...angles respectively, from the equality of certain of their parts. He never notices the case of two triangles having two sides of the one equal to two sides of the other respectively, and an angle opposite to equal sides equal in both. This is probably, first, because...

...triangles, which you have learned in this section ? Am. 1. If, in two triangles, two sides of the one are equal to two sides of the other, each to each, and the angles which are included by them are also equal to one another, the two triangles are equal in all...

...greater than DE, it shall subtend a greater angle at С : for С А В and С DE are, in this case, two triangles having two sides of the one equal to two sides of the other, each to each, but the base AB greater than the base DE: therefore the angle А С В (I. 11.) is likewise greater...

...greater than EF. Therefore, " if two triangles," &c. QED PROP. XXV. THEOR. If two triangles have tiro sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other ; the angle also contained by the sides...

...OC< BD + DC ; therefore, still more is BO + OC<BA+AC. PROPOSITION IX. THEOREM. If two triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the third sides will be unequal; and the greater side will belong to the triangle which has...

...meet in one point, are together equal to four right angles. PROP. IV. THEOR. 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 one another, they shall likewise have their...

...possible, and also of many superfluous phrases. For instance, " if there be two triangles which have two sides of the one equal to two sides of the other, each to each, &c." The phrase in italics is not an English idiom, but the literal translation of the Greek '.y.xrepa....

...possible, and also of many superfluous phrases. For instance, " if there be two triangles which have two sides of the one equal to two sides of the other, each to each, &c." The phrase in italics is not an English idiom, but the literal translation of the Greek twrepa....

...which has the greater angle shall be greater than the base of the other. XXV. If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other ; the angle contained by the sides of that...

...lines, a part AE has been cut off equal to C, the less. PROPOSITION IV. THEOREM. 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 one another, thenbases, or third sides,...