Elements of Geometry and Trigonometry |
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Page vii
... Formulas for Oblique - angled Triangles ,. Solution of Oblique - angled Triangles , MENSURATION . 85-92 92-104 Mensuration Defined , 105 The Area of a Parallelogram , 106 • The Area of a Triangle , 106 Formula for the Sine of Half an ...
... Formulas for Oblique - angled Triangles ,. Solution of Oblique - angled Triangles , MENSURATION . 85-92 92-104 Mensuration Defined , 105 The Area of a Parallelogram , 106 • The Area of a Triangle , 106 Formula for the Sine of Half an ...
Page 207
... - abcde :: AB3 : ab3 ; which was to be proved . Cor . Similar pyramids are to each other as the cubes of their altitudes , or as the cubes of any other homologous lines . GENERAL FORMULAS . If we denote the volume of any BOOK VII . 207.
... - abcde :: AB3 : ab3 ; which was to be proved . Cor . Similar pyramids are to each other as the cubes of their altitudes , or as the cubes of any other homologous lines . GENERAL FORMULAS . If we denote the volume of any BOOK VII . 207.
Page 208
Adrien Marie Legendre Charles Davies. GENERAL FORMULAS . If we denote the volume of any prism by V , its base by B , and its altitude by H , we shall have ( P. XIV . ) , V √ = B × H · ( 1. ) If we denote the volume of any pyramid by V ...
Adrien Marie Legendre Charles Davies. GENERAL FORMULAS . If we denote the volume of any prism by V , its base by B , and its altitude by H , we shall have ( P. XIV . ) , V √ = B × H · ( 1. ) If we denote the volume of any pyramid by V ...
Page 233
... FORMULAS . If we denote the convex surface of a cylinder by S , its volume by V , the radius of its base by R , and its alti- tude by H , we have ( P. I. , II . ) , S = 2 πR × H 2aRxH • V R2 x H ( 1. ) ( 2. ) If we denote the volume by ...
... FORMULAS . If we denote the convex surface of a cylinder by S , its volume by V , the radius of its base by R , and its alti- tude by H , we have ( P. I. , II . ) , S = 2 πR × H 2aRxH • V R2 x H ( 1. ) ( 2. ) If we denote the volume by ...
Page 3
... that power : hence the formula , log ( 10 ) ? = p . ( 3. ) If a number is an exact power of 10 , its logarithm is a whole number . If a number is not an exact power of 10 PLANE TRIGONOMETRY INTRODUCTION Definition of Logarithms,
... that power : hence the formula , log ( 10 ) ? = p . ( 3. ) If a number is an exact power of 10 , its logarithm is a whole number . If a number is not an exact power of 10 PLANE TRIGONOMETRY INTRODUCTION Definition of Logarithms,
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
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.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...