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
... Circumference of a Circle , ........ To find the Diameter of a Circle , ... To find the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a Circular Ring ,. 117 118 118 120 125 126 126 127 ...
... Circumference of a Circle , ........ To find the Diameter of a Circle , ... To find the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a Circular Ring ,. 117 118 118 120 125 126 126 127 ...
Page 61
... circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any ...
... circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters are also equal , and each is double the radius . 4. An ARC is any ...
Page 62
... circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the cir- cumference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11 ...
... circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the cir- cumference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11 ...
Page 63
... circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its circumference into two equal parts . F E B For , let AFB be applied to AEB , the diameter AB remaining common ...
... circumference , into two equal parts . Let AEBF be a circle , and AB any diameter : then will it divide the circle and its circumference into two equal parts . F E B For , let AFB be applied to AEB , the diameter AB remaining common ...
Page 64
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB can not meet the circumference in more than two points . For , suppose that AB could meet the circumference in three points . By draw ...
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB can not meet the circumference in more than two points . For , suppose that AB could meet the circumference in three points . By draw ...
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence