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 61
... its chord . 7. A SECTOR is a part of a circle included between an arc and the two radii drawn to its extremities . 8. An INSCRIBED ANGLE is an angle whose vertex is BOOK III The Circle, and the Measurement of Angles,
... its chord . 7. A SECTOR is a part of a circle included between an arc and the two radii drawn to its extremities . 8. An INSCRIBED ANGLE is an angle whose vertex is BOOK III The Circle, and the Measurement of Angles,
Page 62
... INSCRIBED ANGLE is an angle whose vertex is in the 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 ...
... INSCRIBED ANGLE is an angle whose vertex is in the 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 ...
Page 79
... inscribed angle is measured by half of the arc included between its sides . There may be three cases : the centre of the circle may lie on one of the sides of the angle ; it may lie within the angle ; or , it may lie without the angle ...
... inscribed angle is measured by half of the arc included between its sides . There may be three cases : the centre of the circle may lie on one of the sides of the angle ; it may lie within the angle ; or , it may lie without the angle ...
Page 80
... inscribed angle , and let the centre lie within it : then the angle is measured by half of the arc BED . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB by ...
... inscribed angle , and let the centre lie within it : then the angle is measured by half of the arc BED . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB by ...
Page 81
... inscribed in the same segment , are equal ; because they are each measured by half of the same arc BOC . B Cor . 2. Any angle BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circum- ference ...
... inscribed in the same segment , are equal ; because they are each measured by half of the same arc BOC . B Cor . 2. Any angle BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circum- ference ...
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Common terms and phrases
AB² ABCD AC² 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