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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 Elements of Euclid: In which the Propositions are Demonstrated in a New ... - Σελίδα 80
των Euclid - 1776 - 264 σελίδες
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 σελίδες
...mean proportional DB is found. Which was to be done. PROP. XIV. THEOR. Equal parallelograms, which have one angle of the one equal to one angle of the other, ham their sides about the equal angles reciprocally proportional : and parallelograms that have one...

Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1853 - 1218 σελίδες
...2. About a given circle, to describe a 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...

The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 σελίδες
...have those angles equal which are opposite to the homologous sides, PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportional; then, if the remaining angles be each either less or not...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 σελίδες
...the parallelogram BC. Therefore equal parallelograms, &c. QED PROP. XV. THEOR. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional: and triangle* which have one angle...

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

John Playfair - 1842 - 332 σελίδες
...straight linos AB, BC, a mean proportional DB is found. PROP. XIV. PROB. • 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 parallelograms which have one...

Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 σελίδες
...parallelogram в c. Therefore equivalent parallelograms, &c. QED PROP. XV. THEOR. EQUIVALENT triangles, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and triangles which have one angle...

General Report on Public Instruction in the Bengal Presidency

1843 - 582 σελίδες
...angle, and one of the other sides of a triangle are given ; construct it. 4. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional: and triangles which have one angle...

The British Annals of Education for ...: Being The Scholastic ..., Τόμοι 1-2

1844 - 688 σελίδες
...with the touching line, shall be equal to the angles in the alternate segments. 12. 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. MECHANICS AND HYDROSTATICS....

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. those...

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

Euclides - 1845 - 546 σελίδες
...AB, BC, a mean proportional -DB is found. QEF ^ PROPOSITION 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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