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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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 149
by Euclides - 1816 - 528 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...Wherefore, if two triangles, &c. QED PROP. VII. THEOR. Book vi. IF two triangles have one angle of one equal to one angle of the other, and the sides about two other angles proportional ; and if each of the remaining angles be either less, or not less, than...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...a mean proportional between two given straight lines. Prop. XIV. Theor. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proport ional : and parallelograms that have one...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...the triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED 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, or not less,...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814
...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 their equal angles;...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...(Art. 97.) 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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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 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
...the trijiigles shall be equiangular, and have their Cjuil 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, arid 'be tides about the equal angles proportionals, the »angles shall be equiangular, and shall have...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...D. Therefore the 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, and...
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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 to two right angles,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...oiher, have their sides about the equal angles reciprocally proportional : And parallelograms which have 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. Let AB, BC...
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