Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/209

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fghi that may be ſimilar to the trapezium FGHI, and whoſe angles f, g, h, i, may touch the right lines given by poſition, AB, AD, BD, CE, ſeverally according to their order. And then about this trapezium deſcribe a trajectory, that trajectory will be ſimilar to the curve line FGHI.


Scholium.

This problem may be likewiſe conſtructed in the following manner. Joining FG, GH, HI, FI, (Pl. 13. Fig. 4.), produce GF to V, and join FH, IG, and make the angles CAK, DAL equal to the angles FGH, VFH. Let AK, AL meet the right line BD in K and L, and thence draw KM, LM of which let KM make the angle AKM equal to the angle GHI, and be it ſelf to AKM as HI is to GH; and let LN make the angle ALN equal to the angle FHI, and be it ſelf to AL, as HI to FH But AK, KM, AL, LN are to be drawn towards thoſe ſides of the lines AD, AK, AL, that the letters CAKMC, ALKA, DALND may be carried round in the ſame order as the letters FGHIF; and draw MN meeting the right line CE in i. Make the angle iEP equal to the angle IGF and let PE be to Ei, as FG to GI; and through P draw PQf that may with the right line ADE contain an angle PQE equal to the angle FIG, and may meet the right line AB in f, and join fi. But PE and PQ are to be drawn towards thoſe ſides of the lines CE, PE, that the circular order of the letters PEiP and PEQP may be the ſame, aſof the letters FGHIF, and if upon the line fi, in