I resolved to commence, therefore, with the
examination of the simplest objects, not anticipating, however, from this any
other advantage than that to be found in accustoming my mind to the love and
nourishment of truth, and to a distaste for all such reasonings as were
unsound. But I had no intention on that account of attempting to master all
the particular sciences commonly denominated mathematics: but observing that,
however different their objects, they all agree in considering only the
various relations or proportions subsisting among those objects, I thought
it best for my purpose to consider these proportions in the most general
form possible, without referring them to any objects in particular, except
such as would most facilitate the knowledge of them, and without by any
means restricting them to these, that afterwards I might thus be the
better able to apply them to every other class of objects to which they
are legitimately applicable. Perceiving further, that in order to
understand these relations I should sometimes have to consider them one by
one and sometimes only to bear them in mind, or embrace them in the
aggregate, I thought that, in order the better to consider them
individually, I should view them as subsisting between straight lines,
than which I could find no objects more simple, or capable of being more
distinctly represented to my imagination and senses; and on the other
hand, that in order to retain them in the memory or embrace an aggregate
of many, I should express them by certain characters the briefest
possible.
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