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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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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 σελίδες
...DAE of 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...

Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 σελίδες
...angle of the other, the sides about the equal angles are reciprocally proportional ; and if triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, these triangles are equal. BAC equal...

Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 σελίδες
...angle of the other, the sides about the equal angles are reciprocally proportional; and if triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, these triangles are equal. And because...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 σελίδες
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROP. VI. THEOR. If tix>o 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...

Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 210 σελίδες
...triangles will be equiangular. Equal parallelograms, and also equal triangles, which have one angle of one equal to one angle of the other, have their sides...angles reciprocally proportional ; and parallelograms, and also • triangles, which have one angle of one equal to one angle of the other, and their sides...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 σελίδες
...reciprocally proportional. Cor. 3. (Eue. vi. 14.) And, in the same manner, it may be shown, that any two 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 ; and conversely....

A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - 1831 - 282 σελίδες
...a given triangle. 12. Ratios that are the same to the same ratio, are the same to one another. 13. Equal parallelograms, which have one angle of the...about the equal angles reciprocally proportional. M. In a plane triangle, of which the sides are a, b, c, and opposite angles A, B, C, prove that sin.A...

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

John Playfair - 1832 - 358 σελίδες
...5.) to the parallelogram BC. Therefore equal parallelograms, &c. QED PROP. XV. THEOR. Equal triangles which have one angle of the one equal to one angle...about the equal angles reciprocally proportional: Jind triangles which have one angle in the one equal to one angle in the other, and their sides about...

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

John Playfair - 1833 - 346 σελίδες
...to the parallelogram BC. Therefore equal parallelograms, &c. QED PROP. XV. THEOR. * Equal triangles which have one angle of the one equal to one angle...have their sides about the equal angles reciprocally proportiontil : And triangles which have one angle in the one equal to one angle in the other, and...

Library of Useful Knowledge: Natural philosophy, Τόμος 3

1834 - 578 σελίδες
...A c : A 6 : : 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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