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. PROP. III. PROB. From the greater of two given straight lines, to cut off a part equal to the less. 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. 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. A B COR.-Hence every equiangular triangle is also equilateral. |