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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: Together with the Eleventh and Twelfth - Σελίδα 170
των Euclid - 1781 - 520 σελίδες
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 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.,...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 290 σελίδες
...lines AB, BC, a mean proportional DB is found. 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 parallelograms that have one...

Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 246 σελίδες
...angles of the one are equal to the angles of the other, each to each. M. — Draw two triangles having one angle of the one equal to one angle of the other. P. — Let the angle bac be equal to the angle e df. ? M. — If the angle bac be equal to the angle...

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

John Playfair - 1837 - 332 σελίδες
...other, have their sides about the equal angles reciprocally proportional : And pa allelograms which have one angle of the one equal to one angle of the ot/ier, and their sides about the equal angles reciprocally proportional, are equal to one another....

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...

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...

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...

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...




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