RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION XI.

To draw a straight line at right angles to a given straight line, from a given point in the same. be the given straight line, and a given point in it.

Let

It is required to draw a straight line from the point

at right angles to

drawn from the point
is common to the two triangles

shall be at right angles to

; the two

base

; therefore the angle

is equal to the angle

each to each; and the base is equal to the and these two angles are adjacent

ingles. But when the two adjacent angles which one straight line makes with another straight line, are equal to one another, each of them is called a right angle: therefore each of the angles

is a right angle.

Wherefore from the given point

in the given straight line

ingles to

has been drawn at right

COR. By help of this problem, it may be demonstrated that two straight lines cannot have a common segment. If it be possible, let the segment

be common to the two straight lines

From the point

draw

at right angles to

; then because

is a straight line, thereis a straight line, therefore is equal to the angle

the less equal to the greater angle, which is

Therefore two straight lines cannot have a common segment.

RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION X.

To bisect a given finite straight line, that is, to divide it into two equal parts.

shall be cut into two equal parts in the point

RELFE BROTHERS' EUCLID SHEETS.

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

PROPOSITION IX.

Let

To bisect a given rectilineal angle, that is, to divide it into two equal angles.

be the given rectilineal angle.