[ 5°6 ] 
tainment at leafl:, to inquire to what Subje&s this 
kind of Proof may be applied. 
Mathematics contain properly theDo&rine ofMca- 
fure; and the Object of this Science is commonly 
faid to be Quantity; therefore Quantity ought to be 
defined, What may be meafured. Thofe who have 
defined Quantity to be whatever is capable of More 
or Lefs, have given too wide a Notion of it, which 
I apprehend has led fome Perfons to apply mathe- 
matical Reafoning to Subje&s that do not admit 
of it. 
Pain and Pleafure admit of various Degrees, but 
who can pretend to meafure them ? Had this been 
poffible, it is not to be doubted but we fhould have 
had as diftind Names for their various Degrees, as 
we have for Meafures of Length or Capacity ; and 
a Patient fhould have been able to defcribe the 
Quantity of his Pain, as well as the Time it began, 
or the Part it affeded. To talk intelligibly of "the 
Quantity of Pain, we (hould have fome Standard to 
meafure it by ; fome known Degree of it io well 
afeertained, that all Men, when they talked of it, 
fhould mean the fame thing ; we fhould aifo be 
able to compare other Degrees of Pain with this, 
fo as to perceive diftinctly, not only whether they 
exceed or fall fhort of it, but how far, or in what 
proportion; whether by an half, a fifth, or a tenth. 
Whatever has Quantity, or is meafurable, mud 
be made up of Parts, which bear Proportion to one 
another, and .to the Whole; fo that it may be in- 
creafed by Addition of like Parts, and diminifhed 
by Subtraction, may be multiplied and divided, and 
in a* Word, may bear any Proportion to another 
2 Quantity 
