A. Mac Whorter on the Di | sibility of Magnitude. 385 " 
seth this case ioote questions arise ; first, what is the meaning of 
1e term divisible when applied to o mere objects of thought? sec- 
ondly, what is the nature of the conceptions denoted by the terms 
eed line and mathematical point? and thirdly, what is 
vat to divide a mathematic al line at a mathematical point : 
Respecting the first inquiry, it is evident, that while to divide 
:# means primarily to dispart, or disjoin, when materig ewe 
are spoken. of, to divide when used in reference to) ings ich 
are mere objects of thought, must mean simply to istincill 
between them as mere objects of thought ; so that, in this 
infinitely divisible means merely sartingsd distinguishabl 
distinguishable beyond any assignable lim : 
cf _ In the next place a line, by definition, coved the object of th =| 
Bare conception of length or distance, considered as a mere ob- 
ject of thought, apart from the abstract conceptions of breadth and 
depth ; — a point is defined by Legendre to be, ‘a limit ter- 
minating a line.’ i? 
In this definition of a point the abstract notion of length, rep- 
resented by a line, is considered as ceasing or ending, and this 
notion of limit to lengt sbeing a notion of the cessation ue con- 
sequent negation of length, it is a conception which ; 
nature, excludes from itself the conception thus deni 
this view that Euclid defines a point to be “ ft 
parts or which hath no magnitude ;” a definiti impe 
cause not convertible, ri lend “having no pariaer 
tude” not being a poin 
But as in things a given distance is in actual space, 
situation, or position, so in mere objects of thought the coeéxisti 
meecpuons of abstract. length, breadth, and thickness, are view 
as holding such relations to each other, as to authorize the appl 
cation of the term place, or position, borrowed from real exi 
ces and applied to these conceptions in order to denote a pa 
lar relation between them.’ Now as mere objects of thoughts ai 
given conception is just what tt 2s, AND NOT ANOTHER Concep 
Thus, in answer to the second inquiry, it appears that a 
ematical Be peommecely the object of the abstract co 
length or distance ; and in respect te a pe 
appears, fire nak it is not a thing “ re” and i 
existence, but on rary, i 
