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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. "
Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...
von John Mason Good - 1819
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...proportional between two given straight lines. PROP. 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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Papers for the Schoolmaster

1852
...About a given circle, to describe i 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...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 173 Seiten
...shall have to the second a greater ratio than the fifth has to the sixth. 8. Equal triangles which have one angle of the one equal to one angle of the other have the sides about the equal angles reciprocally proportional ; and conversely. 9. If two planes...
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Papers for the Schoolmaster

1851
...the whole triangle and to one another. PAPERS FOE THE SCHOOLHASTEB. 2. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. .3. Equiangular paralellograms...
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The Bible Question Decided in a Correspondence

Rev. William R. Williams - 1852
...A b : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that 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 are equiangular, and consequently similar...
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The English Journal of Education, Band 6

1852
...each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular paralellograras...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...parallelogram BC. Therefore, equal parallelograms, etc. QED PROPOSITION XV. THEOR. Equal triangles which have one angle of the one equal to one angle of the other, have their sidis about the equal angles reciprocally proportional; and triangles which have one angle...
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Public Education: As Affected by the Minutes of the Committee of Privy ...

Sir James Kay-Shuttleworth - 1853 - 500 Seiten
...each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New ..., Bücher 1

Euclides - 1853
...the three angles DEF, EFD, FDE. "Which -was to be proved. PEOP. VI. THEOE. If two triangles have (1) one angle of the one equal to one angle of the other ; (2) the sides about this pair of angles proportional : then these two triangles shall be similar,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 Seiten
...Therefore equal parallelograms, &c. QED PROPOSITION XV. — THEOREM. Eqii.al triangles, which have one angle of the one equal to one angle of the other, have tlieir sides about tlie equal angles reciprocally proportional ; and triangles which have one...
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