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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 ... - Side 143
av Euclid, James Thomson - 1837 - 390 sider
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 sider
...oiher, 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. Let AB, BC...
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## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 sider
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &e. QED D PROP. VI. THEOR. IP two triangles have one angle of the one equal to one...of the other, and the sides about the equal angles Eroportionals, the triangles shall be equiangular, and shall ave those angles equal which are opposite...
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## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...parallelogram BC. Therefore equal ograms, Лес. Q. E, D. PROP. XV. THEOR. Equal triangles nhich have have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles nhich have one angle...
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## Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 sider
...the parallelogram ac.d Therefore if equal parallelograms, &C. QED PROPOSITION XV. THEOREM. If equal triangles have one angle of the one equal to one angle of the other, the sides about the equal angles are reciprocally proportional ; and if triangles have one angle of...
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## Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...to FE so is вс to FE, therefore the parallelogram AB is equal to PROPOSITION XV. THEOREM. If equal triangles have one angle of the one equal to one angle of the other, the sides about the equal angles are reciprocally proportional; and if triangles have one angle of...
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## Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which have one angle of the one equal to- one angle of the other, and their sides about the equal angles reciprocally proportional, are equivalent. Let the triangles be...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 sider
...a mean proportional DB is found. Whieh was to be done. PROP. XIV. THEOR. Equal parallelograms whieh have one angle of the one equal to one angle of the pther, have their sides about the equal angles reeiproeally proportional : And parallelograms whieh...
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## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...parallelogram BC. Therefore equal pa- * 9' 5rallelograms, &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 triangles whichhave one angle...
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## Natural Philosophy: With an Explanation of Scientific Terms, and an ..., Volum 3

1829
...: A b, that is, A c : Ab : : 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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## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 sider
...Wherefore, if the sides &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of one triangle equal to one angle of the other, and the sides about the equal angles proportional, the triangles will he equiangular, and will have those angles equal which are opposite...
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