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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: The Errors by which Theon, Or Others, Have Long ... - Page 141
by Robert Simson - 1827 - 513 pages
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - Geometry - 1837 - 215 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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...mean proportional DB is found. Which was to be done. PROP. XIV. THEOR. Equal parallelograms, which have one angle of the one equal to one angle of the other, ham 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
...another. 2. 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...equal which are opposite to the homologous sides. 4. Show that straight lines, which are perpendicular to parallel straight lines, are themselves also...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...shall have those angles equal which are opposite to the homologous sides, 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 proportional; then, if the remaining angles be each either less or not less than a...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...the one, equal to one angle (DFE) of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and shall have...equal which are opposite to the homologous sides. From the extremities of EF, one of the sides of the triangle DEF, about the angle DFE, draw EG and...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...the parallelogram BC. Therefore equal parallelograms, &c. 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 triangle* 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 - 317 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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...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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General Report on Public Instruction in the Bengal Presidency

Education - 1843
...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
...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...proportionals, the triangles shall be equiangular. MECHANICS AND HYDROSTATICS. MONDAY, JANUARY 15. 9.. .12. MR. HATHIBON, TRINITY COLLEGE. Pint Division...
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