Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page v
... Book , ..... PAGE . 13 20 50 60 59 82 93 129 BOOK V. Regular Polygons - Measurement of the Circle , 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons , 178 Cylinder , Cone , and Sphere , Spherical Geometry ,
... Book , ..... PAGE . 13 20 50 60 59 82 93 129 BOOK V. Regular Polygons - Measurement of the Circle , 136 BOOK VI . Planes , and Polyedral Angles , 157 BOOK VII . Polyedrons , 178 Cylinder , Cone , and Sphere , Spherical Geometry ,
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 , Area of a Circle , Area of a Sector , .... Area of a Segment , Area of a Circular Ring ,. 117 117 ...
... 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 , Area of a Circle , Area of a Sector , .... Area of a Segment , Area of a Circular Ring ,. 117 117 ...
Page viii
... .. Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a Wedge , 127 Volume of a Prismoid , Volumes of Regular Polyedrons , .. 128 132 ELEMENTS OF GEOMETRY . INTRODUCTION . DEFINITIONS OF TERMS . viii CONTENTS .
... .. Volume of the Frustum of a Pyramid , 125 Volume of a Sphere , 126 Volume of a Wedge , 127 Volume of a Prismoid , Volumes of Regular Polyedrons , .. 128 132 ELEMENTS OF GEOMETRY . INTRODUCTION . DEFINITIONS OF TERMS . viii CONTENTS .
Page 15
... REGULAR POLYGON , is one which is both equilateral and equiangular . 21. Two polygons are mutually equilateral , when their sides , taken in the same order , are equal , each to each : that is , following their perimeters in the same ...
... REGULAR POLYGON , is one which is both equilateral and equiangular . 21. Two polygons are mutually equilateral , when their sides , taken in the same order , are equal , each to each : that is , following their perimeters in the same ...
Page 136
... REGULAR POLYGONS . - AREA OF THE CIRCLE . DEFINITION . 1. A REGULAR POLYGON is a polygon which is both equilateral and equiangular . PROPOSITION I. THEOREM . Regular polygons of the same number of sides are similar . Let ABCDEF and ...
... REGULAR POLYGONS . - AREA OF THE CIRCLE . DEFINITION . 1. A REGULAR POLYGON is a polygon which is both equilateral and equiangular . PROPOSITION I. THEOREM . Regular polygons of the same number of sides are similar . Let ABCDEF and ...
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.