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 v
... Third Books ,. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , PAGE . 9 13 20 50 50 82 8889 59 93 129 136 BOOK VI . Planes , and ...
... Third Books ,. BOOK IV . Proportions of Figures - Measurement of Areas , Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , PAGE . 9 13 20 50 50 82 8889 59 93 129 136 BOOK VI . Planes , and ...
Page 10
... third power . The Radical Sign , √ : Thus , A , B , indicate that the square root of A , and the cube root of B , are to be taken . " When a compound quantity is to be operated upon as a single quantity , its parts are connected by a ...
... third power . The Radical Sign , √ : Thus , A , B , indicate that the square root of A , and the cube root of B , are to be taken . " When a compound quantity is to be operated upon as a single quantity , its parts are connected by a ...
Page 26
... third side . 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 ...
... third side . 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 ...
Page 27
... third , and the difference of any two must be less than the third . PROPOSITION VIII . THEOREM . If from any point within a triangle two straight lines b drawn to the extremities of any side , their sum will be less than that of the two ...
... third , and the difference of any two must be less than the third . PROPOSITION VIII . THEOREM . If from any point within a triangle two straight lines b drawn to the extremities of any side , their sum will be less than that of the two ...
Page 28
... third sides will be unequal ; and the greater side will belong to the triangle which has the greater included angle . In the triangles BAC and DEF , let AB be equal to DE , AC to DF , and the angle A greater than the an- gle D : then ...
... third sides will be unequal ; and the greater side will belong to the triangle which has the greater included angle . In the triangles BAC and DEF , let AB be equal to DE , AC to DF , and the angle A greater than the an- gle D : then ...
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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