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22. Corollary. From the above demon-stration it is manifest that if EF=FG, FIwill be a mean proportional between ECand GK; and that, if Ejf and fg be equal,fi will be a mean proportional between ECand gh

23. Corollary. If through /, k, i, C, I, K,L a curve be described, it will be the log-arithmic curve.

Fig. 26. 24. Problem. Given the tension at the

vertex, to construct an indefinite catenary.

On any indefinite vertical line BD, makeBA perpendicular, and equal to the giventension at the vertex, through A draw AC,making the angle A=56°"28 / and meetingBD in C, with the centre C and distanceCA , cut BD in D; then, through D, drawDE parallel to BA meeting AC producedin E; produce DE, so that DF=DE andtake CV=BA: then, by Case I., article19., shall E, V, and F, be three points inthe proposed catenary; and LCK, drawnthrough C parallel to BA or ED, will be its

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