Elements of Geometry and Trigonometry |
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Page 65
... circumference may be made to pass , and but one . Let A , B , B , and C , be any three points , not in a straight line : then may one circumference be made to pass through them , and but one . Join the points by the lines AB , BC , and ...
... circumference may be made to pass , and but one . Let A , B , B , and C , be any three points , not in a straight line : then may one circumference be made to pass through them , and but one . Join the points by the lines AB , BC , and ...
Page 66
... circumference may be made to pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there would be two ...
... circumference may be made to pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there would be two ...
Page 68
... circumference at the B C E D 0 point ; it is , therefore , tangent to it at that point ( D. 11 ) ; which was to be proved . 2o . Let BD be tangent to the circle at A : then will it be perpendicular to CA. For , let E be any point of the ...
... circumference at the B C E D 0 point ; it is , therefore , tangent to it at that point ( D. 11 ) ; which was to be proved . 2o . Let BD be tangent to the circle at A : then will it be perpendicular to CA. For , let E be any point of the ...
Page 69
... circumference . There may be three cases : both parallels may be secants ; one may be a secant and the other a tangent ; or , both may be tangents . 1o . Let the secants AB AB and DE be parallel then will the intercepted arcs MN and PQ ...
... circumference . There may be three cases : both parallels may be secants ; one may be a secant and the other a tangent ; or , both may be tangents . 1o . Let the secants AB AB and DE be parallel then will the intercepted arcs MN and PQ ...
Page 70
... circumferences intersect each other , the points of in tersection will be in a perpendicular to the straight line ... circumference whose centre is D , they are tant from D : hence , CD is perpendicular to AB middle point ( B. I. , P ...
... circumferences intersect each other , the points of in tersection will be in a perpendicular to the straight line ... circumference whose centre is D , they are tant from D : hence , CD is perpendicular to AB middle point ( B. I. , P ...
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Common terms and phrases
ABCD ACĀ² 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 line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence