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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; viz. the first six books, together with the eleventh ... - Side 153
av Euclides - 1814
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 sider
...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 Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 326 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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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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 sider
...angles reciprocally proportional, are equal to one another; and, conversely, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional . 66 (j) Two triangles are similar,...
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A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - 1831
...Ratios that are the same to the same ratio, are the same to one another. 13. 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. M. In a plane triangle, of which...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 sider
...the triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of tJie other, and the sides about two other angles proportionals, then, if each of the remaining angles...
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Library of Useful Knowledge: Natural philosophy, Volum 3

1834 - 574 sider
...: A b, that is, 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...about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we have seen that the two triangles A bc, A" F'E" are so...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 sider
...and the angle at A to the angle at D. Therefore the triangle ABC is equiangular to the triangle DEF. PROP. VI. THEOR. If two triangles have one angle of...equal angles proportionals, the triangles shall be eo/uiangulart and shall have those angles equal which are opposite to the homologous sides. Let the...
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