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" If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. "
The First Six Books: Together with the Eleventh and Twelfth - Page 170
by Euclid - 1781 - 520 pages
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 352 pages
...BA is equal to FE, and the angle ABC to EFG. PROP. XIX. (114.) Theorem. If two spherical triangles have one angle of the one equal to one angle of the other, and have also the two sides about another angle in each severally equal, and if the third angle, in each,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...parallelogram BO. Therefore equal parallelograms, gtc. QED, PROP. XV. TIIEOR. EQU AL triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles which have one angle....
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...and also touch the chord on the same side as the less circle touches it. (XI 1 1.) If two triangles have one angle of the one, equal to one angle of the other, and also another angle of the one, together with another angle of the other, equal to two right angles,...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 446 pages
...DH in BC, and terminated by the given point D, is a rhombus. PROP. XI. 17. THEOREM. If two triangles have one angle of the one, equal to one angle of the other, and also another angle of the one, together with another angle of the other, equal to two right angles,...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...other, have their sides about the equal angles reciprocally proportional : and parallelograms that iiive one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Prop. XV. Theor....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...?ular to the triangle DEF. Wherefore, if two triangles, &c. QE D PROP. VII. THEOR. 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 angles be either less,...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...equiangular to the triangle DEF. Wherefore, if the sides, &c. Q, ED PROP. VI. THEOR. If two triangles have one angle of the one equal to one angle of the oiker, and the sides about the equal angles proportionals, the triangles shall be equiangular, and...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...THEOR. parallelograms, which have ont angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. And parallelograms that have one angle of the ene equal to one angle of the other, and their tides about the equal angles reciprocally proportional,...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...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 angles be either less,...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...вс to FE, therefore the parallelogram AB is equal to PROPOSITION XV. THEOREM. If equal triangles have one angle of the one equal to one angle of the other, the sides about the equal angles are reciprocally proportional; and if triangles have one angle of...
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