe Bentham newsletter; Find a new page to transcribe in our list of Untranscribed Manuscripts

# JB/135/073/004

Completed

A Segment of a Circle being given to describe
{the Circle} 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 Theor.
If 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
If 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 XXXVII
If 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---

Prop I Prob.
In a given Circle to place a straight
line, equal to a given Straight line,
not greater than the Diameter of
the Circle

Prop VII Prob.
To describe a Square about a
given Circle

Prop XIII Prob.
To 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 Prob.
About 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 Prob.
To inscribe an equilateral &
equiangular hexagon in a given Circle.

Identifier: | JB/135/073/004
"JB/" can not be assigned to a declared number type with value 135.

135

073

the propositions of the third and fourth books of euclid as expressed by simson

004

private material

2

recto

sir samuel bentham

[[watermarks::[tall thin motif with prince of wales feathers] icv]]

46191