by oversight make the figure with one angle more than the
name ordinarily imported, or he intended it should when at first
he thought of his demonstration. This often happens, and is hardly
avoidable in very complex moral ideas, where the same name being
retained, one angle, i.e. one simple idea, is left out, or put in the
complex one (still called by the same name) more at one time than
another. Secondly, From the complexedness of these moral ideas there
follows another inconvenience, viz. that the mind cannot easily retain
those precise combinations so exactly and perfectly as is necessary in
the examination of the habitudes and correspondences, agreements or
disagreements, of several of them one with another; especially where it
is to be judged of by long deductions, and the intervention of several
other complex ideas to show the agreement or disagreement of two remote
ones.

The great help against this which mathematicians find in diagrams and
figures, which remain unalterable in their draughts, is very apparent,
and the memory would often have great difficulty otherwise to retain
them so exactly, whilst the mind went over the parts of them step by
step to examine their several correspondences. And though in casting up
a long sum either in addition, multiplication, or division, every part
be only a progression of the mind taking a view of its own ideas, and
considering their agreement or disagreement, and the resolution of
the question be nothing but the result of the whole, made up of such
particulars, whereof the mind has a clear perception: yet, without
setting down the several parts by marks, whose precise significations
are known, and by marks that last, and remain in view when the memory
had let them go, it would be almost impossible to carry so many
different ideas in the mind, without confounding or letting slip some
parts of the reckoning, and thereby making all our reasonings about it
useless. In which case the cyphers or marks help not the mind at all to
perceive the agreement of any two or more numbers, their equalities or
proportions; that the mind has only by intuition of its own ideas of
the numbers themselves. But the numerical characters are helps to
the memory, to record and retain the several ideas about which the
demonstration is made, whereby a man may know how far his intuitive
knowledge in surveying several of the particulars has proceeded; that so
he may without confusion go on to what is ye