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 vii
... find the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a Circular Ring ,. 117 118 118 120 125 126 126 127 129 130 130 131 131 132 138 PAGE Area of the Surface of a Prism , Area CONTENTS .
... find the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a Circular Ring ,. 117 118 118 120 125 126 126 127 129 130 130 131 131 132 138 PAGE Area of the Surface of a Prism , Area CONTENTS .
Page viii
... Prism , Area of the Surface of a Pyramid , Area of the Frustum of a Cone , ... 184 134 135 Area of the Surface of a Sphere ,. 136 Area of a Zone , 137 Area of a Spherical Polygon , ... 137 Volume of a Prism , 138 Volume of a Pyramid ...
... Prism , Area of the Surface of a Pyramid , Area of the Frustum of a Cone , ... 184 134 135 Area of the Surface of a Sphere ,. 136 Area of a Zone , 137 Area of a Spherical Polygon , ... 137 Volume of a Prism , 138 Volume of a Pyramid ...
Page 189
... prism ; the lines in which the lateral faces meet , are called lateral edges , and the lines in which the lateral faces meet either base are called basal edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis- tance ...
... prism ; the lines in which the lateral faces meet , are called lateral edges , and the lines in which the lateral faces meet either base are called basal edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis- tance ...
Page 190
... PRISM is one whose lateral edges are oblique to the planes of the bases . In this case , any lateral edge is greater than the altitude . 6. Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases ...
... PRISM is one whose lateral edges are oblique to the planes of the bases . In this case , any lateral edge is greater than the altitude . 6. Prisms are named from the number of sides of their bases ; a triangular prism is one whose bases ...
Page 192
... prism is equal to the perim- eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its convex sur- face equal to , ( AB + BC + CD + DE + EA ) × AF . For , the convex surface is equal to the sum of all ...
... prism is equal to the perim- eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its convex sur- face equal to , ( AB + BC + CD + DE + EA ) × AF . For , the convex surface is equal to the sum of all ...
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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