...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 of that...

...another in each of the points С, Е. Join AC, AE, В С, BE. Then because the triangles AD С, ADE have two sides of the one equal to two sides of the other, and have also the included angles ADC, ADE equal to one another, the base А С (I. 4.) is equal...

...be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE. Therefore, 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 ; their bases shall likewise...

...lines which intersect one another, cannot be both parallel to the same straight line." PROP. 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 one another, their bases, or third...

...found that BO + 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...

...as 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....

...as 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....

...another, and likewise those which are terminated in the other extremity. PROP. VIII. THEOR. IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal : (1.) the angle which is contained by the two sides of the one...

...two straight 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,...

...given straight lines : „ to cut oft' a part equal to \ 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 also the angles contained by those sides equal; the bases or third sides of the triangles...