The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 σελίδες |
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Σελίδα 28
... CD , make the alternate angles AEF , EFD , equal to one another ; AB is parallel to CD . A E B G C F Ꭰ For , if it be not parallel , AB and CD being produced , shall meet either towards B , D , or towards A , C ; let them be ...
... CD , make the alternate angles AEF , EFD , equal to one another ; AB is parallel to CD . A E B G C F Ꭰ For , if it be not parallel , AB and CD being produced , shall meet either towards B , D , or towards A , C ; let them be ...
Σελίδα 29
... parallel to CD . Again , because the angles BGH , GHD , are equal ( Hyp . ) to two right angles , and that AGH , BGH ... parallel to CD . Wherefore if a straight line , & c . Q.E.D. PROP . XXIX . THEOREM . If a straight line fall ...
... parallel to CD . Again , because the angles BGH , GHD , are equal ( Hyp . ) to two right angles , and that AGH , BGH ... parallel to CD . Wherefore if a straight line , & c . Q.E.D. PROP . XXIX . THEOREM . If a straight line fall ...
Σελίδα 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 parallel to CD . B E H F C K 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 E H F C K Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel ...
Σελίδα 33
... parallel . Let AB , CD , be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD , are also equal and parallel . A B D Join BC ; and because AB is parallel to CD , and BC meets ...
... parallel . Let AB , CD , be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD , are also equal and parallel . A B D Join BC ; and because AB is parallel to CD , and BC meets ...
Σελίδα 34
Euclid, Samuel A. GOOD. Because AB is parallel to CD , and BC meets them , ( I. 29. ) 1. The alternate angles ABC , BCD , are equal to one another ; and because AC is parallel to BD , and BC meets them , ( I. 29. ) 2. The alternate ...
Euclid, Samuel A. GOOD. Because AB is parallel to CD , and BC meets them , ( I. 29. ) 1. The alternate angles ABC , BCD , are equal to one another ; and because AC is parallel to BD , and BC meets them , ( I. 29. ) 2. The alternate ...
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AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle