Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 7
... of a Circle , To find the length of an Arc , Area of a Circle , Area of a Sector , Arca of a Segment , Area of a Circular Ring , .. 116 116 117 117 118 118 ... 119 ... Area of the Surface of a Prism , Area of CONTENTS . vi.
... of a Circle , To find the length of an Arc , Area of a Circle , Area of a Sector , Arca of a Segment , Area of a Circular Ring , .. 116 116 117 117 118 118 ... 119 ... Area of the Surface of a Prism , Area of CONTENTS . vi.
Page 59
... SEGMENT is a part of a circle included 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 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 within an an arc and the radii drawn to its extremities . 8. An INSCRIBED ANGLE is an angle whose vertex is BOOK III The ...
Page 79
... segment , are equal ; because they are each measured by half of the same arc BOC . D Cor . 2. Any angle BAD , in ... segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi ...
... segment , are equal ; because they are each measured by half of the same arc BOC . D Cor . 2. Any angle BAD , in ... segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi ...
Page 91
... segment that shall contain a given angle . Let AB be the given line . M / E G B -D O. -D 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 , BOOK ...
... segment that shall contain a given angle . Let AB be the given line . M / E G B -D O. -D 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 , BOOK ...
Page 92
... segment AMB be the segment required . M 右 OF A G B E G -D K For , the angle ABF , equal to half of the arc AKB ( P. XXI . ) ; K EBD , is measured by and the inscribed angle AMB is measured by half of the same arc : hence , the angle ...
... segment AMB be the segment required . M 右 OF A G B E G -D K For , the angle ABF , equal to half of the arc AKB ( P. XXI . ) ; K EBD , is measured by and the inscribed angle AMB is measured by half of the same arc : hence , the angle ...
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Common terms and phrases
ABē 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