Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 59
... 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 BOOK III The Circle, and the Measurement of Angles,
... 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 BOOK III The Circle, and the Measurement of Angles,
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 ...
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 ...
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 die 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 die 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 . Then , from what has just measured by half of DE , EB : hence , BAD , which For , draw the diameter AE . been proved , the angle ...
... inscribed angle , and let the centre lie within it then will the angle be measured by half of the arc BED . Then , from what has just measured by half of DE , EB : hence , BAD , which For , draw the diameter AE . been proved , 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
ABĀ² 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