 | John Wright (Mathematician) - 1772 - 298 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 - 120 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... | |
 | 1810 - 554 pages
...ever been deduced. If we could demonftrate, independently of all confideration of parallel lines, that the three angles of a triangle are together equal to two right angles, the object in view would be accomplifhed, and the difficulty, in this part of the Elements, would be... | |
 | Charles Butler - 1814 - 582 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 Playfair - 1822 - 552 pages
...ever been deduced. If we could demonstrate, independently of all consideration of parallel lines, that the three angles of a triangle are together equal to two right angles, the object in view would be accomplished, arid the difficulty, in this part of the Elements, would... | |
 | John Playfait - 1822 - 550 pages
...ever been deduced. If we could demonstrate, independently of all consideration of parallel lines, that the three angles of a triangle are together equal to two right angles, the object in view would be accomplished, and the difficulty, in this pait of the Elements, would be... | |
 | 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... | |
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... the three angles of a triangle are together equal to two right angles, although it is not known to all. 
