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" If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 90
by Dennis M'Curdy - 1846 - 138 pages
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...to the triangle DEF. If, therefore, two triangles have their sides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular,...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...triangles, &c. QED Book IV. a Sup. « 2. 1. b 112. Alg. o 11. Alg. d 2- 4e11 1• PROP. VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, then, if each of the remaining...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROP. VII. THEOR. See N. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then, if each of the remaining...
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Library of Useful Knowledge: Natural philosophy, Volume 3

1834 - 578 pages
...: A b, that is, A c : A 6 : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that if two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 336 pages
...to the triangle DEF. PROP. VI. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be eo/uiangulart and shall have those angles equal which are opposite to the homologous sides. Let the...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...of a greater number of sides have not, necessarily, their sides so related. PROP. 32. (Eue. vi. 6.) If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the two triangles shall be...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...equiangular to the triangle DEF. Wherefore, " if the sides," &c. QED Hook VI. PROP. VI. THEOR. ' ' ' If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. Q,. ED PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...he equiangular, and shall have those angles equal which are opposite to the. homologous sides. VII. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, then, if each of the remaining...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...D. Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals ; the remaining angles are equal,...
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