Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/205



To decribe a trapezium given in kind, the angles whereof may be o placed in repect offout right lines given by poition, that are neither all parallel among themelves nor converge to one common point, that the everal lines.. Pl. 13. Fig. 1.

Let the four right lines ABC, AD, BD, CE, be given by poition; the firt cutting the econd in A, the third in B, and the fourth in C; and uppoe a trapezium fghi is to be decribed, that may be imilarl to the trapezium FGHI; and whoe angle L equal to the given angle F, may touch the right line ABC; and the other angles g, h, i, equal to the other given angles G, H, I, may touch the other lines AD, BD, CE, repectively. Join FH, and upon FG, FH, FI decribe as many egments of circles FSG, FTH, FVI; the firt of which FSG may be capable of an angle equal to the angle BAD; the econd FTH capable of an angle equal to the angle CBD; and the third FVI of an angle equal to the angle ACE. But the egments are to be decribed towards thoe ides of the lines FG, FH, FI, that the circular order of the letters FSGF may be the ame as of the letters BADB, and that the letters FTHF may turn about in the ame order as the letters CDBC, and the letter FIVIF in the ame order