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" If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal. "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 93
by Euclides - 1858
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...than EF, the side opposite EFG; but EG is equal to BC, therefore BC is greater thanEF. XXIV. If two triangles have two sides of the one respectively equal to two sides of the other, but the base of the one greater than the base of the other, the angle also contained by the sides of...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...here represented, still our demonstration is alike applicable to either case. COT. Conversely. If two triangles have two sides of the one respectively equal to two sides of the other, and the third side of the first greater than the third side of the second, the included angle of the...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 470 pages
...here represented, still our demonstration is alike applicable to either case. Cor. Conversely. If two triangles have two sides of the one respectively equal to two sides of the other, and the third side of the first greater than the third side of the second, the included angle of the...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...(t/~), therefore EG is greater than EF. PROPOSITION XXV. THEOREM. — If two triangles (ABC and DEF) hme two sides of the one respectively equal to two sides of the other (BA and AC to ED and DF), and if the third side (BC) of the one be greater than the third side (EF)...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...vertical angle, ACB. РДRЬППЯАRY THEOREM, that may be demonstrated by superposition, " If two Дз have two sides of the one respectively equal to two sides of the other, and the . opp. one of the sides in the firstequal to the /.opp. to the equal side in the second,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...then the angle of one triangle is supplemental to the other. Hence the following property : — If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal. A distinction ought to be made...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...then the angle of one triangle is supplemental to the other. Hence the following property : — If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal. A distinction ought to be made...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...parts alone are never enough to determine a triangle. UNEQUAL TRIANGLES. 293. Theorem — When two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third side in that triangle which has the greater angle, is greater...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...triangle . ....... I. 41. * ' The 4th, 8th, 24th, and,<25th propositions may be announced together thus : — ' if two triangles have two sides of the...angle opposed to it in the one is greater or less tliau or equal to the angle opposed to it in the other, or vice versd.' — Lardner, 4. The complements...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...then the angle of one triangle is supplemental to the other. Hence the following property : —If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal. A distinction ought to be made...
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