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
... between an arc and its chord .. 7. A SECTOR is a part of a circle included within an an arc and the radii drawn to its extremities . 8. An INSCRIBED ANGLE is an angle whose vertex is The Circle, and the Measurement of Angles, 6899.
... between an arc and its chord .. 7. A SECTOR is a part of a circle included within an an arc and the radii drawn to its extremities . 8. An INSCRIBED ANGLE is an angle whose vertex is The Circle, and the Measurement of Angles, 6899.
Page 60
... INSCRIBED ANGLE is an angle whose vertex is in the circumference , and whose sides are chords . о 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 ...
... INSCRIBED ANGLE is an angle whose vertex is in the circumference , and whose sides are chords . о 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 ...
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 ...
... 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 ...
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 altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence