166 ADVANCEMENT OF LEARNING. [Book 



matics are those sciences belonging which handle quantity determi 

 nate, merely severed from any axioms of natural philosophy ; and 

 these are two, Geometry, and Arithmetic ; the one handling quantity 

 continued, and the other dissevered. 



Mixed hath for subject some axioms 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 perspicuity, nor accommo 

 dated unto use with sufficient dexterity, without the aid and inter 

 vening of the mathematics ; of which sort are perspective, music, 

 astronomy, cosmography, 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 mathe 

 matics, in that they do remedy and cure many defects in the wit and 

 faculties intellectual. For, if the wit be 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 maketha quick eye, and a body ready to put itself into all 

 postures ; so in the mathematics, that use which is collateral and inter- 

 venient, is no less worthy than that which is principal and intended. 



And as for the mixed mathematics, I may only make this predic 

 tion, that there cannot fail to be more kinds of them as nature grows 

 further disclosed. 



Thus much of natural science, or the part of nature speculative. 



For Natural Prudence, or the part operative of natural philosophy, 

 we will divide it into three parts, experimental, philosophical, and 

 magical ; which three parts active have a correspondence and analogy 

 with the three parts speculative, natural history, physic, and meta- 

 physic ; for many operations have been invented sometimes by a 

 casual incidence and occurrence, sometimes by a purposed experiment ; 

 and of those which have been found by an intentional experiment, 

 some have been found out by varying or extending the same experi 

 ment, some by transferring and compounding divers experiments, 

 the one into the other, which kind of invention an empiric may 

 manage. 



Again, by the knowledge of physical causes, there cannot fail to 

 follow many indications and designations of new particulars, if men in 

 their speculation will keep one eye upon use and practice. But these 

 are but coastings along the shore, premcndo littus iniqunm : for, 

 it scemeth to me, there can hardly be discovered any radical or funda 

 mental alterations and innovations in nature, either by the fortune 

 and essays of experiments, or by the light and direction of physical 

 causes. 



If therefore we have reported metaphysic deficient, it must follow, 

 that we do the like of natural magic, which hath relation thereunto. 

 For as for the natural magic whereof now there is mention in books, 

 containing certain credulous and superstitious conceits and observa 

 tions of sympathies, and antipathies, and hidden proprieties, and some 



