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" If two triangles have the three angles of one equal to the three angles of the other, each to each, do you think the two triangles are necessarily alike in every respect ? 5. "
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Strona 12
autor: Daniel Cresswell - 1817 - Liczba stron: 436
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - 1816 - Liczba stron: 294
...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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A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - Liczba stron: 410
...manifest, therefore, that DAB is the triangle which was to be constructed. PROP. XVI. 24. THEOREM. If two right-angled triangles have the three angles...triangle be equal to the hypotenuse of the former. Let ACB and EDF be two right angled ^, AD C EG F DEF, is equal to the hypotenuse AB, of the A ABC....
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A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - Liczba stron: 410
...manifest,. therefore, that DAB is the triangle which was to be constructed. PROP. XVI. 24. THEOREM. If two right-angled triangles have the three angles...side of the one be equal to the perpendicular let fail from the right angle upon the hypotenuse of the other, then shall a side of this latter triangle...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - Liczba stron: 272
...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 ...

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, James Thomson - 1837 - Liczba stron: 390
...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 - 1845 - Liczba stron: 352
...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 - 1870 - Liczba stron: 224
...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, Tomy 1-2

Edinburgh Mathematical Society - 1894
...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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