| Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...conditions. Wherefore, universally, if two triangles have two sides &c. Which was to be demonstrated. **THEOREM. — If two triangles have two sides of the one, equal to two sides of the** other respectively, but the third side of the one is greater than the third side of the other ; the... | |
| Euclid - 1835 - 540 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... | |
| 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 - 359 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 to the... | |
| Mathematics - 1836 - 472 pages
...shall be less than the other two sides of the triangle, but shall contain a greater angle. XXIV. If two **triangles have two sides of the one equal to two sides of the other, each to each,** but the angle contained by the two sides of the one greater than the angle contained by the two sides... | |
| 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.... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...which the vertex of one triangle is upon a side of the other, needs no demonstration. PROPOSITION VIII. **THEOREM. If two triangles have two sides of the one...sides of the other, each to each, and have likewise** their bases equal, the angle which is contained by the two sides of the one shall be equal to the angle... | |
| Euclid - Geometry - 1837 - 410 pages
...line equal 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...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
...rectilineal angle equal to a given rectilineal angle. Proved by Proposition VIII. PROPOSITION XXIV. **Theorem. If two triangles have two sides of the one equal to two sides of the other, each to each,** but the angle contained by two sides of one of them greater than the angle contained by the two sides... | |
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