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" 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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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - 1878
...For the same reason, AB -\- BO AC : hence AB > AC— BC (Ax. 5). AB xvn. Theorem. In any triangle, the sum of the three angles is equal to two right angles. HYPOTH. Let ABC be any triangle. To BE PROVED. ZA -f- B + ACB = 2R. PROOF. Through the vertex of either...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable, Adrien Marie Legendre - 1881
...that the angle FEG is the supplement of the angle BAC. PROPOSITION XXIX. THEOREM. In every triangle the sum of the three angles is equal to two right angles. Let ABC be any triangle. Produce the side CA towards D ; and at the point A draw AE, parallel to BC....
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Selected Propositions in Geometrical Constructions and Applications of ...

Adrien Marie Legendre - Geometry - 1882 - 176 pages
...The sum of two angles of a triangle is $ of a right angle ; what is the other angle equal to ? Since the sum of the three angles is equal to two right angles (P. XXV), the other angle must be equal to f of a right angle. 5. — One of the acute angles of a...
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THE JOURNAL OF SPECULATIVE PHILOSOPHY

WILLIAM T HARRIS - 1884
...If expressed, however, it would be something like this : " We have now shown that in this triangle the sum of the three angles is equal to two right angles ; but that is nothing peculiar or characteristic of the triangle before us, and it is therefore true...
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The Journal of Speculative Philosophy: Ed. by Wm. T. Harris ..., Volume 18

William Torrey Harris - Philosophy - 1884
...It' expressed, however, it would be something like this : " We have now shown that in this triangle the sum of the three angles is equal to two right angles ; but that is nothing peculiar or characteristic of the triangle before us, and it is therefore true...
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The American practical navigator: being an epitome of navigation and ...

Nathaniel Bowditch, Philip Henry Cooper, United States. Navy Dept. Bureau of Navigation - Nautical astronomy - 1888 - 647 pages
...therefore the lines AB, CD, cannot meet, and must be parallel. IX. In any right-lined triangle, ABC, the sum of the three angles is equal to two right angles. To prove this, produce BC (in the fig. Theorem VII) toward D; then (by VII) the external angle ACD...
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Geometrical Researches on the Theory of Parallels

Nikolaĭ Ivanovich Lobachevskiĭ - Geometry, Non-Euclidean - 1891 - 50 pages
...Therefore |-(S— -) is the size 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. If three planes cut each other in parallel lines, then the sum of the three surface angles equals...
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The Colliery engineer pocket-book of principles rules, formulæ, and tables ...

Thomas J. Foster - Coal mines and mining - 1891 - 415 pages
...side. 7. In an isosceles triangle the angles opposite the equal sides are equal. 8. In any triangle the sum of the three angles is equal to two right angles, or 180°. 9. If two angles of a triangle are given, the third may be found by subtracting their sum...
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Coal and metal miners' pocketbook of principles, rules, formulas, and tables ...

International Correspondence Schools - History - 1900 - 637 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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An Elementary Course of Instruction for Mine Foremen and Pit Bosses

Floyd Davis - Mining engineering - 1900 - 124 pages
...hypothenuse, while the other two sides are called the base and perpendicular. In any plane triangle the sum of the three angles is equal to two right angles. Q. 63. What are some of the plane geometrical figures bounded by four lines? A. A quadrilateral is...
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