Cm] 
From a number propos d fubftradt an Unit, let that be 
Numerator, and to it add an Unit, let that be Denominator , 
and call that fradion N. 
Then Nf NfNfNfNfNfN^ &c. is 
I 3 5* 7 9 n n .J, 
Equal to half the Hyperbohck Logarithm fought* 
EXAMFLE in the Number 2. 
iV 
The Fracftion is I ^^1 3 333353= 3333331 
3, 37037c— = 1x^4,5 6 
5, A^.ii$i=~ ^230 
The Rank N is eafily 7? 4^72:^==: 
made by dividing evry 9, jog—— ^-^j^ 
precedingnumberby ^'^^^ 5* 
, 34^^733 
69314(56 which is 
The Hyperbolick Logarithm of 2 fought. 
1 want time to confider the pr^ mifes, but hope you will, 
(in regard you feem to think it ftrange that any difficulties 
Ihould remain about Cubicks that are not prefentlyrefolved) 
your confiderations wherein will be very acceptable and 
worthy publick view. 
Other Series in Print of Mercators^ &c, difpatch not as this 
doth neither thereby can the Logarithm of 1 be eafily made, 
but by making the Logarithms of fuch mixt numbers or fracti- 
ons that multiplied together make the refult 2 juft as 2x1 1^=3; 
whence having and finding that of i|, you prefently have 
the Logarithm of 3. 
2 2 A Cardanick^ Equation that is a Cubick one wanting the 
fecond term, may be multipHed or divided by a rank of con- 
tinual proportionals, fo as to render the coefficient of the 
roots canonick, that is, to make it the fame with the iEqua- 
tions of the Table, that find the Sine, Tangent, or Secant 
of the third part of that arch to which any Sine, Tangent, 
or Secant is propounded, and fo finding the roots in the ta- 
bles, thofe fought are thence obtained by Mukiphcation or 
Divifion- Yea, and the coefficient of the roots may in like 
manner be rendred an Unit and then the Refolvends fought 
in a table of the fums or differences of the Cubes of num- 
Bers and their roots, fliall help you to fuch roots, as multipli- 
ed or divided as aforefaid fhall be the true ones fought. 
23 It is an enquiry worth confideration, whether two of 
the roots of a biquadratick may not be kept conftant, and 
the 
