| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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 ... | |
| 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,... | |
| 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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