RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION XXI.

If from the ends of a side of a triangle, there be drawn two straight lines to a point within the riangle; these shall be less than the other two sides of the triangle, but shall contain a greater angle.

, the ends of the side within the triangle.

, let the

the other two sides of the triangle,

but shall contain an angle

greater than the angle

Produce

to meet the side

in

Because two sides of a triangle are greater than the third side, therefore the two sides

; to each of these unequals add

Again, because the exterior angle of a triangle is greater than the interior and opposite

angle; therefore the exterior angle

of the triangle

is greater than the interior of the triangle

; for the same reason the exterior angle
is greater than the interior and opposite angle
is greater than the angle

and opposite angle

strated, that the angle

the angle

greater than the angle

Therefore, if from the ends of the side, &c.

; and it has been demon

; much more therefore is

RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION XX.

Any two sides of a triangle are greater together than the third side.

Let

be a triangle.

Then

any two sides of it together shall be greater than the third side, viz., the sides

and that the greater angle is subtended by the greater side; therefore the side

the angle

is greater than the angle

is greater

than the side

; but

is equal to

and

are greater than

are greater than

; also that

therefore the sides

; in the same manner it may be demonstrated, that the sides

Therefore any two sides, &c.

are greater than

RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION XIX.

The greater angle of every triangle is subtended by the greater side, or, has the greater side opposite to it.