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
... truths evolved . The term solid , used not only by LEGENDRE , but by many other authors , to denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a science , which deals only with the abstract.
... truths evolved . The term solid , used not only by LEGENDRE , but by many other authors , to denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a science , which deals only with the abstract.
Page 55
... denote their ratio . If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B MA A = whence , mA : mB :: A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four quantities ...
... denote their ratio . If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B MA A = whence , mA : mB :: A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four quantities ...
Page 86
... 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 C , and on DE , lay off DG equal to the side B ; draw GE D H ...
... 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 C , and on DE , lay off DG equal to the side B ; draw GE D H ...
Page 147
... to it . Let P denote the K ; it will bisect Prolong 40 to AB at I and circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we shall have ( P. IX . ) , P : P : OK or OA ' : OI BOOK V. 147.
... to it . Let P denote the K ; it will bisect Prolong 40 to AB at I and circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we shall have ( P. IX . ) , P : P : OK or OA ' : OI BOOK V. 147.
Page 149
... the inscribed polygon , and PQ the side of the circumscribed polygon of double the number of sides ( P. VII . ) . Draw CE , CP , СЕ , СР , см , E P M Q D B and CF. C Denote the area of the given inscribed polygon by P BOOK V. 149.
... the inscribed polygon , and PQ the side of the circumscribed polygon of double the number of sides ( P. VII . ) . Draw CE , CP , СЕ , СР , см , E P M Q D B and CF. C Denote the area of the given inscribed polygon by P BOOK V. 149.
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence