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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 of Geometry: From the Latin Translation of Commandine. To ... - Page 161
by John Keill - 1733 - 397 pages
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - Electronic book - 1795 - 400 pages
...triangle DEF. Wherefore, if two triangles, &c. Q^ E. D f PROF. PROP. VII. THEO R. IF two triangles have one angle of the one equal to one angle of the other, and the fides about two other angles proportionals, then, if each of the remaining angles be either...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 351 pages
...other, have their fides about the equal angles reciprocally proportional : And parallelograms that have one angle of the one equal to one angle of the other, and their fides about the equal angles reciprocally proportional, are equal to one another. Let AB,...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...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 angles be either...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...Therefore, equal parallelograms, &c. Q. E« D. • Book VI. PROP. XV. THEOR. EQUAL 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 in the one equal to one angle in the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...DB is found. Which was to be done. PROP. XIV. THEOR. EQUAL parallelograms, which have one angle of one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms which have one angle of one equal to one angle of the...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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, and shall have...
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814
...a6=the square of the product, wherefore ^ai^zthe 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 their equal angles;...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...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, and shall have...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...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...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...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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