Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 7
... 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 , Arca of a Segment , Area of a Circular Ring , .. 116 116 117 117 118 118 ... 119 ... Area of the Surface ...
... 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 , Arca of a Segment , Area of a Circular Ring , .. 116 116 117 117 118 118 ... 119 ... Area of the Surface ...
Page 59
... 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 . an 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 . an 4. An ARC is any ...
Page 60
... circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are in the circumfer- ence , and whose sides are chords . 10. A SECANT is a straight line which · cuts the circumference in two points ...
... circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are in the circumfer- ence , and whose sides are chords . 10. A SECANT is a straight line which · cuts the circumference in two points ...
Page 61
... 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 . A E 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 . A E For , let AFB be applied to AEB , the diameter AB remaining common ...
Page 62
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB cannot meet the circumference in more than two points . For , suppose that they could meet in three points . We should then have ...
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB cannot meet the circumference in more than two points . For , suppose that they could meet in three points . We should then have ...
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Common terms and phrases
AB² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following