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Prefat. 12)
Proportion
Similar
Greater
Less
repeated it exactly measures the consequent of the second
pair, these two pairs are said to be in the same
Proportion. but if it falls that of being equal to it,
this last pair is said to be in the greater Proportion,
and if it excedes it this second Pair is said to be
in the less proportion. This is all for the purpose of
understanding the 5th Book that we want to know, namely if
the proportion in one pair be equal to greater or less than that
between another , how much greater we have no occasion to know as yet.
change the
order of comparison
and the proportion
is changed from
greater to less
&
Proportions
proper
Names of
Names expressive of each individual Proportion you as yet
do not want. but when it is wanted it can only
be found by finding a common measure that will exactly
measure both pairs. It is from relative number of aliquots
contained by homo numbers that the must save
as a mark of distinction such name as duplicate
triplicate quadruplicate & subduplicate subtriplicate &c
but these names are as yet useless.
of a pair of quantities considered
Incommensur:
accuracy of
If a pair of Incommensurables you may divide one of the Numbers
into aliquots so small as that of a common measure be taken
equal to one of them, what this common measure will want
of measuring the other Number will shall be less than what
a Phisical Circle or triangle would way from
a Mathematical one.
Examine what Hume, D'Alembert, Helvetius, Locke, &c have said
concerning the Metaphysical part of Mathematics.
Identifier:  JB/135/040/004 "JB/" can not be assigned to a declared number type with value 135.



not numbered 

135 

040 
prefat. 

004 

copy/fair copy sheet 
4 

recto 
f9 / f10 / f11 / f12 

sir samuel bentham 
[[watermarks::[gr with crown] [pro patria motif]]] 

46158 
