The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Σελίδα 15
E A For if the angle CBA be equal to the angle ABD , each of them is a right angle ( Def . 10 ) . But if the angles CBA , ABD , be unequal , from the point B draw BE at right angles ( I. 11 ) to CD . Therefore the angles CBE , EBD ( Def ...
E A For if the angle CBA be equal to the angle ABD , each of them is a right angle ( Def . 10 ) . But if the angles CBA , ABD , be unequal , from the point B draw BE at right angles ( I. 11 ) to CD . Therefore the angles CBE , EBD ( Def ...
Σελίδα 27
Therefore also the three angles C A B , ABC , A CB are equal ( Ax . 1 ) to two right angles . Wherefore , if a side of any triangle be produced , & c . Q. E. D. COR . 1. - All the interior angles of any rectilineal figure together with ...
Therefore also the three angles C A B , ABC , A CB are equal ( Ax . 1 ) to two right angles . Wherefore , if a side of any triangle be produced , & c . Q. E. D. COR . 1. - All the interior angles of any rectilineal figure together with ...
Σελίδα 76
76 EUCLID'S ELEMENTS . are together less than two right angles ( I. 17 ) , and BAC has been proved to be a right angle . Therefore ABC is less than a right angle . Wherefore the angle in a segment ABC greater than a semicircle is less ...
76 EUCLID'S ELEMENTS . are together less than two right angles ( I. 17 ) , and BAC has been proved to be a right angle . Therefore ABC is less than a right angle . Wherefore the angle in a segment ABC greater than a semicircle is less ...
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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