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... angles equal; and conversely if two angles of a triangle are equal, two of the sides are equal. 3. If two triangles have the three sides of one equal to the three sides of the other, each to each, do you think the two triangles are alike in every...
A Supplement to the Elements of Euclid - Page 2
by Daniel Cresswell - 1819 - 410 pages
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...proposition, of the first Book of Euclid's Elements. (Art. 99.) PROP. XI. (99.) Theorem. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each, the three sides of the one shall, also, be equal to the three sides of the other, each to each, to...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...the other, that which has the greater surface shall have the greater perimeter. PROP. XXVI. (xiv.) If two right-angled triangles have the three angles...triangle be equal to the hypotenuse of the former. (XV.) If the sides of any given equilateral and equiangular figure of more than four sides, be produced...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...C, the angle В А С is likewise equal to the ande EDF. Therefore, &c. PROP. 16. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the othrr, each to...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...А' С, the angle BAG is likewise equal to the angle ED F. Therefore, &c. PROP. 1C. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the other, each to...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...triangles, &c. PROP. XXVI. THEOR. IF two angles of one triangle be equal to two angles of another, each to each, and if a side of the one be equal to a side of the other similarly situated in respect to those angles ; then (1.) the remaining sides are...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...triangles, &c. PROP. XXVI. THEOR. — If two angles of one triangle be equal to two angles of another, each to each, and if a side of the one be equal to a side of the other similarly situated with respect to those angles; (1) the remaining sides are equal,...
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Elementary Trigonometry

James Hamblin Smith - Trigonometry - 1870 - 224 pages
...given, we cannot determine the sides, because an infinite number of triangles may be constructed with the three angles of the one equal to the three angles of the other, each to each. 173. "We shall denote the angles of a triangle by the letters A, Б, C ; the sides respectively opposite...
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Papers for teachers

1880
...in K. Then AH, HD are parallelograms. Now in the triangles AFB, DFC, the three angles of the one are equal to the three angles of the other, each to each, and the side AB to DC ; therefore BF is equal to FD and AF to FC (I. 26). Then in the two triangles FBH,...
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Proceedings of the Edinburgh Mathematical Society, Volumes 1-2

...of the ordinary " ambiguous case " of Plane Geometry. § 7. The polar theorem of Euclid I. 8. If two triangles have the three angles of the one equal to the three angles of the other, the triangles are either congruent or symmetric. The polar theorems of Euclid I. 24 and I. 25. § 8....
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Elements of Geometry

George Cunningham Edwards - Geometry - 1895 - 332 pages
...BC is not parallel to DE is an erroneous one. 64. THEOREM. If two triangles have the three angles of one equal to the three angles of the other, each to each, the ratio of any two sides of one will equal the ratio of the corresponding * sides of the other. Fio....
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