The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Σελίδα 24
and D , in the point G. Then GEF is a triangle , and its exterior angle AEF is greater ( I. 16 ) than its interior and opposite angle EFG . But the angle A EF is equal ( Hyp . ) to the angle EF G. Therefore the angle A EF is both ...
and D , in the point G. Then GEF is a triangle , and its exterior angle AEF is greater ( I. 16 ) than its interior and opposite angle EFG . But the angle A EF is equal ( Hyp . ) to the angle EF G. Therefore the angle A EF is both ...
Σελίδα 25
If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; the exterior angle equal to the interior and opposite angle upon the same side of the straight line ; and the two interior ...
If a straight line fall upon two parallel straight lines , it makes the alternate angles equal to one another ; the exterior angle equal to the interior and opposite angle upon the same side of the straight line ; and the two interior ...
Σελίδα 27
falls upon them , the exterior angle E C D is equal ( I. 29 ) to the interior and opposite angle A B C. But the angle A CE was shown to be equal to the angle BAC . Therefore the whole exterior angle A C D is equal ( Ax . 2 ) to the two ...
falls upon them , the exterior angle E C D is equal ( I. 29 ) to the interior and opposite angle A B C. But the angle A CE was shown to be equal to the angle BAC . Therefore the whole exterior angle A C D is equal ( Ax . 2 ) to the two ...
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A B C ABCD altitude applied base bisected Book Cassell's centre circle circumference cloth coincide common cone Const contained Corollary cylinder definition demonstration described diagonal diameter divided double draw Edition equal equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half Illustrated inscribed interior join less magnitudes manner meet multiple parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proportionals proposition proved pyramid ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle sphere square straight lines A B taken THEOREM third touch triangle triangle ABC twice vertex Vols Wherefore whole