 | William Alexander Myers - Circle-squaring - 1873 - 238 pages
...equal to D; therefore A is to B as D is to C. [ V. 7.] But if four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; [VI. 16.] therefore the rectangle contained by A and C is equal to the rectangle contained by B and... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...not contain the same integral number of those parts; but they do (by the definition); PROPOSITION V. If four straight lines are proportional the rectangle contained by the extremes is equal to that contained by the means. Let the four straight lines a, b, c, d be proportional. Then rect. (a,... | |
 | William Alexander Myers - Circle-squaring - 1874 - 207 pages
...equal to D', therefore A is to B as D is to C. [7. 7.] But if four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; [ VI. 16.] therefore the rectangle contained by A and C is equal to the rectangle contained by B... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...vertically opposite. PROP. XII.— THEOREM. (Euc. VI. 16, 17.) If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; and conversely. Let AB, CD, E and P be four straight lines which are proT: F portionals; it is required... | |
 | Euclides - 1874 - 342 pages
...Therefore, equal triangles, &c. QED PROPOSITION 16. — Theorem. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; and conversely, if the rectangle contained by the extremes be equal to the rectangle contained by the... | |
 | Richard Wormell - 1876 - 268 pages
...FE = GB BF; therefore А В : FE = В С FE; THEOREM LXXVI. // four straight lines be proportionals the rectangle contained by the extremes is equal to the rectangle contained by the means. Сonversely, if the rectangle contained by the extremes be equal to the rectangle contained by the... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...equal to the rectangle contained by the means the four straight lines are proportional. COR. If three straight lines are proportional the rectangle contained by the extremes is equal to the square on the mean ; and, conversely, if the rectangle contained by the extremes of three straight... | |
 | D. Tierney - 1877 - 126 pages
...and therefore BD : EF :: BE : EC, which was to be proved. 9. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. On a given straight line describe an isosceles triangle equal to a given triangle. Let EF (fig. 6)... | |
 | Āryabhaṭa - 1878 - 100 pages
...or the rectangle AB. AB." PROP. xxu. THEOREM. (E. 6. 16).. If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; and conversely, if two rectangles are equal, the straight lines containing them are proportionals.... | |
 | London univ, exam. papers - 1878 - 164 pages
...(3)^ = 8,^ = 6. (4)^ = 4,^ = 3,2=2. 10. (a) TA, Art. 359. (b) If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; and conversely (Euc. VI. 16). (f) Now T = -> hence -£x-,=-xr. *'•*-. bc bocb a2 ab 9 ,, -b2=w... | |
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If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means. 
