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 18
... distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn ...
... distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn ...
Page 26
... distance from A to C , measured on any broken line AB , BC , is greater than C B the distance measured on the straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ; which was to be proved . Cor . If from both ...
... distance from A to C , measured on any broken line AB , BC , is greater than C B the distance measured on the straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ; which was to be proved . Cor . If from both ...
Page 34
... distance is the longer . Let A be a given point , DE a given straight line , AB a perpendicular to DE , and AD , AC , AE oblique lines , BC being equal to BE , and BD greater than BC . Then AB is less than any of the oblique lines , AC ...
... distance is the longer . Let A be a given point , DE a given straight line , AB a perpendicular to DE , and AD , AC , AE oblique lines , BC being equal to BE , and BD greater than BC . Then AB is less than any of the oblique lines , AC ...
Page 35
... distance from a point to a line . Cor . 2. From a given point to a given straight line , only two equal straight lines can be drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the ...
... distance from a point to a line . Cor . 2. From a given point to a given straight line , only two equal straight lines can be drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the ...
Page 42
... distance between AB and CD , at the points F and E. Draw also FG . The lines FH and EG are parallel ( P. XVIII . ) : hence , the alternate angles HFG and FGE are equal ( P. XX . , C. 2 ) . The lines AB and CD are parallel , by ...
... distance between AB and CD , at the points F and E. Draw also FG . The lines FH and EG are parallel ( P. XVIII . ) : hence , the alternate angles HFG and FGE are equal ( P. XX . , C. 2 ) . The lines AB and CD are parallel , by ...
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Common terms and phrases
ABē ABCD ACē adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence