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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: The Errors by which Theon, Or Others, Have Long ... - Page 141
by Robert Simson - 1827 - 513 pages
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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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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 - Euclid's Elements - 1826 - 320 pages
...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 Philosophical Magazine: Or Annals of Chemistry, Mathematics ..., Volume 4

Physics - 1828
...together equal to two right angles. 81. If two triangles have one angle in one equal to one angle in the other, and the sides about the equal angles proportionals,...equal which are opposite to the homologous sides. 82. Find the angles which the sides of a regular pentagon make with each other. 83. In any triangle...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...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 - Geometry - 1830 - 272 pages
...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 - Astronomy - 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 - Euclid's Elements - 1832 - 333 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROP. VI. THEOR. If two triangles have one angle of the one equal to one angle...homologous sides. Let the triangles ABC, DEF have the angle BAG in the one equal to the angle EDF in the other, and the sides about those angles propdrtionals;...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 333 pages
...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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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...triangle DEF. Wherefore, if the sides, &c. <?. /.•./,. ' n. . 'PROPOSITION VI. THEOR. — If two triangles have one angle of the one, equal to one...have those angles equal which are opposite to the funuologous sides. Let the triangles ABC, DEF have the angle BAC in the one, equal to the angle EDF...
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