THE SECOND BOOK 267 



ledge) to delight in the spacious liberty of generalities, as 

 in a champion region, and not in the inclosures of particu- 

 larity; the Mathematics of all other knowledge were the 

 goodliest fields to satisfy that appetite. But for the placing 

 of this science, it is not much material : only we have 

 endeavoured in these our partitions to observe a kind of 

 perspective, that one part may cast light upon another. 



The Mathematics are either Pure or Mixed. To the 

 Pure Mathematics are those sciences belonging which 

 handle Quantity Determinate, 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 

 subtlety nor demonstrated with sufficient perspicuity nor 

 accommodated unto use with sufficient dexterity, without 

 the aid and intervening of the Mathematics : of which sort 

 are Perspective, Music, Astronomy, Cosmography, Archi- 

 tecture, 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 that 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 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 



