C ^5 ) 
Which IS the Logarithm of 2; to thirty two places^ and ob- 
tained by five Diviiions with very fmall Divifirsy all which is 
much lefs work than iioiply multiplying the Series into the 
faid Mukipiicator 43429 5cc. 
Before I pals on to the con^erfe of this Problem^ or to fhew 
how to find the Number appertaining to a Logarithm afligned, 
it will be requifite to advercife the Reader^ that thsre is a fmall 
miftake in the aforefaid Mr. James Gregorfs Vera Quadratura 
Circuit & HjperhoU, publilhed at Padua Anno 1667, wherein 
he applies his Quadrature of the Hyperbola to the making 
the Logarithms ; In pag, 48. he gives the Computation of 
the Lord iV^p^ir's Logarithni of lo^ to five and twenty pla- 
ces, and finds it z^oi^^ ^o()2^<)^o^^ 62^01^^-] o inftead of 
a3o25'85'o92994o4j684oi799ij erring in the eighteenth Fi- 
gure, as I was affured upon my own Examination of the 
Number I here give you, and by comparifon thereof with 
the fame wrought by another hand, agreeing therewith to 
57 of the 60 places. Being defirous to be fatisfied how this 
difference arofe, I took the no fmall trouble of examining 
Mr. Gregorfs Work, and at length found that in the infcri- 
bed Feljgon of ^12 Sides, in the eighteenth Figure was a o 
inftead of 9, which being rec^^ified, and the fubfequent Work 
corrected therefrom, the refult did agree to a Unite with ouf 
Number. And this I propofe not to Cavil at an eafie mi- 
ftake in managing of lb vait Numbers, efpecially by a Hand 
that has fo well deferved of the Mathematical Sciences, but 
to fhew the exad coincidence of two fb very differing Me- 
thods to make Logarithms, which might btherwife have been 
queftioned. 
From the Logarithm given to find what ratio it expreffes, 
is a Problem that has not been (b much confidered as the for- 
mer, but which is folved with the like eafe, and demonftra- 
ted by a like Procefs, from the fame general Theorem of 
Mr. Nemon : For as. the Logarithm of the ratio of i to i+^ 
was proved to be i — ij and that of the ratio of i 
I 
to I — ^ to be I • — 1 — ^1 : fo the Logarithm , which we 
will from. henceforth call L, being given, i +L will be equal 
to I -j-^l ^ in the one cafe ; and i — L will be equal to 
I — f 
