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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. "
Elements of Plane Geometry According to Euclid - Page 129
by Andrew Bell - 1837 - 240 pages
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 pages
...isosceles triangle having each of the angles at the base one-third of the third angle. 2. 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...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...2. & H. 6 22, V. 7 6, VI. 8 Sim. 9 Cone. 10 H. 11 22, V. 16, V. PROP. 7. — 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...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861
...the other, have their sides about the equal angles reciprocally proportional, and parallelograms that 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. 9. Prove...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861
...angle. 4. To describe an equilateral and equiangular hexagon in a given circle. 5. If two triangles have one angle of the one equal to one angle of the other and the sides about two other angles proportionals, and if each of the remaining angles be not less...
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Liber Cantabrigiensis: An Account of the Aids Afforded to Poor ..., Volume 2

Robert Potts - 1863
...sides produced. Also describe a circle touching three sides of a parallelogram. 6. 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, triangle shall be equiangular, and shall have...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864
...is obtuse-angled, prove that the centre of the circumscribing circle is outside of the triangle. 11. 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. 12. Let...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...8. Cor.) therefore between the two given straight lines AB, BC, a mean proportional DB is found. QEF PROPOSITION XIV. THEOREM. Equal parallelograms, which have one angle of the one equal to one avgle of the other, have their sides about Che equal angles reciprocally proportional: and conversely,...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1883
...angles at B reciprocally proportional, the order of the proportion being DB is to BE as GB is to BF. PROPOSITION XIV. THEOREM. Equal parallelograms, which...about the equal angles reciprocally proportional. Let AB, BC be equal Oa, having L FBD= L EBG. Then must DB be to BE as GB is to BF. Place the /Us so...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...equal to one angle of the other, 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,...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...similar, and those angles which are opposite to the homologous sides are equal. THEOR. 5. If two triangles have one angle of the one equal to one angle of the other, and the sides about one other angle in each proportional, so that the sides opposite the equal angles...
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