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" If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.... "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 28
by George Roberts Perkins - 1856 - 235 pages
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...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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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...have the same relation to each other as Props. 4 and 8, and the four may be combined thus : — If two triangles have two sides of the one respectively equal to two sides of the other, the remaining side of the one will be greater or less than, or equal to, the remaining side of the...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 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 first...
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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 Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...triangle is supplemental to the other. Hence the following property : — If two triangles have two si-les 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 between...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...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, these Дs...
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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 between...
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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 between...
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Treatise on Plane and Solid Geometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry, Modern - 1864 - 292 pages
...a radius, describe a circumference in the plane MN, cutting CD at D. Then the triangles ACD and ACB have two sides of the one respectively equal to two sides of the other. But the third side AD is longer than the third side AB (530). Therefore, the angle ACD is greater than...
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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 between...
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