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 iii
... denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a science which deals only with the abstract properties and relations of figured space . The term volume has been introduced in its place ...
... denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a science which deals only with the abstract properties and relations of figured space . The term volume has been introduced in its place ...
Page 57
... denote their ratio . If we multiply each term of this fraction by m , its value will not be changed ; and we shall have , mB B = ; whence , MA : mB :: A : B ; та A which was to be proved . PROPOSITION VIII . THEOREM . If four quantities ...
... denote their ratio . If we multiply each term of this fraction by m , its value will not be changed ; and we shall have , mB B = ; whence , MA : mB :: A : B ; та A which was to be proved . PROPOSITION VIII . THEOREM . If four quantities ...
Page 88
... denote the given sides , and A the given angle . Draw the indefinite line DF , and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the side and on DE , lay off DG equal to the sideCB ; draw E H B C GH ...
... denote the given sides , and A the given angle . Draw the indefinite line DF , and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the side and on DE , lay off DG equal to the sideCB ; draw E H B C GH ...
Page 94
... denoted by the symbol ° ; thus , 25 ° is read 25 degrees , etc. Since a quad- rant contains 90 ° , the whole circumfer- ence contains 360 ° . A right angle , as CAD , which is the unit of measure for angles , being measured by a ...
... denoted by the symbol ° ; thus , 25 ° is read 25 degrees , etc. Since a quad- rant contains 90 ° , the whole circumfer- ence contains 360 ° . A right angle , as CAD , which is the unit of measure for angles , being measured by a ...
Page 153
... to it . Prolong AO to E. Let P denote the circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we have ( P. IX . ) , P : 0 :: :: OK or OA : 012 : hence , by division ( B. II . , P. BOOK V. 153.
... to it . Prolong AO to E. Let P denote the circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we have ( P. IX . ) , P : 0 :: :: OK or OA : 012 : hence , by division ( B. II . , P. BOOK V. 153.
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence