($69) 
and Records ) can never happen alike. And thefe remarqueg 
being given , the year of the fulian Period is by the former Rule 
infallibly found. 
This Fmodk ufed by the faid Arch-bifliop in hk Anmls^ and is 
by him accounted to exceed the hgeoiiliQ FForld 709, years, 
Thofe^ that defire further fatisfadion about zAIras^ Epochasl 
and Periods^ may repaire to many Authors, and among them to 
Gregorjs Pi^ftkumdy in Englifh , Jiehici Chronologia ^ 't/Egidii 
Strmchii Brevimum chrmdogicnm^v^ho is one of the lateft Au- 
thoi^. 
Now as to the Prohkme it felf, it may be thus propofed. 
: Jnj Numher of Dwi[ors , together with their Remainders after 
I)ivi(ion^ being frofafej^ 1 0 find-the j)iq^^^^ 
% : This thus geoerally propofed is no new Probleme^ and was re- 
folved long fince, by ^ohn Gejfius , by the help of particular Mul=- 
tipliers, fuch as thofe above-mentioned, and publifht by Alftedi- 
us in his Encyclol^.ddi a in J^. 1630^ md by Fan- Schooten in bi^. « 
Mifcellames, 
We (hall clear up, 1^vhat Authors haveomitted concerning the 
Definition and Demonstration of fuch fixed Multipliers, ^c. An J 
therefore fay, that each Multiplier is relative to.theDivifor^ to 
which it belongs, and thus define it § 
It is fuch a Number^ as Dmiied hftherefisf the Divifers, or 
their FroduEl , the Remainder is o^ hut Divided bj its om Divifor ^ 
the Remainder is an Unit, 
We require the Divifors propofed to be Primitive each to 0- 
ther, i, e, that no two or more of them can be reduced to lefler 
terms by any common Divifor. For, if fo^ the Queftion may be 
pfsihle in it felf^ but not refolvable by help of fuch Multiphers ^ 
fuch being impoffible to be found. The reafon is, becaufe the 
Product of an Odd and an Even Number is alvvayes Even^ and 
that divided byjri Even Number^ leaves either Nothings or ao; 
EvcnKumber^ ' 5 t 
T^ r Tte Multipliers -relati¥e?^^^^^ 
Dmfors 1 9>, hereto are ^ h'""^ 
ThQ Definition affords light enough for the difcovery of thefe 
-i^um.bei$, To i^ftance in the firfi : The Produii; of and 15 
is- 
