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

the given rectilineal angle.

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

i on

In , take any points

and join

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

and

Then the angle be equal to

shall be

, so that

to

to

equal to the angle

Because

are equal to

each to each, and the base

is equal

to the base ; therefore the angle is equal to the angle

Wherefore, at the given point in the given straight line

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, and

greater than

; and
greater than

and greater than

; and

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

each

; then the triangle

shall have its sides equal to the three straight lines

; therefore also

; and

straight lines,

is equal to

is equal to ;

therefore the three are respectively equal to the three,

; and therehas its three sides

equal to the three given

fore the triangle

straight lines