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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 First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 143
by Euclid, James Thomson - 1837 - 390 pages
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1848
...definition will satisfy one of the tests of the former. 2. Give a proof of the following proposition : " 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 less, or not less...
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General Report on Public Instruction, in the Lower Provinces of the Bengal ...

Bengal (India) - 1848
...definition will satisfy one of the tests of the former. 2. Give a proof of the following proposition : " 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 less, or not less...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...mean 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
...to one another. 2. 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...the sides about the equal angles proportionals the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous...
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Papers for the Schoolmaster

1851
...similar to 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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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 173 pages
...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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The Bible Question Decided in a Correspondence

Rev. William R. Williams - 1852
...: A b,. that is, A c : 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...the sides about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we have seen that the two triangles A bc, A!'...
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The English Journal of Education, Volume 6

Education - 1852
...triangles on 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 Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853
...hence AB is to BC as DE to EF, and BC to CA as EF to FD. . Which was to be proved. PEOP. VII. THEOE. If two triangles have (!•) one angle of the one equal to one angle of the other ; (2) the sides about one of the other two pairs of angles proportionals ; and if each of the third...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...equiangular to the triangle def Wherefore, if two triangles, &c. QED PROPOSITION VII. — THEOREM. If two triangles have one angle of the one equal to one angle of tJie other, and the sides about two other angles proportionals, then if each of tlie remaining angles...
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