Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Page vii
... Area , or Contents of a Surface , .. 347 Unit of Measure for Surfaces , - 347 Area of a Square , Rectangle , or ... Find the Circumference or Diameter of a Circle , .. 354 To find the Length of an Arc ,. 355 Area of a Circle , ... 356 ...
... Area , or Contents of a Surface , .. 347 Unit of Measure for Surfaces , - 347 Area of a Square , Rectangle , or ... Find the Circumference or Diameter of a Circle , .. 354 To find the Length of an Arc ,. 355 Area of a Circle , ... 356 ...
Page 92
... find how many times this unit is contained in the base of any rectangle , and also , how many times it is contained ... Area of the rectangle . Scholium 2. In geometry , the product of two lines fre quently means the same thing as their ...
... find how many times this unit is contained in the base of any rectangle , and also , how many times it is contained ... Area of the rectangle . Scholium 2. In geometry , the product of two lines fre quently means the same thing as their ...
Page 147
... find the polygons P ' and p ' , which have double the num- ber of sides . PROPOSITION XII . PROBLEM . To find the approximate area of a circle whose radius is unity . Let the radius of the circle be 1 ; the side of the in- scribed ...
... find the polygons P ' and p ' , which have double the num- ber of sides . PROPOSITION XII . PROBLEM . To find the approximate area of a circle whose radius is unity . Let the radius of the circle be 1 ; the side of the in- scribed ...
Page 153
... area CA = X CA2 , " that is , the area of a circle is equal to into the square of the radius . Scholium 1. Let CA ... find the circumference when the radius is given ; and for effecting this , it is enough to know the ratio of the ...
... area CA = X CA2 , " that is , the area of a circle is equal to into the square of the radius . Scholium 1. Let CA ... find the circumference when the radius is given ; and for effecting this , it is enough to know the ratio of the ...
Page 225
... area FDMBE be revolved about the radius CA it will generate a spherical segment . It is required to find the measure of this segment . The solid generated by the circular segment DMB is measured by ( P. 16 ) TX BD XEF : the frustum of ...
... area FDMBE be revolved about the radius CA it will generate a spherical segment . It is required to find the measure of this segment . The solid generated by the circular segment DMB is measured by ( P. 16 ) TX BD XEF : the frustum of ...
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Common terms and phrases
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices
Popular passages
Page 27 - If two triangles have two sides of the one equal to two sides of the...
Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 26 - The sum of any two sides of a triangle is greater than the third side.
Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 93 - The area of a parallelogram is equal to the product of its base and altitude.
Page 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 323 - 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 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.