divine Providence over all things, to which there are other Gods
subordinate, how men are in respect of them. The end of Mathe∣matick
is, to know the nature of a superficies and a solid, and to
consider the motion and revolution of celestiall bodies, the con∣templation
whereof must first be proposed in briefe. Thus Plato
useth to confirm the acutenesse of the minde, for it sharpeneth
the understanding, and rendreth it more ready towards the con∣templation
of divine things. That which considereth Numbers,
being likewise a part of Mathematicks, conferreth not a little to
the understanding of things that are; It frees us from the
errour and ignorance which attend sensible things, and condu∣ceth
to the right knowledge of the essence of things: It likewise
renders a man expert in military affairs, especially towards the
ordering of an Army by the science of Tacticks. Geometry also
conferteth much towards the understanding of good it selfe, if a
man pursue it not only for mechanicall dimension, but that he
may by the helps thereof ascend to things which are not, busying
himselfe about those which are in continuall generation and
motion. Stereometry likewise is exceeding usefull, for after the
second accretion followeth this contemplation, which holdeth
the third room. Astronomy also is usefull as a fourth discipline,
whereby we consider the motions of Heaven and the Starres,
and the author of night and day, months and years. Thus by a
familiar kinde of way, finding out him who made all these, and
by these disciplines, as from certain rudiments or elements pro∣ceeding
to things more sublime. Likewise Musick is to be learnt,
which relateth to hearing; for, as the eyes are created for Astro∣nomy,
so are the ears for Harmony: and as when we apply our
selves to Astronomy, we are led from visible things, to the divine
invisible ••ffence; so when we receive the Harmony of voice in at
our ears, from audible things, we ascend by degrees to those
which are perceived by Intellect, unlesse we pursue Mathema∣ticall
disciplines to this end, the contemplation thereof will be
imperfect, unprofitable, and of no value. We must therefore pre∣sently
proceed from those things which are perceived by the
eyes and ears, to those which reason only discerneth; for, Mathe∣matick
is only a preface to divine things. They who addict them∣selves
to Arithmetick and Geometry, desire to arrive at the
knowledge of that which is, which knowledge they obtain no
otherwise then as by a dream, but really they cannot attain it,
because they know not the principles themselves, nor those
things which are compounded of the principles: neverthelesse,
they conduce to those things which we mentioned; wherefore
Plato will not have such disciplines to be called Sciences. Dia∣lectick
method proceeds in such manner, that by Geometricall
Hypotheses, it ascendeth to first principles, which are not taken
upon Hypotheses. For this reason he calleth Dialectick a Science;