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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. "
Elements of Arithmetic, Algebra, and Geometry - Strona 169
autor: George Lees - 1826
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A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - Liczba stron: 410
...figure FDHG, having its base DH in BC, and terminated by the given point D, is a rhombus. PROP. XI. 17. THEOREM. If two triangles have one angle of the one, equal to ons angle of the other, and also another angle of the one, together with another angle of the other,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - Liczba stron: 516
...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 angle of the other, and the sides about the equal angles Eroportionals, the triangles shall be equiangular, and shall ave those angles equal...
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A Supplement to the Elements of Euclid

Daniel Cresswell - 1825 - Liczba stron: 582
...part of the base of the triangle, and having its extremity in a given point of that base. XI. 'l'ii. If two triangles have one angle of the one, equal to one angle of the other, and also another angle of the one, together with. another angle of the other, equal to two right angles,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - Liczba stron: 372
...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 - Liczba stron: 180
...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 Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - Liczba stron: 320
...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 - Liczba stron: 513
...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 Index, Tom 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 one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we have seen...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - Liczba stron: 272
...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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