| John Taylor - Mathematics - 1707 - 608 pages
...two Square r, then V*t obtufe : If they be equal^ 'tis ri ht ^ // the Square of the faid Side be left **than the Sum of the Squares of the other two Sides, the Angle** is acute. PROP. §3. PROP. II. Two fide f, and an Angle oppojite to one of them in an Oblique-angled... | |
| Edward Riddle - Nautical astronomy - 1824 - 572 pages
...removed, by the consideration that when the square of the side opposite the angle computed is greater **than the sum of the squares of the other two sides, the angle** must be obtuse ; otherwise the angle is acute. As a small arc can be found more correctly by even proportion... | |
| Nathan Scholfield - 1845 - 896 pages
...XXIV. immediately follows, that is, it the square of any side of a triangle be equivalent to the sum of **the squares of the other two sides, the angle opposite the former** shall be right; for these propositions show, that if such equivalence exist, the angle can neither... | |
| Alpheus Crosby - Geometry - 1847 - 190 pages
...aACD ? ni ADC yx BCD? .-. InfDBC, BCawBD? •». But, as AD = AC, BD sw BA + AC ? § 78. THE OR. X- **Any side of a triangle is less than the sum of the** other two. [Proved by the aid of Theor. IX] $79. a.) AsBC<BA + AC, BC — ACswBA? 30.3-. And BC —... | |
| Elias Loomis - Conic sections - 1860 - 246 pages
...each, and the angle A to the angle D. Therefoxe, if two triangles, &c. PROPOSITION VIII. THEOREM. v **Any side of a triangle is less than the sum of the** other-two Let ABC be a triangle; any one of its aides is less than the sum of the other two, viz.:... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 pages
...BOOK I. 61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. **Any side of a triangle is less than the sum of the** other two. In the triangle ABC, any one side, C as AB,is less than the sum of the other two sides,... | |
| Benjamin Greenleaf - Geometry - 1861 - 628 pages
...ABC is 61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. **Any side of a triangle is less than the sum of the** other two. In the triangle ABC, any one side, as AB, is less than the sum of the other two sides, AC... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...isosceles. 61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. **Any side of a triangle is less than the sum of the** other two. In the triangle ABC, any one side, as AB,is less than the sum of the other two sides, AC... | |
| Benjamin Greenleaf - Geometry - 1868 - 338 pages
...isosceles. 61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. **Any side of a triangle is less than the sum of the** other two. In the triangle ABC, any one side, as AB, is less than the sum of the other two sides, AC... | |
| Henry William Watson - Geometry - 1871 - 320 pages
...together less than the two sides BA and AC. Produce BD to meet the side AC in the point E. Because **any side of a triangle is less than the sum of the** two remaining sides, n therefore BE is less than BA+AE; add EC to each, therefore BE + EC is less than... | |
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