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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.

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EUCLID'S ELEMENTS.

BOOK I.

PROPOSITION I. PROBLEM.

On a given finite straight line, to describe an equilateral triangle.

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From a given point, to draw a straight line equal to a given finite straight line.

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PROP. III. PROB.

From the greater of two given straight lines, to cut off a part equal to the less.

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If two triangles have two sides of the one respectively 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.

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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.

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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.

A

B

COR.-Hence every equiangular triangle is also

equilateral.

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