[ 3+1 3 
Two different methods have been taken by the 
writers who have treated of their properties ; the 
one, and the more antient, is to deduce them from 
the properties of the cone itfelf j the other is to con- 
lider the curves, as generated by the conffant motion 
of two or more ftrait lines moving in a given plane, 
by certain laws. 
There are various methods of generating thefe 
curve lines in piano ; one method will give fome 
properties very ealilyj but others, with much trouble: 
while, by another mode of defcription, fome pro- 
perties may be readily derived, which, by the for- 
mer, were not fo ealily come at : fo that it appears 
there may be a manner of defcribing the curves fimi- 
lar to the Conic Sections, by the motion of lines on 
a plane, which, in general, fhall produce the moll 
effential properties, with the greateft facility. 
That excellent mathematician, the late William 
Jones, Efq; F. R. S. had drawn up fome papers on 
the defcription of thefe curves, or lines of the fecond 
kind, very different from what he gave in his Synopfn 
'Palmariorum Mathcfeos , published in the year i 706 ; 
or from that of any other writer on this fubjedt. A 
copy of thefe papers he was pieafed to let me take 
about the year 1740. He had not finifhed them as 
he intended ; but, in their prefent Hate, they appear 
of too much confequence to be loPc ; as, it is much 
to be feared, his own copy, together with many 
other valuable papers, are ; and therefore, I am 
defirous of preierving them in the Philofophical 
Y v 2 Tranf- 
a 
