 | 1901 - 548 sider
...circle, show that the rectangle AE-EB is equal to the rectangle CE- ED. (6) If three straight lines be proportional, the rectangle contained by the extremes is equal to the square on the mean. From B, one of the vertices of the parallelogram ABCD a straight line is drawn, cutting the diagonal... | |
 | Association for the Improvement of Geometrical Teaching - 1903 - 342 sider
...is to the rectangle BD as the base OC is to the base OD, IV. 12. therefore OA : OB : : OC : OD. QED COR. If three straight lines are proportional, the...the square on the mean the lines are proportional. * Ex, 37. Apply Theor. 10 to shew that, if two chords of a circle intersect either within or without... | |
 | Euclid - 1904 - 488 sider
...A AYC = the A DAZ ; and similarly that the A BXC = the A BDZ.] 354 PROPOSITION 16. THEOREM. If four straight lines are proportional, the rectangle contained by the extremes is equal to the rectangle contained by the means. Conversely, if the, rectangle contained by the extremes is equal... | |
 | Euclid - 1908 - 456 sider
...DE, being equal to the rectangle BC, BD, is also given. PROPOSITION 1 7. If three straight lines be proportional, the rectangle contained by the extremes is equal to the square on the mean ; and, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines... | |
 | Walter Percy Workman - 1908 - 228 sider
...proportional to the squares of the radii of their circumcircles. 313. THEOREM [Ar.10]. — If four lines are proportional the rectangle contained by the extremes is equal to the rectangle contained by the means ; and conversely. Cf. § 285 (v). (i) Given that P : Q = S : T (Fig.... | |
 | Kevin L. SJ Flannery - 2001 - 364 sider
...constructed using lines AB and CB, since, as is proved at Elem. vi,17, "if three straight lines be proportional, the rectangle contained by the extremes is equal to the square on the 3o. "AKpov KCU. u,eow \6yov eOOeta TeTufjcrfku XeyeTa1, oTav g 1ix; r[ 6\r] rrpoc TO a, oi1Tux, TO... | |
 | Chris Pritchard - 2003 - 572 sider
...have those angles equal, the sides about which are proportional. Prop. 17: If three straight lines be proportional, the rectangle contained by the extremes is equal to the square on the mean; and, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines... | |
 | Peter M. Engelfriet - 1998 - 516 sider
...Jt0!BHiiMffi»}gft:i:ft»**s±aft# J&^B£»J§F'3j|IftJ&**»±itLft}jJ&^BP = » &* it Heath If three straight lines be proportional, the rectangle contained by the extremes is equal to the square on the mean; and, if the rectangle contained by the extremes be equal to the square on the mean, the straight lines will... | |
 | Euclid - 452 sider
...AC), DE, being equal to the rectangle BC, BD, is also given. PROPOSITION 17 If three straight lines be proportional, the rectangle contained by the extremes is equal to the square on the mean; and, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines... | |
 | Edinburgh Mathematical Society - 1900 - 410 sider
...AC = AD : AE. Cor. If AC be equal to AD, the proposition may be stated : If three straight lines be proportional, the rectangle contained by the extremes is equal to the square on the mean. Conversely : if the rectangle contained by the extremes be equal to the square on the mean, the three... | |
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If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. 
