58 jMifcellanea Curio [a. 



ufe of them : Contenting themfelves with the 

 Tables of them as they find them, without da- 

 ring to queftion them, or caring to know how 

 to recline them, fliould they be found amifs; 

 being I fuppofe under the apprehenfion of fome 

 great difficulty therein. For the fake of fuch 

 the following Traft is principally intended,but 

 not without" hopes however to produce fome- 

 thing that may be acceptable to the molt know- 

 ing in thefe matters. 



But firft,it may be requifite to premife a de- 

 finition of Logarithms, in order to render the 

 enfuing Difcourfe more clear, the rather be- 

 caufe the old one Numerorum froyortionalium 

 stqui differentes comites, feems too fcanty to de- 

 fine them fully. They may more properly be 

 faid to be Ktumeri Rationum Exfonentes : Where- 

 in we confider ratio as a Ouantitasjul generis, 

 beginning from the ratio oi equality, or_ 1 to 

 1=0 ? being Affirmative when the ratio is m- 

 creafmg, as of Unity to a greater Number, 

 but Negative when decreafing ^ and thefe ra- 1 

 tiones we fuppofe to be meafured by the Num- I 

 berof ratiuncuU contained in each. Now thefe 

 ratiuncuU are fo to be underftood as in a 

 continued Scale of Proportionals infinite in 

 Number between the two terms of the ratio, j 

 " which infinite Number of mean Proportionals j 

 Is to that infinite Number of the like and equal 

 ratiuncuU between any other two terms, as 

 the Logarithm of the one ratio is to the Loga- 

 rithm of the other. Thus, if there be fuppo- 

 fed hetween 1 and 10 an infinite Scale of mean I 

 Proportionals, whofe Number is ioocoo, eh:.l 

 in infinitum 5 between 1 and 2 there fhali be j 

 30102, &c. of fuch Proportional^aiid between! 



