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 v
... Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , 82 6899 59 93 129 136 BOOK VI . Planes , and Polyedral Angles , . 157 BOOK VII . Polyedrons , ... 178 Cylinder , Cone , and Sphere , BOOK VIII .
... Problems relating to the Fourth Book , BOOK V. Regular Polygons - Measurement of the Circle , 82 6899 59 93 129 136 BOOK VI . Planes , and Polyedral Angles , . 157 BOOK VII . Polyedrons , ... 178 Cylinder , Cone , and Sphere , BOOK VIII .
Page vii
... Regular Polygon , 114 To find the Circumference of a Circle , 116 To find the Diameter of a Circle , 116 To find the length of an Arc , 117 Area of a Circle , Area of a Sector , Area of a Segment , Area of a Circular Ring , 117 118 118 ...
... Regular Polygon , 114 To find the Circumference of a Circle , 116 To find the Diameter of a Circle , 116 To find the length of an Arc , 117 Area of a Circle , Area of a Sector , Area of a Segment , Area of a Circular Ring , 117 118 118 ...
Page viii
... 124 Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a Wedge , 127 Volume of a Prismoid , 128 Volumes of Regular Polyedrons ,. 132 ELEMENTS OF GEOMETRY . INTRODUCTION , 1. QUANTITY is anything viii CONTENTS .
... 124 Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a Wedge , 127 Volume of a Prismoid , 128 Volumes of Regular Polyedrons ,. 132 ELEMENTS OF GEOMETRY . INTRODUCTION , 1. QUANTITY is anything viii CONTENTS .
Page 15
... REGULAR POLYGON , is one which is both equilateral and equiangular . 21. Two polygons are equilateral , or mutually equilateral , when their sides , taken in the same order , are equal , each to each that is , following their perimeters ...
... REGULAR POLYGON , is one which is both equilateral and equiangular . 21. Two polygons are equilateral , or mutually equilateral , when their sides , taken in the same order , are equal , each to each that is , following their perimeters ...
Page 135
... , VII . , VIII . , and IX . , a polygon may be constructed similar to either of two given similar polygons , and equal to their sum , or to their difference . BOOK V. REGULAR POLYGONS . -ARE A OF THE CIRCLE BOOK IV . 135.
... , VII . , VIII . , and IX . , a polygon may be constructed similar to either of two given similar polygons , and equal to their sum , or to their difference . BOOK V. REGULAR POLYGONS . -ARE A OF THE CIRCLE BOOK IV . 135.
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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