Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 5
... relating to the Fourth Book , 129 BOOK V. Regular Polygons - Measurement of the Circle , 136 ...... BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons , ........ 178 BOOK VIII . Cylinder , Cone , and Sphere ,
... relating to the Fourth Book , 129 BOOK V. Regular Polygons - Measurement of the Circle , 136 ...... BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons , ........ 178 BOOK VIII . Cylinder , Cone , and Sphere ,
Page 6
From the Works of A. M. Legendre Adrien Marie Legendre. BOOK VIII . Cylinder , Cone , and Sphere , ..... Spherica ! Geometry , .. BOOK IX . PAGE . ...... • 210 PLANE TRIGONOMETRY . INTRODUCTION . Definition of Logarithms , .. Rules for ...
From the Works of A. M. Legendre Adrien Marie Legendre. BOOK VIII . Cylinder , Cone , and Sphere , ..... Spherica ! Geometry , .. BOOK IX . PAGE . ...... • 210 PLANE TRIGONOMETRY . INTRODUCTION . Definition of Logarithms , .. Rules for ...
Page 8
... Cone , Area of the Surface of a Sphere , Area of a Zone , Area of a Spherical Polygon , Volume of a Prism , .... PAGE . 120 120 121 ... 122 122 123 124 124 125 .... 126 127 128 132 Volume of a Pyramid , ..... Volume of the Frustum of a ...
... Cone , Area of the Surface of a Sphere , Area of a Zone , Area of a Spherical Polygon , Volume of a Prism , .... PAGE . 120 120 121 ... 122 122 123 124 124 125 .... 126 127 128 132 Volume of a Pyramid , ..... Volume of the Frustum of a ...
Page 209
... polyedral angle . Furthermore , no other regular polygons can be grouped so as to form a salient polyedral angle ; therefore , Only five regular polyedrons can be formed . 14 BOOK VIII . THE CYLINDER , THE CONE , AND BOOK VII . 209.
... polyedral angle . Furthermore , no other regular polygons can be grouped so as to form a salient polyedral angle ; therefore , Only five regular polyedrons can be formed . 14 BOOK VIII . THE CYLINDER , THE CONE , AND BOOK VII . 209.
Page 210
... CONE , AND THE SPHERE . DEFINITIONS . 1. A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . E P H N K Thus , if the rectangle ABCD be turned about the side AB , as an axis , it ...
... CONE , AND THE SPHERE . DEFINITIONS . 1. A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . E P H N K Thus , if the rectangle ABCD be turned about the side AB , as an axis , it ...
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Common terms and phrases
AB² 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