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" 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 which are opposite to the homologous sides. "
Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ... - Page 161
by John Keill - 1733 - 397 pages
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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 have to one another the...
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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 which...
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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...
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The English Journal of Education, Volume 6

Education - 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 have to one another the...
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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...
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Public Education: As Affected by the Minutes of the Committee of Privy ...

Sir James Kay-Shuttleworth - Church and education - 1853 - 500 pages
...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 hare to one another the...
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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
...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 - Geometry - 1853 - 147 pages
...the triangle def Wherefore, if the sides, &c. QED PROPOSITION VI. — THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, tJie triangles shall be equiangular, and shall...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...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. Let AB,...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 318 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 sfdes about the equal angles reciprocally proportional; And triangles which have one angle in the one...
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