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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 books of the Elements of Euclid, with numerous exercises - Σελίδα 124
των Euclides - 1853 - 147 σελίδες
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 σελίδες
...triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. — 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 remaining angles are equal, each to each, viz....

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 σελίδες
...equiangular to 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, the triangles shall be equiangular, and shall have...

Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 σελίδες
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — If two triangles have one angle of the one equal to one angle of the oiher, and the sides about the equal angles proportionals, the triangles shall be equiangular, and...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 σελίδες
...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. First,...

Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 σελίδες
...; and therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which have one angle of the one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3....

Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 166 σελίδες
...parallelogram are equal : p. 34ofb. 1. 15 Th. Equal triangles which have an angle of one equal to an angle of the other, have their sides about the equal angles reciprocally proportional : and triangles are equal, which have an angle of one equal to an angle of the other, and the sides about...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 334 σελίδες
...angle of the other, have their sides about the equal angles reciprocally proportional : arallelograms which have one angle of the one equal to one angle of And par the other, and their sides about the equal angles reciprocally proportional, are equal to one...

Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1848 - 394 σελίδες
...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...

The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 σελίδες
...those angles equal which are opposite to the homologous sides. PROP. VII. THEOREM. 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...

General Report on Public Instruction, in the Lower Provinces of the Bengal ...

Bengal (India) - 1848 - 520 σελίδες
...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...




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