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 66
... radius equal to OA , it will pass through A , B , and C. Again , is the only point which is equally distant from A , B , and C for , DE contains all of the points which are equally distant from A and B ; and FG all of the points which ...
... radius equal to OA , it will pass through A , B , and C. Again , is the only point which is equally distant from A , B , and C for , DE contains all of the points which are equally distant from A and B ; and FG all of the points which ...
Page 68
... radius at its ex- tremity , it will be tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it will be perpendicular to the radius drawn to that point . 1 ° . Let BD be ...
... radius at its ex- tremity , it will be tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it will be perpendicular to the radius drawn to that point . 1 ° . Let BD be ...
Page 69
... radius CH perpendicular to the chord MP ; it will also be per- pendicular to NQ ( B. I. , P. XX . , C. 1 ) , and I will be at the middle point of the arc MHP , and also of the arc NHQ hence , MN , which is the difference of HN and HM ...
... radius CH perpendicular to the chord MP ; it will also be per- pendicular to NQ ( B. I. , P. XX . , C. 1 ) , and I will be at the middle point of the arc MHP , and also of the arc NHQ hence , MN , which is the difference of HN and HM ...
Page 77
... radius , the arc intercepted between the sides of the angle may be taken as the measure of the angle . In Geometry , the right angle which is measured by a quarter of a circumference , or a quadrant , is taken as a unit . If , therefore ...
... radius , the arc intercepted between the sides of the angle may be taken as the measure of the angle . In Geometry , the right angle which is measured by a quarter of a circumference , or a quadrant , is taken as a unit . If , therefore ...
Page 78
... radius CD . The external angle DCE , of the triangle DCA , is equal to the sum of the opposite interior angles CAD and CDA ( B. I. , P. XXV . , C. 6 ) . But , the triangle DCA being isosceles , the angles D and A are equal ; therefore ...
... radius CD . The external angle DCE , of the triangle DCA , is equal to the sum of the opposite interior angles CAD and CDA ( B. I. , P. XXV . , C. 6 ) . But , the triangle DCA being isosceles , the angles D and A are equal ; therefore ...
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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