The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 11
... Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II ...
... Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II ...
Side 32
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . E For , if it be not parallel , AB and CD being produced shall meet ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . E For , if it be not parallel , AB and CD being produced shall meet ...
Side 33
... parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . IF a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the ...
... parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . IF a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the ...
Side 34
... parallel to the same straight line are parallel to one another . Let AB , CD , be each of them parallel to EF , AB is also parallel to CD . B K F K C- D E Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel ...
... parallel to the same straight line are parallel to one another . Let AB , CD , be each of them parallel to EF , AB is also parallel to CD . B K F K C- D E Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel ...
Side 35
... parallel to the given straight line BC . Which was to be done . PROP . XXXII . THEOR . Ir a side of any triangle be ... parallel ( 31. 1. ) to the straight line AB ; and be- cause AB is parallel to CE and AC meets them , the al- ternate ...
... parallel to the given straight line BC . Which was to be done . PROP . XXXII . THEOR . Ir a side of any triangle be ... parallel ( 31. 1. ) to the straight line AB ; and be- cause AB is parallel to CE and AC meets them , the al- ternate ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore