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" 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 shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. "
Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ... - Page 161
by John Keill - 1733 - 397 pages
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...parallelogram BC. Therefore equal parallelograms, &c. Q, ED PROP, XV. THEOR. triangles 'which have one angle of the one equal to one angle of the other, have their sides about >k> equal angles reciprocally proportional : And triangles mhich have one angle in the one equal to...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...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 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...to the triangle DEF. Wherefore, if two triangles, &c. QE D PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, then, if each of the remaining angles be either...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 516 pages
...Therefore, equal parallelograms, &c., QED PROP. XV. THEOR. EAUAL triangles, which have one angle ofthe one equal to one angle of the other,- have their sides about the equal angles reciprocally proportional; and triangles which have one angle in the one equal to one angle in the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...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 in the me equal to on« angle in the...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...triangle DEF. If, therefore, two triangles, &c. QED* PROPOSITION VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportional, then if each of the remaining angles be either less...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pages
...therefore, two triangles have their «ides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and have those...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...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...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...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...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...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 about the equal angles reciprocally proportional ; and parallelograms, and also • triangles, which have one angle of one...
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