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
... manner impairing the gener- ality of the 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 ...
... manner impairing the gener- ality of the 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 ...
Page vi
... Manner of Using the Table ... Multiplication by Logarithms , Division by Logarithms , .. Arithmetical Complement , .. Raising to Powers by Logarithms , Extraction of Roots by Logarithms , PLANE TRIGONOMETRY . Plane Trigonometry Defined ...
... Manner of Using the Table ... Multiplication by Logarithms , Division by Logarithms , .. Arithmetical Complement , .. Raising to Powers by Logarithms , Extraction of Roots by Logarithms , PLANE TRIGONOMETRY . Plane Trigonometry Defined ...
Page 22
... manner , we find , ACD + ACE ACD + DCB ; and , taking away the common angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the angles about C is a right angle , all of the others are right angles also ...
... manner , we find , ACD + ACE ACD + DCB ; and , taking away the common angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the angles about C is a right angle , all of the others are right angles also ...
Page 25
... manner that the angle A shall coincide with the angle D , the side AB taking the direction DE , and the side AC the direction DF . Then , because AB is equal to DE , the ver- tex B will coincide with the vertex E ; and because AC is ...
... manner that the angle A shall coincide with the angle D , the side AB taking the direction DE , and the side AC the direction DF . Then , because AB is equal to DE , the ver- tex B will coincide with the vertex E ; and because AC is ...
Page 40
... manner , it may be proved that the sum of HGA and GHC is equal to two right angles . Cor . 1. If HGB is a right angle , GHD is a right angle also : hence , if a line is perpendicular to one of two par- allels , it is perpendicular to ...
... manner , it may be proved that the sum of HGA and GHC is equal to two right angles . Cor . 1. If HGB is a right angle , GHD is a right angle also : hence , if a line is perpendicular to one of two par- allels , it is perpendicular to ...
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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