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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. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 172
by Euclides - 1838
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...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., those which are...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...Therefore the triangle ABC is equiangular to the triangle DEF. 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 those angles equal...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 246 pages
...angles of the one are equal to the angles of the other, each to each. M. — Draw two triangles having one angle of the one equal to one angle of the other. P. — Let the angle bac be equal to the angle e df. ? M. — If the angle bac be equal to the angle...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...AB, BC, a mean proportional DB is found. 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 parallelograms that have one...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1853 - 1218 pages
...About a given circle, to describe a triangle equiangular to a given triangle. 3. 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...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...equiangular, and have their equal angles opposite to homologous sides. 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 proportional, the triangles shall be equiangular, and shall have those angles equal...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...proportional DB 6 ' is found. Which was to he done. PROP. XIV. TIIEOR. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sidei about the equal angles reciprocally proportional: and parallelograms that have one...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...parallelogram AB is equal (9. 5.) to the parallelogram BC. 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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...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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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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