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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. "
Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund Stone - Page 31
by Euclid - 1728
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...triangle DEF. Wherefore if two triangles, &c. Q^ ED b. 32. i. c. 4. 6. f' *• i. PROP. VII. THEOR. IF two triangles have one angle of the one equal to one angle of the other, and the fides about two o. ther 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 Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QE D, 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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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...shall be equiangular, and have their equal angles opposite to the homologous sides. Prop. VI. Theor. If two triangles have one angle of the one equal to one angle of the other, and tbe sides about the equal angles proportionals, the triangles shall be equiangular,...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...a •••• b : ai=the square of the product, wherefore ^/afc=the product. 234. Prop. 23. Hence, if two triangles have one angle of the one equal to one angle of the other, they will have to each other the ratio compounded of the ratios of the sides about...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, Ike. QED 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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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...two given circles, 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...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...having its base 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...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...triangle ABC is 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,...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 272 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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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 228 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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