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
... To find the Diameter of a Circle , 116 To find the length of an Arc , Arca of a Circle , Area of a Sector , ..... Area of a Segment , .... Area of a Circular Ring ,. 117 117 118 118 119 PAGE . Area of the Surface of a Prism , CONTENTS . vi.
... To find the Diameter of a Circle , 116 To find the length of an Arc , Arca of a Circle , Area of a Sector , ..... Area of a Segment , .... Area of a Circular Ring ,. 117 117 118 118 119 PAGE . Area of the Surface of a Prism , 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 by 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 by an arc and the two 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 . C 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 . C 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 . O -D G B 阻 K Produce AB towards D ; DBE equal to the given angle ; at B construct the angle draw BO perpendicular to BE , and at the middle point G , BOOK III . 91.
... segment that shall contain a given angle . Let AB be the given line . O -D G B 阻 K Produce AB towards D ; DBE equal to the given angle ; at B construct the angle draw BO perpendicular to BE , and at the middle point G , BOOK III . 91.
Page 92
... segment AMB be the segment required . M M VE G -D 0 . A -D K For , the angle ABF , equal to half of the arc AKB ( P. XXI . ) ; AMB is measured by half of the EBD , is measured by and the inscribed angle same arc : hence , the angle AMB ...
... segment AMB be the segment required . M M VE G -D 0 . A -D K For , the angle ABF , equal to half of the arc AKB ( P. XXI . ) ; AMB is measured by half of the EBD , is measured by and the inscribed angle same arc : hence , the angle AMB ...
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Common terms and phrases
ABē ACē 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