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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. "
A Collection of Problems and Examples Adapted to the "Elementary Course of ... - Página 112
de Harvey Goodwin - 1851 - 173 páginas
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Natural Philosophy: With an Explanation of Scientific Terms, and ..., Volume 3

1829
...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...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 páginas
...of the ratios of the sides about the equal angles, or as the rectangles under those sides . G6 (/) Triangles which have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, are equal to one another; and, conversely,...
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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 the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 páginas
...is equal (9. 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 of the other have their sides about the equal angles reciprocally proportional: Jind triangles which have one angle in...
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Library of Useful Knowledge: Natural philosophy, Volume 3

1834
...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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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...the altitude of the first, the two triangles will be equal to one another (11. Cor. 2.). PROP. 40. Triangles which have one angle of the one equal to one angle of the other, are to one another in the ratio which is compounded of the ratios of the sides about the equal angles....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 páginas
...other, have their sides about the equal angles reciprocally proportional : And parallelograms that 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,...
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Elements of Geometry, Theoretical and Practical: Including Constructions of ...

Eugenius Nulty - 1836 - 220 páginas
...Multiply these equal ratios, and there will result ABС:DEF::AС.BG: DF.EH(th.T). THEOREM XXIV. 69. Two triangles which have one angle of the one equal to one angle of the other, are proportional to the products of the sides which contain those angles. E в Let AB С, DEF be two...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 páginas
...of the other, 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. XV. Equal...
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The Element of Geometry

John Playfair - 1836 - 114 páginas
...other, have their sides about the equal angles reciprocally proportional ; and parallelograms that 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,...
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