RELFE BROTHERS' EUCLID SHEETS. PROPOSITIONS 1-26, BOOK I, ARE NOW PUBLISHED IN A SIMILAR FORM TO THIS. PROPOSITION IV. If two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise the angles contained by those sides equal to each other; they shall likewise have their bases or third sides equal, and the two triangles shall be equal, and their other angles shall be equal, each to each, viz., those to which the equal sides are opposite. triangle be equal to the base ; and the triangle to the ; and the other angles to which the equal sides are opposite shall be equal, For, if the triangle be on and the straight line be applied to the triangle on ; then the point is equal to ; and point because shall fall on because the angle shall coincide with the point also the point do not coincide with the base enclose a space, which is impossible. Therefore the base triangle coinciding with may shall coincide with the is equal to the angle because therefore is equal to ; but the shall coincide if the base would does coincide with coincides with the whole triangle remaining angles of one triangle coincide with the equal to them, viz., the angle to the angle and is equal to it; and the whole and is equal to it; also the remaining angles of the other, and are Therefore, if two triangles have two sides of the one equal to two sides, &c. to RELFE BROTHERS' EUCLID SHEETS. PROPOSITIONS 1-26, BOOK I, 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. and be the two given straight lines, of which Let It is required to cut off from is the greater. the greater, a part equal to the less. RELFE BROTHERS, 6, CHARTERHOUSE BUILDINGS, LONDON, E.C. |