( 1 5 ^ ) 
... 
fcription of Lines) and to determine the Dimen- 
irons of the Locus of P, and to lhew how to draw 
Tangents to it to determine its Afymptotes, and 
other Properties of it. I had obferved in 1719, 
that by increafing the Number of Poles and Angles 
beyond two, the Dimenfions of the Locus of P, did 
not rife above thofe of the Lines of the Second Or- 
der, while the Interfedions moved on Right Lines ; 
and therefore I did not think it of ufe to me then to 
take more Poles than two, fince by taking more, the 
Defcriptions became more complex without any 
Advantage. When the Interfedions are carried 
over Curve Lines, the Dimenfions of the Locus of 
P rife higher, but the Curves defcribed, have Tunffa 
'Duplicia, or Multiplicia , as well as when two 
Poles only are affumed ; and therefore this Specula- 
tion is more curious than ufeful. However, I fhall 
iubjoin feme of the Theorems that I found on this 
Subject concerning the Dimenfions of the Locus of 
P, and the drawing Tangents to it. 
1. If in Fig . 6. youfuppofe Q^and R to be car- 
ried over Curve Lines of the Dimenfions m and n 
relpedively, then the Point P may defcribe a Lo- 
cus of 2 m n Dimenfions. 
2, If in Fig . 8, you fuppofe L, Q, R, M, N, to 
be carried over Curve Lines of the Dimenfions w, //, 
r, s y ty refpedively, the Locus of P may arife to 
2 mnr st Dimenfions, but no higher ; and if in place 
of Lines revolving about the Poles, you ufe invari- 
ble Angles, the Dimenfions of the Locus of P will 
rife no higher. 
V 01 n . 
c muiKpi-r 0 
1 
