Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page v
... . 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 . 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 vi
From the Works of A.M. Legendre Adrien Marie Legendre. Cylinder , Cone , and Sphere , Spherical Geometry , ...... BOOK VIII . PAGE . 210 BOOK IX . 235 PLANE TRIGONOMETRY . INTRODUCTION . Definition of Logarithms , Rules for ...
From the Works of A.M. Legendre Adrien Marie Legendre. Cylinder , Cone , and Sphere , Spherical Geometry , ...... BOOK VIII . PAGE . 210 BOOK IX . 235 PLANE TRIGONOMETRY . INTRODUCTION . Definition of Logarithms , Rules for ...
Page 209
... 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 R BOOK VIII . THE CYLINDER , THE CONE , AND BOOK VII . 209.
... 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 R BOOK VIII . THE CYLINDER , THE CONE , AND BOOK VII . 209.
Page 210
... cylinder FGCQ - P . The fixed line AB is called the axis of the cylinder ; the curved surface generated by the side CD , opposite the axis , is called the convex surface of the cylinder ; the equal circles FGCQ , and EHDP , generated by ...
... cylinder FGCQ - P . The fixed line AB is called the axis of the cylinder ; the curved surface generated by the side CD , opposite the axis , is called the convex surface of the cylinder ; the equal circles FGCQ , and EHDP , generated by ...
Page 211
... cylinder , when its bases are in- scribed in the bases of the cylinder . In this case , the cylinder is said to be circumscribed about the prism . The lateral edges of the inscribed prism are elements of the surface of the circumscribing ...
... cylinder , when its bases are in- scribed in the bases of the cylinder . In this case , the cylinder is said to be circumscribed about the prism . The lateral edges of the inscribed prism are elements of the surface of the circumscribing ...
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Common terms and phrases
AB² ABCD AC² 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.