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 65
... passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in the same straight line , one circumference may be made to pass , and ...
... passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in the same straight line , one circumference may be made to pass , and ...
Page 66
... pass through these points , and " but one ; which was to be proved . only point Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there " would be two circumferences passing ...
... pass through these points , and " but one ; which was to be proved . only point Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there " would be two circumferences passing ...
Page 72
... pass through a common point of that line , are tangent to each other at that point . And if a straight line be drawn tangent to one of the circles at their common point , it will be tangent to them all at that point . Scholium . From ...
... pass through a common point of that line , are tangent to each other at that point . And if a straight line be drawn tangent to one of the circles at their common point , it will be tangent to them all at that point . Scholium . From ...
Page 77
... without the angle . 1o . Let EAD be an inscribed an- gle , one of whose sides AE passes through the centre : then will it be measured by half of the arc DE . E For , draw the radius CD . The external angle BOOK III . 77.
... without the angle . 1o . Let EAD be an inscribed an- gle , one of whose sides AE passes through the centre : then will it be measured by half of the arc DE . E For , draw the radius CD . The external angle BOOK III . 77.
Page 89
... pass a circumference through any three points not in a straight line . If the points are vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle ...
... pass a circumference through any three points not in a straight line . If the points are vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle ...
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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