Lemma XXVII.
To deſcribe a trapezium given in kind, the angles whereof may be ſo placed in reſpect offout right lines given by poſition, that are neither all parallel among themſelves nor converge to one common point, that the ſeveral lines.. Pl. 13. Fig. 1.
Let the four right lines ABC, AD, BD, CE, be given by poſition; the firſt cutting the ſecond in A, the third in B, and the fourth in C; and ſuppoſe a trapezium fghi is to be deſcribed, that may be ſimilarl to the trapezium FGHI; and whoſe 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, reſpectively. Join FH, and upon FG, FH, FI deſcribe as many ſegments of circles FSG, FTH, FVI; the firſt of which FSG may be capable of an angle equal to the angle BAD; the ſecond FTH capable of an angle equal to the angle CBD; and the third FVI of an angle equal to the angle ACE. But the ſegments are to be deſcribed towards thoſe ſides of the lines FG, FH, FI, that the circular order of the letters FSGF may be the ſame as of the letters BADB, and that the letters FTHF may turn about in the ſame order as the letters CDBC, and the letter FIVIF in the ſame order
