RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION IV.

If two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise the angles contained by those sides equal to each other; they shall likewise have their bases or third sides equal, and the two triangles shall be equal, and their other angles shall be equal, each to each, viz., those to which the equal sides are opposite.

triangle

be equal to the base

; and the triangle

to the

; and the other angles to which the equal sides are opposite shall be equal,

For, if the triangle

be on and the straight line

be applied to the triangle

on

; then the point

is equal to

; and

point

because

shall fall on

because the angle

shall coincide with the point

also the point
point was shewn to coincide with the point
with the base ; because the point

do not coincide with the base enclose a space, which is impossible.

Therefore the base

triangle

coinciding with

may

shall coincide with the

is equal to the angle because

therefore

is equal to

; but the

shall coincide

if the base

would

does coincide with coincides with the whole triangle remaining angles of one triangle coincide with the equal to them, viz., the angle

to the angle

and is equal to it; and the whole and is equal to it; also the remaining angles of the other, and are

Therefore, if two triangles have two sides of the one equal to two sides, &c.

to

RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION III.

From the greater of two given straight lines to cut off a part equal to the less.

and be the two given straight lines, of which

Let

It is required to cut off from

is the greater.

the greater, a part equal to

the less.

RELFE BROTHERS, 6, CHARTERHOUSE BUILDINGS, LONDON, E.C.