| Robert Simson - Trigonometry - 1835 - 544 pages
...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... | |
| Mathematics - 1835 - 684 pages
...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... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...has just been 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... | |
| Mathematics - 1836 - 488 pages
...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... | |
| John Playfair - Geometry - 1836 - 148 pages
...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... | |
| Education - 1836 - 502 pages
...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.... | |
| Schoolmaster - 1836 - 926 pages
...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.... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...to A 15. the line € might be produced, till it and the part added would be equal to AB. PROP. IV. THEOREM. IF two triangles have two sides of the one equal to two sides of the other, each to each ;t and have also the angles contained by those sides equal to one another : (!..) they have likewise... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...shows that the 2. hat Z BDC < ZBCD \ ition is fa(se 3. that Z BDC also = Z BCD . PROPOSITION VIII. Theorem. 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, the angle contained by the two sides of the one shall be equal... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...from AB the greater of two straight lines, a part AE has been cut off equal to C the less. PROP. 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, their bases, or third... | |
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