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
... Formulas for Oblique - angled Triangles ,. Solution of Oblique - angled Triangles , 85-92 92-104 MENSURATION . 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 , 85-92 92-104 MENSURATION . 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
... FORMULAS . If we denote the volume of any pris.n by V , its base by B , and its altitude by II , we shall have ( P. XIV . ) , V = BX II · • ( 1. ) If we denote the volume of any pyramid by V , its base by B , and its altitude by II , we ...
... FORMULAS . If we denote the volume of any pris.n by V , its base by B , and its altitude by II , we shall have ( P. XIV . ) , V = BX II · • ( 1. ) If we denote the volume of any pyramid by V , its base by B , and its altitude by II , we ...
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 II , we have ( P. I. , II . ) , • S = 2R × II V = R2 × H · ( 1. ) ( 2. ) If we denote the convex ...
... 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 II , we have ( P. I. , II . ) , • S = 2R × II V = R2 × H · ( 1. ) ( 2. ) If we denote the convex ...
Page 3
... equal to the exponent of 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.
... equal to the exponent of 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.
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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