RELFE BROTHERS' EUCLID SHEETS.

PROPOSITIONS 1–26, BOOK 1, 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.

is the greater.

Let and be the two given straight lines, of which
It is required to cut off from the greater, a part equal to

the less.

From the point

draw the straight line

at the

equal to

;

and from the center cutting in the point Then

distance

describe the circle

shall

off, equal to

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

PROPOSITION I.

To describe an equilateral triangle upon a given finite straight line.
Let be the given straight line.
It is required to describe an equilateral triangle upon

From the center

at the distance

describe the circle

;

from the center

; and

at the distance describe the circle

;

and from one of the points in which the circles cut one another, draw the straight lines

to the points

Then shall be an equilateral triangle. Because the point is the center of the circle

therefore is equal to because the point is the center of the circle

therefore is equal to it has been proved that is equal to

; therefore

are each of them equal to ; but things which are equal to the same thing are equal to one another; therefore is equal to ; wherefore

are equal to one another : and the triangle is therefore equilateral, and it is described upon the given straight line

; but

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