IQO PHILOSOPHICAL TRANSACTIONS. [aNNO 1738. 



By these examples it appears, that the solution is universal in all respects; for 

 the first two, compared with the last two, serve to show that it is not confined 

 to any particular parts of the orbit, but extends to all degrees of mean anon)aly: 

 and by comparing the second with the last, it sufficiently appears to be univer- 

 sal with respect to the several degrees of eccentricity ; since in one the equation 

 of the centre, for the reduction of the mean to the true motion, is not so 

 much as the 1 70th part of the whole ; whereas in the other it amounts to almost 

 3000 times as much as the mean motion itself. 



Postscript. — On reviewing the reflections on the quadrature of the circle, 

 Mr. M. believes it may be necessary, to prevent any mistake that may arise 

 from the different opinions that obtain about the nature of mathematical quan- 

 tity, to explain himself a little on that head ; as also to add a few words to show 

 how the method of quadrature, by limiting polygons, takes place in other 

 figures, as well as the circle. 



He takes then a mathematical quantity, and that for which any symbol is put, 

 to be nothing else but number with regard to some measure which is considered 

 as one. For we cannot know precisely and determinately, that is, mathemati- 

 cally, how much any thing is, but by means of number. The notion of con- 

 tinued quantity, without regard to any measure, is indistinct and confused ; and 

 though some species of such quantity, considered physically, may be described 

 by motion, as lines by points, and surfaces by lines, and so on ; yet the mag- 

 nitudes or mathematical quantities are not made by that motion, but by 

 numbering according to a measure. 



Accordingly, all the several notations that are found necessary to express the 

 formations of quantities, refer to some office or property of number or measure ; 

 but none can be interpreted to signify continued quantity, as such. 



Thus some notations are found requisite to express number in its ordinal 

 capacity, or the numerus numerans, as when one follows or precedes another, 

 in the first, second or third place, from that on which it depends ; as the quan- 

 tities X, r, X, oc, X, referring to the principal one x. 



So, in many cases, a notation is found necessary to be given to a measure, as 

 a measure ; as for instance. Sir Isaac Newton's symbol for fluxion x ; for this 

 stands for a measure of some kind, and accordingly he usually puts an unit for 

 it, if it be the principal one on which the rest depend. 



So some notations are expressly to show a number in the form of its com- 

 position, as the index to the geometrical power x", denoting the number of 

 equal factors which go to its composition, or what is analogous to such. 



But that there is no symbol or notation, but what refers to discrete quantity, 

 is manifest from the operations, which are all arithmetical. 



