Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 55
... denote their ratio . B will A If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B = ; MA Α : whence , mA : mB A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four ...
... denote their ratio . B will A If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B = ; MA Α : whence , mA : mB A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four ...
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 G E 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 G E H ...
Page 147
... at I and Prolong AO to E. be perpendicular to it . Let P denote the circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we shall have ( P. IX . ) , Pp : OK ' or ΟΑ Ο4 ' : ΟΙ BOOK V. 147.
... at I and Prolong AO to E. be perpendicular to it . Let P denote the circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we shall have ( P. IX . ) , Pp : OK ' or ΟΑ Ο4 ' : ΟΙ BOOK V. 147.
Page 149
... inscribed • polygon , and PQ the side of the circumscribed polygon of double the number of sides ( P. VII . ) ? Draw Draw CE , CP , СЕ , см , and CF. E P M F B A Denote the area of the given inscribed polygon by p BOOK 149 V ..
... inscribed • polygon , and PQ the side of the circumscribed polygon of double the number of sides ( P. VII . ) ? Draw Draw CE , CP , СЕ , см , and CF. E P M F B A Denote the area of the given inscribed polygon by p BOOK 149 V ..
Page 150
From the Works of A. M. Legendre Adrien Marie Legendre. Denote the area of the given inscribed polygon by p , the area of the given circumscribed polygon by P , and the areas of the inscribed and circumscribed polygons having double the ...
From the Works of A. M. Legendre Adrien Marie Legendre. Denote the area of the given inscribed polygon by p , the area of the given circumscribed polygon by P , and the areas of the inscribed and circumscribed polygons having double the ...
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ABē ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following