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
... find the Diameter of a Circle , 116 To find the length of an Arc , 117 Area of a Circle , Area of a Sector , Area of a Segment , Area of a Circular Ring , 117 118 118 119 Area of the Surface of a Prism , Area of CONTENTS . vi.
... find the Diameter of a Circle , 116 To find the length of an Arc , 117 Area of a Circle , Area of a Sector , Area of a Segment , Area of a Circular Ring , 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 The Circle ...
... 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 The Circle ...
Page 79
... segment , are equal ; because they are each measured by half of the same arc BOC . B D 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 . B D 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 . M O A G -D B K M -D 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 O A G -D B K M -D 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 . A M K F M Ꮐ B -D EBD , is measured by and the inscribed angle For , the angle ABF , equal to half of the arc AKB ( P. XXI . ) ; AMB is measured by half of the same arc angle AMB is equal to the ...
... segment AMB be the segment required . A M K F M Ꮐ B -D EBD , is measured by and the inscribed angle For , the angle ABF , equal to half of the arc AKB ( P. XXI . ) ; AMB is measured by half of the same arc angle AMB is equal to the ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence