| John Wright (Mathematician) - 1772 - 302 pages
...ninety degrees. The ambiguity is avoided, if the fum of the other two angles be known ; becaufe [32. IJ **the three angles of a triangle are together equal to two right angles.** PROP. V. THEOR. Fig. 14. 5. The fum of any fwofides, BA.and AC, of any triangle ABC, is to the difference... | |
| Benjamin Donne - 1796 - 118 pages
...perpendicular to another. A THEOREM, a fpeculative propof1tion, the truth of which may be demonftrated ; as **the three angles of a triangle are together equal to two right angles,** or 1 80 degrees. 46. A DEMONSTRAT1ON is the proof of the truth of any aflertion. 47. Though it be our... | |
| Leonhard Euler - 1802 - 696 pages
...impoffible to draw any concluiion, with refpect to real objects : thus, when I have demonftrated that **the three angles of a triangle are together equal to two right angles,** this is a property belonging only to an abilract triangle, and not at all to one really exifting. But... | |
| John Leslie - 1809 - 542 pages
...An exterior angle of a triangle is equal to both its opposite interior angles, and all the interior **angles of a triangle are together equal to two right angles. The** exterior angle BCD, formed by the production of the side AC of the triangle ABC, is equal to the two... | |
| 1810 - 556 pages
...confequence, till now, has ever been deduced. If we could demonftrate, independently of all confideration **of parallel lines, that the three angles of a triangle...equal to two right angles, the object in view would be** accomplifhed, and the difficulty, in this part of the Elements, would be entirely overcome. Now, the... | |
| Charles Butler - 1814 - 568 pages
...draw DF parallel to CE, and ECDF will be the rectangle contained by A and B, as was required ". « **The three angles of a triangle are together equal to two right angles** (Enclid 38. 1.) that is, to 180°; wherefore if the sum of two angles of a triangle be subtracted from... | |
| John Playfait - 1822
...fundamental truths of the science of geometry. Among those analytical methods of demonstration, to which **an allusion is made above, we were long since particularly...would be accomplished, and the difficulty, in this** pait of the Elements, would be enVOL. rv. Y tirely overcome. Now, the theorem just mentioned would... | |
| 1826 - 628 pages
...line, are true for the perpendicular. The Problem for drawing parallel lines may follow here. Theorem. **The three angles of a triangle are together equal to two right angles.** For a demonstration, see any treatise on geometry. Theorem. Lacroix, No. 54. The parts AC and BD, (fig.... | |
| Pierce Morton - 1830 - 584 pages
...notwithstanding, of opinion, that the grand truth with which it is so intimately connected, viz., that " **the three angles of a triangle are together equal to two right angles,"** may be referred to the general principle of liomogeneity. Of this it is unnecessary to suy more in... | |
| 1831 - 532 pages
...has been before proved that the angle ADe is an acute angle of 90 degrees, whence it follows that as **the three angles of a triangle are together equal to two right angles, the** remaining angle fh D must likewise be an acute angle of 90 degrees, and, as before, since the two augles/DA... | |
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