Mijcellanea Curt of a. 39 



1 and 3 there will be 47712 &c. of them? 

 which Numbers therefore are the Logarithm* 

 of the r axioms of i to 10, i to 2, and 1 to 3? 

 and not fo properly to be called the Logarithms 

 of 10, 2 and 3. 



But if inftead of fuppofing the Logarithms 

 compofed. of a number of equal RatiuncuU, 

 proportional to each ratio, we fhall jf take 

 the ratio of Unity to any number to cjonfifl: 

 always of the fame infinite number of Ra- 

 tiuncuU, their magnitude, in this cafe, will 

 be as their number in the former ; wherefore 

 if between Unity and any Number propofed, 

 there be taken any infinity of mean Proportio- 

 nals, the infinitely little augment or decre- 

 ment of the firft: of thofe means from Unity, 

 will be a ratiuncula, that is, the momentum or 

 fluxion of the ratio of Unity to the faid Num- 

 ber : And feeing that in thefe continual Pro- 

 portionals all theratiuncuL are equal,their Sum, 

 or the whole ratio will be as the faid momentum 

 is dire&ly 5 that is, the Logarithm of each 

 ratio will be as the Fluxion thereof. Where- 

 fore if the Root of any infinite Power be ex- 

 tracted out of any Number, the differentioia of 

 the faid Root from Unity,fhall be as the Loga- 

 rithm of that Number. So that Logarithms 

 thus produced may be of as many forms as you 

 pleafe to afTume infinite Indices of the Power 

 whofe Root you feek : as if the Index be fuppo- 

 fed ioooooe^c, infinitely, the Roots (hall be the 

 Logarithms invented by the Lord Napeir but 

 if the faid Index were 2$025%$ 7 &c.Mi'. Br i<rgs\ 

 Logarithms would immediately be produced. 

 And if you pleafe to ftop at any number of 

 Figures, and not to continue them on, it will 

 D 4 fnffice 



