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
... INSCRIBED ANGLE is an angle whose vertex is BOOK III The Circle, and the Measurement of Angles, 8889.
... 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
... angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides ...
... angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is measured by half of the arc included between its sides ...
Page 78
... angle DCE , of the triangle DCA , is equal to the sum of the opposite interior angles CAD and CDA ( B , L , P. XXV ... inscribed angle , and let the centre lie within it then will the angle be measured by half of the arc BED : For , draw ...
... angle DCE , of the triangle DCA , is equal to the sum of the opposite interior angles CAD and CDA ( B , L , P. XXV ... inscribed angle , and let the centre lie within it then will the angle be measured by half of the arc BED : For , draw ...
Page 79
... angles BAC , BDC , BEC , inscribed in the same segment , are equal ; because they are each measured by half of the same arc BOC . C Cor . 2. Any angle BAD , in- scribed in a semi - circle , is a right an- gle ; because it is measured by ...
... angles BAC , BDC , BEC , inscribed in the same segment , are equal ; because they are each measured by half of the same arc BOC . C Cor . 2. Any angle BAD , in- scribed in a semi - circle , is a right an- gle ; because it is measured by ...
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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