THE

FIGURES OF EUCLID

WITH THE ENUNCIATIONS,

AS PRINTED IN

EUCLID'S ELEMENTS

OF

PLANE GEOMETRY,

By W. D. COOLEY, A.B.

LONDON:

WHITTAKER AND CO., AVE MARIA LANE.

PRINTED BY J. HOLMES, TOOK'S COURT, CHANCERY LANE.

1840.

127

EUCLID'S ELEMENTS.

BOOK I.

PROPOSITION I. PROBLEM.

On a given finite straight line, to describe an

equilateral triangle.

From a given point, to draw a straight line equal

to a given finite straight line.

H

D

с

B

B

PROP. III. PROB.

From the greater of two given straight lines, to

cut off a part equal to the less.

B

PROP. IV. THEOREM.

If two triangles have two sides of the one re

spectively equal to two sides of the other, and the angles contained by those equal sides also equal; then their bases or third sides are also equal: and their remaining angles opposite to equal sides are respectively equal: and the triangles are equal in every respect.

AA

PROP. V. THEOR.

In an isosceles triangle the internal angles at

the base are equal; and when the equal sides are produced, the external angles at the base are also equal.

COROLLARY.-Hence it follows that every equilateral triangle is also equiangular.

PROP. VI. THEOR.

In any triangle if two angles are equal, the sides

opposite to them are also equal.