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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. "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 35
by George Roberts Perkins - 1860 - 443 pages
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 294 pages
...semicircumference. PROP. III. (86.) Theorem. If 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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...straight line AD from the vertex A to the point D the middle of the base BC ; the two triangles ABD, ADC, will have the three sides of the one, equal to the three sides of the other, each to each, namely, AD common to both, AB — AC, by hypothesis, and BD = DC, by construction ; therefore...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...arc AMD will be equal to the arc ENG. For, if the radii CD, OG, be drawn, the two triangles ACD, EOG, will. have the three sides of the one equal to the three sides of the other, each to each, namely, AC = EO, CD = OG and AD=. EG ; therefore these triangles are equal (43) ; hence...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...straight line AD from the veriest A to the point D the middle of the base BC ; the two triangles ABD, ADC, will have the three sides of the one, equal to the three sides of the . other, each to each, namely, AD common to both, AB = AC, by hypothesis, and BD = DC, by construction ; therefore...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...AMD will be equal to the arc EJVG. For, if the radii CD, OG, be drawn, the two triangles ACD, EOG, will have the three sides of the one equal to the three sides of the other,~each to each, namely, AC= EO, CD = OG and AD — EG ; therefore these triangles are equal (43)...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 272 pages
...base at right angles. OF GEOMETRY. Book I. s Sup. PROP. IV. THEOREM. If two triangles, ABC and DEF, have the three sides of the one equal to the three sides of the other, each to each, viif. AB to DE, AC to DF, and BC to EF, the triangles are equal in every respect. Let...
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...their parts ; they are not different, therefore, but equal; and we say, universally, When two triangles have the three' sides of the one equal to the three sides of the other respectively, the angles will also be equal, respectively, and the two triangles will be equal in all their parts....
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A concise system of mathematics

Alexander Ingram - Mathematics - 1830 - 120 pages
...one and the same great circle, 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....
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...the three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the othrr, each to each, viz. those which are opposite to the equal angles.* Let the spherical triangles...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...and С с ; draw P О perpendicular to Ce; and join OQ. Then, because the triangles С P с, С Q с have the three sides of the one equal to the three sides scribe two circles, and kt them cut one another in P; and from P draw PM perpendicular to А В : then...
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