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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. "
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Page 81
by Daniel Cresswell - 1817 - 436 pages
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...parallelogram в c. Therefore equivalent parallelograms, &c. QED PROP. XV. THEOR. EQUIVALENT 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...straight linos AB, BC, a mean proportional DB is found. PROP. XIV. PROB. • Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And parallelograms which have one...
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General Report on Public Instruction in the Bengal Presidency

Education - 1843 - 582 pages
...angle, and one of the other sides of a triangle are given ; construct it. 4. 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...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...this line makes with the touching line, shall be equal to the angles in the alternate segments. 12. 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. MECHANICS AND HYDROSTATICS....
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...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, each to each, viz....
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — If two triangles have one angle of the one equal to one angle of the oiher, and the sides about the equal angles proportionals, the triangles shall be equiangular, and...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...AB, BC, a mean proportional -DB is found. QEF ^ PROPOSITION XIV. THEOREM. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and conversely, parallelograms...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...halves of parallelograms, upon the same base, and having the same altitude, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about these angles reciprocally proportional ; and if two triangles have one angle of...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...parallelogram BC. Wherefore, Equal parallelograms *rc. QED 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...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which have one angle of the one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3....
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