( ) 
drawing Tangents to it, and determining its Afymp- 
totes. I alfo drew from it at that time a Method 
of defcribing a Conick Se&ion through live given 
Points a . This encouraged me to fubftitute Curves 
for the Right Lines, to fee if by this Method 1 could 
be enabled to carry on my Theorems about the De- 
fcriptions of Lines through given Points to the 
higher Orders of Lines Some of the Theorems I 
found at that time, I now fend you. In Novem- 
ber 17x1, looking into Sir Ifaac's Trincipia , I faw 
that the Defcription of the Conick Section by three 
Right Lines, moving as above, about three Poles,, 
couid be immediately drawn from his xoth Lemma, 
which itfelf is a Cafe of this Defcription. This gra- 
dually led me to feek Geometrical Demonftrations 
for the whole, as far as it related to the Conick 
Sedions. I fend you fome Leaves of this Paper 
dated at Nancy , November 1711. Since that time, 
I have not added much to this Subject, but what 
relates to the drawing Tangents, determining the 
Afymptotes, and the Tuntta \ Duplica , or MuLtipli- 
cia of thefe Curves. I confidered it the lefs, that I 
did not find it more advantageous in any refpedls, 
than the Method I had confidered in my Book, or 
more genera!. 
In 1727 I added to a Chapter in my Algebra, 
which is very pubiick in this Place, an Algebraick 
Demonfiration of the Locus, when three Poles are 
employed ; and the Method of defcribing a Conick 
■ <■ , ~ - •• : ; . ? . - -r • 
a The Paper on this Subject I have t is dated July 31, 1722, at Sea, 
lung then m my way to London, going for Cambray, 
Section 1 
