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
... Polygon , .. 351 Area of a Long and Irregular Figure bounded on One Side by a Right Line , ... 351 Area of a Regular Polygon , ... 353 To Find the Circumference or Diameter of a Circle , .. 354 To find the Length of an Arc ,. 355 Area ...
... Polygon , .. 351 Area of a Long and Irregular Figure bounded on One Side by a Right Line , ... 351 Area of a Regular Polygon , ... 353 To Find the Circumference or Diameter of a Circle , .. 354 To find the Length of an Arc ,. 355 Area ...
Page viii
... Polygon , - 367 Of the Regular Polyedrons , .. 367 Theorem , ... 367 Method of Finding the Angle included between two Adjacent Faces of a Regular Polyedron , .. 368 Table of Regular Polyedrons whose Edges are 1 , ......... . 369 ...
... Polygon , - 367 Of the Regular Polyedrons , .. 367 Theorem , ... 367 Method of Finding the Angle included between two Adjacent Faces of a Regular Polyedron , .. 368 Table of Regular Polyedrons whose Edges are 1 , ......... . 369 ...
Page 135
... REGULAR POLYGONS - MEASUREMENT OF THE CIRCLE . DEFINITION . A REGULAR POLYGON is one which is both equilateral and equiangular . A regular polygon may have any number of sides . The equilateral triangle is one of three sides ; the ...
... REGULAR POLYGONS - MEASUREMENT OF THE CIRCLE . DEFINITION . A REGULAR POLYGON is one which is both equilateral and equiangular . A regular polygon may have any number of sides . The equilateral triangle is one of three sides ; the ...
Page 136
... regular polygon , like the angle of an equiangular polygon , is determined by the number of its sides ( B. I. , P. 26 , c . 4 ) . PROPOSITION II . THEOREM . △ regular polygon may be circumscribed by the circumference of a circle , and ...
... regular polygon , like the angle of an equiangular polygon , is determined by the number of its sides ( B. I. , P. 26 , c . 4 ) . PROPOSITION II . THEOREM . △ regular polygon may be circumscribed by the circumference of a circle , and ...
Page 137
... polygon . Cor . 2. To inscribe a regular polygon of any number of sides in a given circle , we have only to divide the circumference into as many equal parts as the poly- gon has sides ; for , when the arcs . are equal , the chords AB ...
... polygon . Cor . 2. To inscribe a regular polygon of any number of sides in a given circle , we have only to divide the circumference into as many equal parts as the poly- gon has sides ; for , when the arcs . are equal , the chords AB ...
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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.