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" For, if the arc AD be drawn from the vertex A to the middle point D of the base, the two triangles ABD, ACD, will have all the sides of the one respectively equal to the corresponding sides of the other... "
Elements of Geometry and Trigonometry: With Notes - Page 187
by Adrien Marie Legendre - 1828 - 316 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...equal sides. THEOREM. 483. In every isosceles spherical triangle Hie angles opposite to the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. Demonstration. 1. Let AB be equal AC (fig. 231); we sayFip. 231. that the angle C will be equal to...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - Architecture - 1823 - 596 pages
...equal. Let the side AB be equal to AC ; then shall the angle C equal the A. angle B. For, suppose AD to be drawn from the vertex A to the middle point D, of the base BC ; then the two triangles ADB, ADC, will have the two sides AB, BD, of the one equal to the two sides...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...equal sides. THEOREM. 483. In every isosceles spherical triangle the angles opposite to the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. Demonstration. 1. Let AB be equal to AC (Jig. 231) ; we say Fig. 331. that the angle C will be equal...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...equal sides. THEOREM. 483. In every isosceles spherical triangle the angles opposite to the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. Demonstration. 1. Let jJD be equal to AC (fig. 231); we say Fig. 231. that the angle C will be equal...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...THEOREM. / ^ 483. In every isosceles spherical triangle the angles opposite to the equal sides arc equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. Demonstration. 1. Let AB be equal to AC (Jig. 231) ; we say Fig• 231. that the angle C will be equal...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...PROPOSITION XIII. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical...the triangle is isosceles. First. Suppose the side AB= AC ; we shall have the angle C=B. For, if the arc AD be drawn from the vertex A to the middle po.int...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...PROPOSITION XIII. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal,- and conversely, if two angles of a spherical...respectively equal to the corresponding sides of the other, namely, AD common, BD = DC, and AB = AC : hence by the last Proposition, their angles will be equal...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 359 pages
...PROPOSITION XIII. THEOREM. . In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. O• First. Suppose the side AB= AC ; we shall have the angle C = B. For, if the arc AD be drawn from...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1839 - 269 pages
...PROPOSITION XIII. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical...First. Suppose the side AB=AC; we shall have the angle C— B. For, if the arc AD be drawn from the vertex A to the middle point D of the base, the two triangles...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...equal sides. THEOREM. 483. In every isosceles spherical triangle the angles opposite to the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, tfie triangle is isosceles. Demonstration. 1. Let AB be equal to AC (fig. 231) ; we Fig. 231. say that...
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