c*Ml 
for the Inveftigation of the Relations of Quantities, to 
have recourfe to very hard Hypothefes; fuch as that of 
Number infinite and indeterminate } and that of Mag- 
nitudes in Statu fieri, exifting in a potential Manner, 
which are actually of no Bignefs. And others, whofe 
Names are truly to be reverenced on account of their 
great and lingular Inventions, have thought it requilite 
to have recourfe even to Principles foreign to Mathe- 
maticks, and have introduced the Confideration of 
efficient Caufes and Phyfical Powers for theProdu&ion 
of Mathematical Quantities 5 and have fpokenof them, 
and ufed them, as if they were a Species of Quantities 
by themfelves. 
N. B. In the following Fropofition I have , for the fake of Brevity , 
made ufe of a peculiar Notation for compofte Numbers (or fuch Quan- 
tities as are analogous to them) whofe Factors are in Arithmetical 
Frogrefjion. 
The Quantity expreffed by this Notation has a double Index : that at 
the Head of the Root at the Right-hand , but feparated by a Hook to 
diftinguifb it from the common Index , denotes the Number of Favors ; 
and that above , within the Hook on the Left-hand, denotes the com- 
mo 7 i Difference of the Fa Hors proceeding in a decreafing or increafwg 
Arithmetical Frogrefjion. 
ay 
Thus the Quantity ^ ~ j. a ( m denotes by its Index m On the Right - 
hand, that it is a compofte Quantity, conf fling offo many Pallors as there 
are Units in the Number m j and the Index et above, on the Left, denotes 
the common Difference of the FaH.ors, decreafing in an Arithmetical 
Frogrejfion, if it be Fofitive ; or increafing, if it be Negative ; and fo 
fignifies, in the common Notation, the compofte Number or Quantity , 
n-j-a. n-j-a — n-j-a — 26t - n-f - a ~“3 A ' fi on% 
2 
For Example : ~ £~ 5 «=^ 5 .n+3. n+i. n— i. 
confifling of fix Fall or s whofe common Difference is 2. After the fame 
manner n _|_^ is ==.n-|-4. n-j-2. n. n— 2. n — 4, confifling of five Fac* 
tors. According to which Method it willeafily appear, that if a be any 
' 2 
Integer , then * will be s= n n— 1. nn-— 9. nn-— 25, 
continued 
