ae = me 
122 OF THE ADVANCEMENT OF LEARNING. [V1.2 
or parts of natural philosophy, and considereth quantity 
determined, as it is auxiliary and incident unto them. 
For many parts of nature can neither be invented with 
sufficient subtilty, nor demonstrated with sufficient per- q 
spicuity, nor accommodated unto use with sufficient dex- : 
terity, without the aid and intervening of the mathematics ; 
of which sort are perspective, music, astronomy, cosmo- 
graphy, architecture, enginery, and divers others. In the 
mathematics I can report no deficience, except it be that 
men do not sufficiently understand the excellent use of the 
pure mathematics, in that they do remedy and cure many 
defects in the wit and faculties intellectual. For if the 
wit be too dull, they sharpen it; if too wandering, they 
fix it; if too inherent in the sense, they abstract it. So 
that as tennis is a game of no use in itself, but of great 
use in respect it maketh a quick eye and a body ready to 
put itself into all postures; so in the mathematics, that 
use which is collateral and intervenient is no less worthy 
than that which is principal and intended. And as for the 
mixed mathematics, I may only make this prediction, 
that there cannot fail tosbe more kinds of them, as nature 
grows further disclosed. Thus much of natural science, 
or the part of nature speculative. 
3. For natural prudence, or the part operative of na- 
tural philosophy, we will divide it into three parts, experi- 
mental, philosophical, and magical: which three parts 
active have a correspondence and analogy with the three 
parts speculative, natural history, physic, and metaphysic. 
For many operations have been invented, sometime by 
a casual incidence and occurrence, sometimes by a pur- 
posed experiment: and of those which have been found 
by an intentional experiment, some have been found out 
by varying or extending the same experiment, some by 
