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

 fghi that may be imilar to the trapezium FGHI, and whoe angles f, g, h, i, may touch the right lines given by poition, AB, AD, BD, CE, everally according to their order. And then about this trapezium decribe a trajectory, that trajectory will be imilar to the curve line FGHI.

This problem may be likewie contructed 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 elf to AKM as HI is to GH; and let LN make the angle ALN equal to the angle FHI, and be it elf to AL, as HI to FH But AK, KM, AL, LN are to be drawn towards thoe ides of the lines AD, AK, AL, that the letters CAKMC, ALKA, DALND may be carried round in the ame 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 thoe ides of the lines CE, PE, that the circular order of the letters PEiP and PEQP may be the ame, aof the letters FGHIF, and if upon the line fi, in