RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION XVI.

If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite

is equal to the angle

each to each, in the triangles

, because they are opposite vertical angles; therefore the base

remaining angles of one triangle to the remaining angles of the other, each to each, to

which the equal sides are opposite; wherefore the angle

; but the angle

is greater than the angle

is equal to the angle ; therefore the angle

is greater than the angle

In the same manner, if the side may be demonstrated that the angle angle

Therefore, if one side of a triangle, &c.

be bisected, and

be produced to

that is, the angle

; it is greater than the

RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION XV.

If two straight lines cut one another, the vertical, or opposite angles shall be equal.

; these angles are together equal to two right angles.

Because the straight line

Again, because the straight line

angles

angle

makes with

; these angles also are equal to two right angles; but the angles have been shewn to be equal to two right angles; wherefore the angles are equal to the angles ; take away from each the common

and the remaining angle is equal to the remaining angle the same manner it may be demonstrated, that the angle

Therefore, if two straight lines cut one another, &c.

In

is equal to the angle

RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION XIV.

If at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles; then these two straight lines shall be in one and the same straight line.

At the point opposite sides of

in the straight line let the two straight lines
make the adjacent angles

upon the

together equal to two

; therefore the adjacent angles are equal to

are equal to two right angles; but the angles two right angles; therefore the angles

angle

; take away from these equals the common angle
is equal to the remaining angle

which is impossible: therefore

are equal to the angles

therefore the remaining

; the less angle equal to the greater,

is not in the same straight line with

And in the same manner it may be demonstrated, that no other can be in the same straight line with it but which therefore is in the same straight line with

Wherefore, if at a point, &c.