RELFE BROTHERS' EUCLID SHEETS.

PROPOSITIONS 1-26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS.

PROPOSITION XXIII.

At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.

Let be the given straight line, and the given point in it, and rectilineal angle.

It is required, at the given point in the given straight line that shall be equal to the given rectilineal angle

the given

to make an angle

In

take any points

, and join

; on

make the triangle

the sides of which shall be equal to the three straight lines

be equal to

to

and

to

Then the angle

shall be

equal to the angle

Because

are equal to

to the base ; therefore the angle

Wherefore, at the given point in the given straight line

each to each, and the base is equal to the angle

is equal

the angle

is

made equal to the given rectilineal angle

RELFE BROTHERS' EUCLID SHEETS.

PROPOSITIONS 1-26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS.

PROPOSITION XXII.

To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third.

Let

be the three given straight lines, of which any two whatever are greater

than the third, namely,

greater than

and greater than ; and

greater than

; and and

It is required to make a triangle of which the sides shall be equal to

each

; then the triangle

at the dis

describe

to the points

shall have its sides equal to the three straight lines

; from the centre

at the distance