7&? Method of
322
FLUXIONS,
will be neceffary to his purpofe, and will befl conduce to the fimthe eafieft, and neateft Solution that may be had, and pleft, yet in
For it is convenient the Problem fhouM the moft general manner. as as be propofed may be, the better to fix the Imaginaparticular tion ; and .yet the Solution mould be made as general as poffible, that it may be the more inftrucHve, and extend to all cafes of a like nature.
Indeed the word datum
is
often ufed in
a fenfe
which
is
fome-
but which ultimately centers in it. As datum, when one quantity is not immediately given, but however is neceffirily infer'd from another,, which other perhaps is neceffarily infer'd from a third, and fo on in a continued Series,
thing different that is call'd a
from
this,
from a quantity, which is known or neceffarily infer'd given before This is the Notion of Euclid'?, fenfe the in explained. data, and other Analytical Argumentations of that kind. Again, that is often call'd a given quantity, which always remains conftant and invariable, while other quantities or circumftances vary ; becaufe fuch as thefe only can be the given quantities in, a Problem, when taken in the foregoing fenfe. To make all this the more fenfible and intelligible, I /hall have, till it is
recourfe to a few pradlical inftances, by way of Dialogue, (which, was the old didadlic method,) between Mafter and Scholar; and this only in the common Algebra or Analyticks, in which I fhall borrow Examples from our Author's admirable Treatife of The chief artifice of this manner of SoluUniverfal Arithmetick.
my
tion will confift in this, that as faft as the Mafter propofes the Conditions of his Queftion, the Scholar applies thole Conditions to
them Analytically, makes all the aeceffary deducfuch confequences from them, in the fame order derives and tions, they are propofed, as he apprehends will be mcft fubfervient to the And he that can do this, in all cafes, after the fureft, fimSolution. readieft manner, will be the beft and ex-tempore Mathematipleft, But this method will be beft explain'd from the cian.
ufe,
argues from
following
Examples.
M.
I.
the
Sum
A
Gentleman being 'willing to diftribiite Abns he intended to diftribute be reprefented by x.
S.
Let
M. Among
S. Let the number of poor be then - would fbme poor people. _}>, M. He wanted 3 fiillings have been the fhare of each. S. Make for lake of the and let the rf, univerfality, 3 pecuniary Unit be then the be to Sum distributed one Shilling ; would have been x-{-a,
=
and"