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" ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. "
Plane Geometry - Page 223
by John Charles Stone, James Franklin Millis - 1916 - 278 pages
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...HG, and of PB to BL or HE. Cor. 1. — By a similar reasoning it may be proved, that triangles, which have an angle of one, equal to an angle of the other, are to each other, in a ratio, compounded of the ratios, of the sides including the equal angles. Cor....
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 166 pages
...have their sides about the equal angles reciprocally proportional : and triangles are equal, which have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional. Given two equal triangles ABC, ADE,...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...equal angles are reciprocally proportional (AB to BC as 1.I! to BD. And if two triangles (ABD and CBL), have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, they will be equal to one another....
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 520 pages
...be : BC ; and by making C the centre, that be : BC :: ac : AC. COR. 1. Conversely, if two triangles have an angle of one equal to an angle of the other, and the sides forming the equal angles proportionals, the triangles will be similar. COR. 2. Hence,...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 pages
...equal angles are reciprocally proportional (AB to BC as LB to BD). And if two triangles (ABD and CBL), have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, they will be equal to one another....
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Questions and Exercises on Stewart's Lessons in Elementary Physics

George Anthony Hill - Physics - 1880 - 204 pages
...equiangular with respect to each other. (b) K they have their homologous sides proportional. (c) If they have an angle of one equal to an angle of the other, and the sides including these angles proportional. (18) The perpendicular upon the hypothenuse of a...
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College Algebra

Webster Wells - Algebra - 1890 - 560 pages
...similar, as also are the triangles EOG and COD ; for, by Geometry, two triangles are similar when they have an angle of one equal to an angle of the other, and the including sides proportional. Then the figure OFEG is similar to OBDC, and hence OFEG is a...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...onehalf of it. 4. The two tangents to a circle from an outside point are equal. 5. If two triangles have an angle of one equal to an angle of the other they are to each other as the product of the sides including the equal angles. 6. From the obtuse angle...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...its other sides, an incorrect method. PROPOSITION VIII. THEOREM 398. The areas of two triangles which have an angle of one equal to an angle of the other are to each other as the products of the sides including those angles. GIVEN — the triangles ADE...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...its other sides, an incorrect method. PROPOSITION VIII. THEOREM 308. The areas of two triangles which have an angle of one equal to an angle of the other are to each other as the products of the sides including those angles. GIVEN — the triangles ADR...
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