[ 507 ] 
Quantity of the fame kind, that one Line or Num- 
ber can bear to another. That this is effential to 
all mathematical Quantity, is evident from the firft 
Elements of Algebra, which treats of Quantity in 
general, or of thofe Relations and Properties which 
are common to all Kinds of Quantity. Every alge- 
braical Quantity is fuppofed capable not only of 
being increafed and diminifhed, but of being exa&ly 
doubled, tripled, halted, or of bearing any aflignable 
Proportion to another Quantity of the fame kind. 
This then is the Chara&eriftic of Quantity 5 what- 
ever has this Property may be adopted into Mathe- 
matics i and its Quantity and Relations may be mea- 
sured with mathematical Accuracy and Certainty. 
Sect. 2. 
Of jP roper and Improper Quantity. 
There are fome Quantities which may be called 
Troper, and others Improper. This Diftin&ion is 
taken notice of by Ariftotle ; but it deferves fomc 
Explication. 
I call that Proper Quantity which is meafured by 
its own Kind; or which of its own Nature is capa- 
ble of being doubled or tripled, without taking in 
any Quantity of a different Kind as a Meafure of it. 
Thus a Line is meafured by known Lines, as Inches, 
Feet, or Miles; and the Length of a Foot being 
known, there can be no Queftion about the Length 
of two Feet, or of any Part or Multiple of a Foot. 
And this known Length, by being multiplied or di- 
vided, is fufficient to give us a diftin6t Idea of any 
Length whatfoever. 
X xx 
Improper 
