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 CorrectedDesilver & Thomas, 1834 - 419 sider |
Inni boken
Resultat 1-5 av 100
Side 10
... 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 28
... 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 29
... parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . Ir 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 . Ir 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 30
... parallel to the same straight line are parallel to one another . Let AB , CD , be each of them parallel to EF , AB is also paral- lel to CD . A G B Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight ...
... parallel to the same straight line are parallel to one another . Let AB , CD , be each of them parallel to EF , AB is also paral- lel to CD . A G B Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight ...
Side 31
... parallel ( si . 1. ) to the straight line AB ; and be- cause AB is parallel to CE and AC meets them , the al- ternate angles BAC , ACE are equal ( 29. 1. ) Again ; B because A is parallel to CE , and BD falls upon them , the exte- rior ...
... parallel ( si . 1. ) to the straight line AB ; and be- cause AB is parallel to CE and AC meets them , the al- ternate angles BAC , ACE are equal ( 29. 1. ) Again ; B because A is parallel to CE , and BD falls upon them , the exte- rior ...
Andre utgaver - Vis alle
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
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 point given ratio given straight line gnomon greater join less Let ABC multiple opposite parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third tiple triangle ABC triplicate ratio vertex wherefore