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Books Books 51 - 60 of 61 on In any triangle, the sum of the three angles is equal to two right angles, or 180..  
" In any triangle, the sum of the three angles is equal to two right angles, or 180. "
Introduction and books 1,2 - Page 218
by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908
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The Monist, Volume 13

Philosophy - 1903
...further develop Lobatchevsky's idea. Among other things, he proves that "if in any rectilinear triangle the- sum of the three angles is equal to two right angles, so is this also the case for every other triangle," that is to say, each instance is a sample of the...
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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 339 pages
...lines everywhere equidistant from one another." One of Legendre's alternatives is, " There exists a triangle in which the sum of the three angles is equal to two right angles." One of the latest attempts to suggest a substitute is that of the Italian Ingrami (1904), " Two parallel...
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Coal Miners' Pocketbook: Formerly The Coal and Metal Miners' Pocketbook ...

Thomas J. Foster - Coal mines and mining - 1916 - 1172 pages
...side. 9. In an isosceles triangle, the angles opposite the equal sides are equal. 10. In any triangle, the sum of the three angles is equal to two right angles, or 180. 11. If two angles of a triangle are given, the third may be found by subtracting their sum...
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Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - Mathematics - 1954 - 389 pages
...Therefore (S ^l is the si2e of the quadrilateral ABCD and at the same time also that of the spherical triangle in which the sum of the three angles is equal to S. 28 THEOBY OF PABALLELS. 28. If three planes cut each other in parallel iines, then the gum of the...
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Geometry and the Visual Arts

Daniel Pedoe - Mathematics - 1976 - 296 pages
...one of two parallels, it will intersect the other also (Proclus, fifth century AD); There exists a triangle in which the sum of the three angles is equal to two right angles (Legendre, 1752-1833); Given any three points not in a straight line, there exists a circle passing...
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Writings of Charles S. Peirce: 1857-1866

Charles Sanders Peirce - Mathematics - 1982 - 736 pages
...Review. The author says: We draw or conceive a particular triangle for the sake of demonstrating that the sum of the three angles is equal to two right angles; having gone through a series of successive intuitions, we arrive at last at the demonstrated truth...
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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - Mathematics - 1999 - 275 pages
...angles in triangle ABC is not greater than two right angles. PROPOSITION XX. THEOREM. In any triangle, the sum of the three angles is equal to two right angles. Having already proved that the sum of the three angles of a triangle cannot exceed two right angles,...
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Geometry: Our Cultural Heritage

Audun Holme - Mathematics - 2002 - 378 pages
This book contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in ...
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The Thirteen Books of Euclib's Elements.

Euclid - Geometry - 1925
...Parallels remain, throughout their length, at a finite distance from one another. (3) There exists a triangle in which the sum of the three angles is equal to two right angles (Legendre). (4) Given any figure, there exists a figure similar to it of any size we please (Wallis,...
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Journal of the Elisha Mitchell Scientific Society, Volume 23

Natural history - 1907
...theorems: 1 . In a triangle, the sum of the three angles can never be greater than two right angles. 2. If the sum of the three angles is equal to two right angles in one triangle, it is equal to two right angles in every triangle. But Euclid's geometry can be built...
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