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" If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. "
Elements of the Geometry of Planes and Solids: With Four Plates - Page 20
by Ferdinand Rudolph Hassler - 1828 - 159 pages
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An Introduction to the Theory and Practice of Plane and Spherical ...

Thomas Keith - Navigation - 1810 - 478 pages
...construetion, also AB is common to the two triangles ABC and ADB, therefore the three sides of the one are equal to the three sides of the other, each to each. The angles -which are opposite to the equal sides in each triangle are equal. For, Produce the sides BC and BD...
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814 - 582 pages
...true, are not in all cases so ; one may be true, and the other false : thuğ, tin proposition, " If two triangles have the three sides of the one respectively equal to the three sides of the other, the three angles of the one will be respectively equal to the three augles of the other," may be proved...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...true, are not in all cases so ; one may be true, and the other false : thus, the proposition, " If two triangles have the three sides of the one respectively equal to the thrte sides of the other, the three angles of the one will be icspectirely equal to the three angles...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 352 pages
...two spherical triangles * on the same sphere, or on equal spheres, have the three sides of the one equal to the three sides of the other, each to each, the angles also of the one shall be equal to the angles of the other, each to each, to which thevequal sides are...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...same manner, it may be proved, that AH is equal to DF ; hence the two triangles AGH, and DEF having the three sides of the one respectively equal to the three sides of the other are equal in every respecta ; and therefore, the angle at A equal to the angle at D, the angle AGH,...
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An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - Navigation - 1826 - 504 pages
...through two given points on the surface of the sphere. Hence, the three sides of the one triangle being equal to the three sides of the other, each to each, the triangles are equal. (Prop, vu.) Secondly, let the triangles be situated on contrary sides of the centre...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 246 pages
...the angle D, it must necessarily be greater. PROPOSITION XXV. THEOREM. Two triangles are equal which have the three sides of the one respectively equal to the three sides of the other. For the angle included between any two sides in the one triangle must be equal to the angle included...
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A Concise System of Mathematics ...

Alexander Ingram - Mathematics - 1830 - 458 pages
...meet in the poles of that circle. PROP. V. If two spherical triangles have the three sides of the one equal to the three sides of the other, each to each, the angles which are opposite to the equal sides are likewise equal ; and conversely. PROP. VI. If two sides and...
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Geometry, plane, solid, and spherical. To which is added, in an appendix ...

Pierce Morton - 1830 - 300 pages
...equal to AG (I. 4.). Therefore, lastly, because the triangles AHF, AH G have the three sides of the one equal to the three sides of the other, each to each, the angle AHF is equal to the angle AHG (I. 7.); and they are adjacent angles; therefore, each of them...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...equal to AG (I 4 ) Therefore, lastly, because the triangles AHF, AH G have the three sides of the one equal to the three sides of the other, each to each, the angle AHF is equal to the angle AH G (I. 7.) ; and they are adjacent angles : theretore, each of them...
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