( 1 45 ) 
leded this at that time, as of no ufe to me j con- 
fining my felf to two Poles only, and varying the 
Motions of the Angles as you find them in my 
Book. I found this by inquiring in how many 
Points the Locus could cut a Right Line drawn in 
its Plane, and found, by a Method I often ufe in my 
Book, that it could meet it in two Points only. 
Having found then, that three or more Poles, 
were of no more Service than two, while the In- 
terfedions were carried over fixed Right Lines ; I 
thought it needlefs to profecute that Matter then, 
fince by increafing the Number of Poles, my De- 
fcriptions would become more complex without any 
Advantage. Butin June or July, iyn, upon the - 
Hint Igot from Mr. Sympfon of Mr. ‘Pappus’s Po- 
rifms, I faw that what he has there ingenioufly de- 
monftrated, might be confidered as a Cafe of the 
above-mentioned Defcription of a Conick Sedion, 
by the Rotation of any Number of Angles about 
as many Poles 5 the Interfedions of their Legs, in 
the mean time, being carried over fixed Right Lines, 
excepting that of two of them which defcribes the 
Locus. For by fubftituting Right Lines in place of 
the Angles, in certain Situations of the Poles and 
of the fixed Right Lines, the Locus becomes a Right 
Line; as for Example, in the Cafe of three Poles, 
when thefe three are in one Right Line, in which 
Cafe the Locus is a Right Line, which is a Cafe of 
the Porifm. 
’Twas this led me to confider this Subjed anew; 
and firft I demonftrated the Locus to be a Conick 
Sedion algebraically ; and found Theorems for 
T 2, drawing 
