Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 24
... Let DC meet AC and BC at C , making the sum of the angles DCA and DCB equal to two right angles : then will CB be ... ABC and DEF , let AB be equal to DE , AC to DF , and the angle 24 GEOMETRY .
... Let DC meet AC and BC at C , making the sum of the angles DCA and DCB equal to two right angles : then will CB be ... ABC and DEF , let AB be equal to DE , AC to DF , and the angle 24 GEOMETRY .
Page 25
... ABC and DEF , let the angle B be equal to the angle E , the angle to the angle F , and the side BC to the side EF : then A A B will the triangles be equal in all their parts . E D For , let ABC be applied to DEF in such a manner that ...
... ABC and DEF , let the angle B be equal to the angle E , the angle to the angle F , and the side BC to the side EF : then A A B will the triangles be equal in all their parts . E D For , let ABC be applied to DEF in such a manner that ...
Page 26
... Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side AC . For , the distance from A to C , measured on any broken line AB , BC , A4 C is greater than the distance measured on the ...
... Let ABC be a triangle : then will the sum of any two sides , as AB , BC , be greater than the third side AC . For , the distance from A to C , measured on any broken line AB , BC , A4 C is greater than the distance measured on the ...
Page 28
... let AB be equal to DE , AC to DF , and the angle A greater than the an- gle D : then will BC be greater than EF ... ABC , it may be on the side BC , or it may be within the tri- angle ABC . Each case will be considered separately . 1o ...
... let AB be equal to DE , AC to DF , and the angle A greater than the an- gle D : then will BC be greater than EF ... ABC , it may be on the side BC , or it may be within the tri- angle ABC . Each case will be considered separately . 1o ...
Page 30
... ABC and DEF , let AB be equal to DE , AC to DF , and BC to EF : angles be equal in all their parts . For , since the sides AB , AC , are equal to DE , DF , each to each , if the angle A were greater than D , it would follow , by the ...
... ABC and DEF , let AB be equal to DE , AC to DF , and BC to EF : angles be equal in all their parts . For , since the sides AB , AC , are equal to DE , DF , each to each , if the angle A were greater than D , it would follow , by the ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence