Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 18
... distance between any two points is mea- sured on the straight line which joins them . 13. Through the same point , only one line can be drawn parallel to a given line .. POSTULATES . 1. A straight line can be drawn between any two ...
... distance between any two points is mea- sured on the straight line which joins them . 13. Through the same point , only one line can be drawn parallel to a given line .. POSTULATES . 1. A straight line can be drawn between any two ...
Page 26
... distance from A AC . 2 to C , measured on any broken line AB , BC , A is greater than 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 ...
... distance from A AC . 2 to C , measured on any broken line AB , BC , A is greater than 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 ...
Page 34
... distance will be 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 will AB be less than any of the oblique ...
... distance will be 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 will AB be less than any of the oblique ...
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. 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 hypothesis : hence ...
... distance between AB and CD , at the points F and E. 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 hypothesis : hence ...
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Common terms and phrases
ABĀ² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following