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 vii
... the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a Circular Ring ,. 117 118 118 120 125 126 126 127 129 130 130 131 131 132 138 PAGE Area of the Surface of a Prism , Area CONTENTS . vii.
... the Length of an Arc , .. Area of a Circle , .... Area of a Sector , Area of a Segment ... Area of a Circular Ring ,. 117 118 118 120 125 126 126 127 129 130 130 131 131 132 138 PAGE Area of the Surface of a Prism , Area CONTENTS . vii.
Page 61
... SEGMENT is a part of a circle included between an arc and its chord . 7. A SECTOR is a part of a circle included between an arc and the two radii drawn to its extremities . 8. An INSCRIBED ANGLE is an angle whose vertex is BOOK III The ...
... SEGMENT is a part of a circle included between an arc and its chord . 7. A SECTOR is a part of a circle included between an arc and the two radii drawn to its extremities . 8. An INSCRIBED ANGLE is an angle whose vertex is BOOK III The ...
Page 81
... segment , are equal ; because they are each measured by half of the same arc BOC . B Cor . 2. Any angle BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circum- ference BOD , or by a ...
... segment , are equal ; because they are each measured by half of the same arc BOC . B Cor . 2. Any angle BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circum- ference BOD , or by a ...
Page 93
... segment that shall contain a given angle . Let AB be the given line . M B E G B K K Produce AB towards D ; at B construct the angle DBE equal to the given angle ; draw BO perpendicular to BE , and at the middle point G , of AB , BOOK ...
... segment that shall contain a given angle . Let AB be the given line . M B E G B K K Produce AB towards D ; at B construct the angle DBE equal to the given angle ; draw BO perpendicular to BE , and at the middle point G , of AB , BOOK ...
Page 94
... segment required . M M G B -D K For , the angle ABF , equal to EBD , is measured by half of the arc AKB ( P. XXI . ) ; and the inscribed angle AMB is measured by half of the same arc : hence , the angle AMB is equal to the angle EBD ...
... segment required . M M G B -D K For , the angle ABF , equal to EBD , is measured by half of the arc AKB ( P. XXI . ) ; and the inscribed angle AMB is measured by half of the same arc : hence , the angle AMB is equal to the angle EBD ...
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence