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" ... the three angles of a triangle are together equal to two right angles, although it is not known to all. "
The Works of John Playfair ...: With a Memoir of the Author ... - Page 335
by John Playfair - 1822
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Elements of Trigonometry, Plane and Spherical: With the Principles of ...

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...
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An essay on mechanical geometry, explanatory of a set of models

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...
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Letters of Euler to a German Princess, on Different Subjects in ..., Volume 2

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...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir 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...
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The Edinburgh Review, Volume 15

1810 - 554 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...
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Easy Introduction to Mathematics, Volume 2

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...
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Works, with a memoir of the author, Volume 4

John Playfait - 1822 - 550 pages
...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...
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The Boston Journal of Philosophy and the Arts, Volume 3

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....
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

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...
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The Mechanics' Magazine, Museum, Register, Journal, and Gazette, Volume 15

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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