CHAP. VI.] PURE AND MIXED MATHEMATICS. 149 



perfection. As for the Pythagorical and mystical arithmetic, 

 which began to be recovered from Proclus, 6 and certain 

 remains of Euclid, it is a speculative excursion, the mind 

 having this misfortune, that when it proves unequal to solid 

 and useful things, it spends itself upon such as are unpro 

 fitable. 



Mixed mathematics has for its subject axioms and the 

 parts of physics, and considers quantity so far as may be 

 assisting to illustrate, demonstrate, and actuate those; for 

 without the help of mathematics many parts of nature could 

 neither be sufficiently comprehended, clearly demonstrated, 

 nor dexterously fitted for use. And of this kind are per 

 spective, music, astronomy, cosmography, architecture, and 

 mechanics. In mixed mathematics we at present find no 

 entire parts deficient, but foretell there will be many found 

 hereafter, if men are not wanting to themselves; for if phy 

 sics be daily improving, and drawing out ne\v axioms, it will 

 continually be wanting fresh assistances from mathematics; 

 so that the parts of mixed mathematics must gradually grow 

 more numerous. 



We have now gone through the physical sciences, am* 

 marked out the waste ground in them. If, however, we 

 have departed from the ancient and received opinions, and 

 arrayed opponents against us, we have not affected contra 

 diction, and therefore will not enter into the lists of conten 

 tion. If we have spoken the truth, 



&quot; Non caniinus surdis ; respondent omnia sylvae,&quot; f 

 the voice of nature will cry it up, though the voice ot 

 man should cry it down ; and as Alexander Borgia was wont 

 to say of the expedition of the French against Naples, that 

 they came with chalk in their hands to mark up their lodg- 



versse,&quot; in two volumes 4to., printed at Halle in the year 1715 ; or for a 

 more cursory view, Father Castel s &quot; Mathe matique Universelle,&quot; pub 

 lished in the year 1731 ; but for the history of mathematics, see Vossius 

 &quot; De Universoe Matheseos Natura et Constitutione ;&quot; the &quot;Almagest&quot; of 

 Ricciolus; Morhof s &quot; Polyhist. Mathemat. ;&quot; and Wolfius s &quot; Commen- 

 tatio de Scriptis Mathematicis,&quot; at the end oi the second volume of his 

 &quot; Elementa Matheseos Universae;&quot; Montucla s &quot;Hist. Math.;&quot; and De 

 la Croix s &quot; Analysis ol Infinites.&quot; Ld. 



e He ought to have said Irom lamblicus. Proclus was, like himself, 

 totally ignorant even, of thQ little mathematical learning extant io Uif 

 day. . &amp;lt; &amp;lt; Virg. Ecioguea, x. $, 



