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 14
... AC , is an angle . The lines AB and AC are called sides , and their common point A , is called the ver- -B tex . An ... equal . The first fine is then said to be perpendicular to the second . 13. An OBLIQUE ANGLE is formed by one ...
... AC , is an angle . The lines AB and AC are called sides , and their common point A , is called the ver- -B tex . An ... equal . The first fine is then said to be perpendicular to the second . 13. An OBLIQUE ANGLE is formed by one ...
Page 24
... equal to two right angles , the two lines met will form one and the same straight line . 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 the prolongation of AC . D A- B E ...
... equal to two right angles , the two lines met will form one and the same straight line . 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 the prolongation of AC . D A- B E ...
Page 25
... AC to DF , and the angle A to the angle D : then will the triangles be equal in all their parts . For , let ABC be ... AC the direction DF equal to DE , the vertex B will coincide with the vertex E ; and because AC is equal to DF , the ...
... AC to DF , and the angle A to the angle D : then will the triangles be equal in all their parts . For , let ABC be ... AC the direction DF equal to DE , the vertex B will coincide with the vertex E ; and because AC is equal to DF , the ...
Page 26
... equal to EF , the vertex C will coincide with the vertex F ; and because the angle C is equal to the angle F , the ... AC . For , the distance from A to C , measured on any broken line AB , BC , A4 C is greater than the distance measured on ...
... equal to EF , the vertex C will coincide with the vertex F ; and because the angle C is equal to the angle F , the ... AC . For , the distance from A to C , measured on any broken line AB , BC , A4 C is greater than the distance measured on ...
Page 27
... equal to AC , we have , BD + DC < BA + AC . But it was shown that BO + OC is less than BD + - DC ; still more , then , is BO + OC less than BA + AC ; which was to be proved . PROPOSITION IX . THEOREM . If two triangles have two BOOK I. 27.
... equal to AC , we have , BD + DC < BA + AC . But it was shown that BO + OC is less than BD + - DC ; still more , then , is BO + OC less than BA + AC ; which was to be proved . PROPOSITION IX . THEOREM . If two triangles have two BOOK I. 27.
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Common terms and phrases
ABē ACē 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