Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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Page 59
... 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 BOOK III The Circle, and the Measurement of Angles, 6889.
... 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 BOOK III The Circle, and the Measurement of Angles, 6889.
Page 60
From the Works of A.M. Legendre Adrien Marie Legendre. 8. An 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 in the circumfer- ence ...
From the Works of A.M. Legendre Adrien Marie Legendre. 8. An 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 in the circumfer- ence ...
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 lic 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 lic 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 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 equal ...
... inscribed in a segment less than a semi - circle , is 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 equal ...
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Common terms and phrases
ABĀ² ABCD adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed cone consequently convex surface cosec Cosine Cosine D Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area following RULE Formula frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC log cot log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle principle demonstrated prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar slant height solution sphere spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prism triedral angle upper base vertex volume whence write the following