Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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137PRÆFATIO ita numeros, vel quantitates non analyticas nun- quam provenire ex analyticarum additione, ſub- ductione, multiplicatione, diviſione, radicum ex- tractione, ſed ex ſexta hac operatione; ita ut hæc noſtra inventio addat arithmeticæ aliam operatio- nem, & geometriæ aliam rationis ſpeciem, idem enim eſt (ſicut in hoc tractatulo demonſtro) ratio- nem circuli ad diametri quadratum in analytica ſeu illa rationis ſpecie hactenus cognita exhibere, ac rationem inter quadrati latus & ejuſdem diame- trum in commenſur abilibus: verum certè eſt me hanc demonſtrationem integram ad phraſem geo- metricam non reduxiſſe, nam ut hoc perficiatur, opus eſt non parvo volumine de quantitatum analy- ticarum mutuo inter ſe relatione & incommenſura- bilitate in genere, quod miror nullum unquam ſcripſiſſe, cum in his tam latè pateant inventio- num campi; nam ex his petenda eſt demonſtratio, quod meſolabium non poſſit perfici ope regulæ & circi- ni, item quod non ſemper & quando æquationes affectæ poſſunt reduci ad puras, item quod neceſſaria ſit ad minimum talis generis curva ad mechanicam talium æquationum reſolutionem, cum talibus innumeris, quæ à præſtantioribus geometris impoſ- ſibilia eſſe deprehenduntur ex analyſi, & à rudio- ribus quotidie & fruſtra quæruntur. Scripſit Eu- clides decimum ſuum librum ſolummodo (niſi in pau- cis quibuſdam propoſitionibus generalibus) de incom- @nenſurabilitate facta ab extractione radicis quadra-

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Scan	Original
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