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 59
... its chord . 7. A SECTOR is a part of a circle included by 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, 8889.
... its chord . 7. A SECTOR is a part of a circle included by 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, 8889.
Page 60
... 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 circum- ference . 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 circum- ference . The sides are chords . 10. A SECANT is a straight ...
Page 77
... 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 78
... inscribed angle , and let the centre lie within it then will the angle be 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 ...
... inscribed angle , and let the centre lie within it then will the angle be 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 ...
Page 79
... inscribed in a segment less than a semi - circle , is B B obtuse ; for it is measured by half the arc BAC , greater than a semi - circumference . Cor . 4. The opposite angles A and C , of an inscribed quadrilateral ABCD , are together ...
... inscribed in a segment less than a semi - circle , is B B obtuse ; for it is measured by half the arc BAC , greater than a semi - circumference . Cor . 4. The opposite angles A and C , of an inscribed quadrilateral ABCD , are together ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence