De Problemate Quodam Algebraico, Deque Evolutione Mechanicae Cujusdam Curvae Inter Infinitas Hypermechanicas, Quae Determinatae Aequationi Satisfaciunt. Auctore Pio Fantoni, Mathematico Bononiensi. Communicated by Sir Horace Mann, His Majesty's Envoy at Florence

H. Mann, P. Fantonus
1767 Philosophical Transactions of the Royal Society of London  
quae determinatae aequationi satisfaciunt. curvae inter infinitas hypermechanicas, deque evolutione mechanicae cujusdam XXXIV. De problemate quodam Algebraico, Pio Fantoni , 358-371, published 1 January 1767 57 1767 Phil. Trans. Email alerting service here corner of the article or click this article -sign up in the box at the top right-hand Receive free email alerts when new articles cite http://rstl.royalsocietypublishing.org/subscriptions , go to: Phil. Trans. To subscribe to on July 20, 2018
more » ... to on July 20, 2018 http://rstl.royalsocietypublishing.org/ Downloaded from on July 20, 2018 http://rstl.royalsocietypublishing.org/ Downloaded from [ 35« ] X X X IV . D e Problemate Algebraic deque evolutione mechan vce 'inter infinitas , qu# determ inate cequationifatisf. Pio Fantoni, M athem atico Bononienfi. Com municated by S ir Horace Mann, M a je fty s Envoy a t Florence. U I in computationibus analyticis verfari folet, animum non modo in intendere, quibus problemata dedu* curitur ad aequationes, fed maximam ubique exoptat concinnitatem* atque elegantiam, ut univerfi operis apparatus, conftru&io, utilitafque commendentur. Quantum vero elaborationis, ac lludii plerumque ad haec. lingula requiratur, ii probe intelligunt excellentiffimi viri, qui fe jamdudum algebrae dediderunt. Veruntamen fateri ultro debent, non mediocrem allquando utilitatem obtineri poffe ex hujulce potius, quam illius methodi applicatione. Fit enim non raro, ut cum quaeftionem aliquam fubtili licet ingenio verfatus fu eris, alia tandem method us meliori aufpicio fufcepta, illico tibi elargiatur clariorem uberioremque ejufdem quaeftionis folutionem, ex qua multa praeterea obtineas quae admireris. Id vero mihi Read June 2S » A^V V i ea praefidia folet on July 20, 2018 http://rstl.royalsocietypublishing.org/ Downloaded from L 3 5 9 ] in fublimi pmblemate quodam algebraico, an bene feliciterque contigerit, veftro judicio, Academici fapientiflimi, quod maximi facio, decernendum relinquo. Si interea, ut exoro, hanc meam elucubrationem fumma humanitate veftra excipietis, ea deinceps utar in aliis non contemnendis rebus turn phyiicis, turn mechanicis, ut veftra fapientia duce, facilius ad quafdam naturae adhuc reconditas leges pervenire poflim. Nunc porro velim intelligatis, me in hoc afgumento analytico, de quo loquor, tria maxime prasftitifle. Primum enim curvam quandam exploravimus fuis coordinatis ad axem,& licet lediffimls prae-' M is ufi fuerimus in feparatione indeterminatarutn, licet inveftigationem noftram fatis ultro promotam eonfpexerimus, in aequationem tandem, *ut dicunt, hypermechanicam irrumpere opus fuit, in earn v i delicet, quae expofcit mechanicam quadraturam curvarum exigentium primo mechanicam circuli quadrate ram. Ex hac autem fere inextricabili coriftrudione-n6n ea certe confedaria, quae in vbtis erant, erui degantifEme potuiffent. Qjjare difficuffate yeluti ■commoti, fatis Opportune curvam tibftratTi ab axe ad. focum deduximus, atque hoc modo univerfum tllud opus, cujus dilucide enodandi fpem onanetn atitea demifimus, ed tandem feliciter perduximus, ut ipfutn * re£te effet" nobifque plene iatisfaceret;' At veto in hac fecunda problematis mei parte dutn contendo, dum ill am conftanti animo defugio permechanicam coriftrudionem, atque ad pore the-1 chaoicahi properoy1 invenio tandem in infinite dur*varum by pcrmechanicar um familia, quae peculiar cuidam
doi:10.1098/rstl.1767.0036 fatcat:6ut6dli4qvdbjdvwkzswhtvbne