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 of Relation between Functions and Arcs ,. Functions of Double and Half Arcs , Additional Formulas ... Formula for the Sine of Half an Angle , .. 108 Area of a Trapezoid , 112 Area of a Quadrilateral , 112 Area of a ...
... Formulas of Relation between Functions and Arcs ,. Functions of Double and Half Arcs , Additional Formulas ... Formula for the Sine of Half an Angle , .. 108 Area of a Trapezoid , 112 Area of a Quadrilateral , 112 Area of a ...
Page 207
... :: 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.
... :: 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
Adapted to the Course of Mathematical Instruction in the United States 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 x H • • · ( 1 ...
Adapted to the Course of Mathematical Instruction in the United States 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 x H • • · ( 1 ...
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 = 2TR X H • • V = TR2 × H • • ུ་ེེེ ( 1. ) ( 2. ) If we denote the ...
... 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 = 2TR X H • • V = TR2 × H • • ུ་ེེེ ( 1. ) ( 2. ) If we denote the ...
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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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB 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 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 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 polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence