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. |