no Of the Advancement of Learning. L i b. Ilf^ 



could be content, that this Science^ might even command and over- 

 rule rhyficl{. For it is come to pals, by what fate I know not, that 

 Alathemntick^ and Logick^^ which (hould carry themfelvcs as hand- 

 maids to Thyfick^^ boafting their certainty above it , take upon 

 them a command and Dominion. But we do not (p much ftand 

 upon the rank and dignity of this Science ^ let us confider the thing it 

 felf. 



^ Mathematickf are either Pure or Mixt''-, to Ture Matbematick/^ thofe 

 Sciences are referred , which handle ^antity altogether abftrafted 

 from Matter, and Phyfical Axioms. They are two, Geometry^ and 

 Arithmetic^ ; the one handling ^antity continued , the other dijfc' 

 vered. Which two Arts have indeed been inquired into, with fub- 

 tilty and induftry, but neither to the labours of Euclid in Geometry^ 

 hath there been any thing of any worth added by pofterity , in fo 

 many centuries of years fince he flouritht ; nor hath the Doftrine 

 of Holids , for the ufe and excellency of the knowledge , been 

 laboured and advanced by Writers Ancient or Modern. And in 

 Arithmetical there hath not been found out apt and fufficient variety 

 of compendious ways for fupputations ; efpecially about Progrejjions y 

 whereof there is great ufe in the Phyficks. Nor is the Algebra^ or 

 Art of £^«<»//tf« well perfefted ; but that Pythagorical and MynicalA" 

 rithmetic^, which is begun to be revived out of Proclus^ and fome 

 Remains of Euclid 5 is a fpacious field of fpeculation : Forfuch is the 

 jiature of Min^ that if it he not able to comprehend folids^ it vpajies itfclf 

 in unprofitable niceties. 



§ Mtxt Mathematick^^ hath for fubjedt Axioms^ and portions of Pity- 

 fick^j and confiders ^/4///;/;, as it is auxiliary to enlighten, demon- 

 ftrate , and aftuate them. For many parts of Nature can never be 

 with fufficient fubtilty comprehended, nqr demonftrated with fufl 

 ficicnt perfpicuity, nor accommodated to ule with fufficient dexterity 

 and certainty, without the Aid and intervening of the Aluthetaa- 

 ticks. Of which fort are PerfpeQive , Alufick,^ Ajironomy, Cofmogra^ 

 fhy^ Archite&ure^ Ingenarie , and divers others. But in Mixt Mathe- 

 tnaticks^ I can now report no entire portions Deficient 5 I rather make 

 this prediftion, that there will be more kinds of them invented by 

 pofterity , if men be not wanting to themfelves. For as Phyfical 

 knowledge daily grows up , and new Axioms of nature arc dif^ 

 clofed , there will be a neceffity of new Mathematick inventions , 

 and fo at laft more Mixt Mathematicks will be contrived. And 

 nopp Toe have pajfed through the l^orpledgc of Nature , and have no- 

 ted the Deficients therein. Wherein if we have departed from the 

 Ancient and received opinons , and thereby have moved contradi- 

 ftion 5 for our part , as we affeB not to dijfent ^ fo rve purpofc not to 

 contend. If it be truth , 



virg. Bu. t^on C^mmus furdif^ refpondcnt omniafylv£'j 



col. 



The voice of nature will cry it up, though the voice of man (hould 



cry it down. And as Alexander Borgia was wont to fay, of the Ex- 



viil. Hift. pcdition of the French for Naples, that they came with chall^ in their 



^''- hands 



