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 5
... 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 ...
Σελίδα 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 . A E B G C F Ꭰ For , if it be not parallel , AB and CD being ...
... 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 . A E B G C F Ꭰ For , if it be not parallel , AB and CD being ...
Σελίδα 29
... parallel to CD . Wherefore if a straight line , & c . Q.E.D. PROP . XXIX . THEOREM . If a straight line fall upon two parallel straight lines , it makes the alter- nate 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 . THEOREM . If a straight line fall upon two parallel straight lines , it makes the alter- nate angles equal to one another ; and the exterior angle equal to the ...
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 31
... parallel to a given straight line . Let A be the given point , and BC the given straight line ; it is re- quired to draw a straight line through the point 4 , parallel to the straight line BC . In BC take any point D , and join AD ; and ...
... parallel to a given straight line . Let A be the given point , and BC the given straight line ; it is re- quired to draw a straight line through the point 4 , parallel to the straight line BC . In BC take any point D , and join AD ; and ...
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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