LiberQuintus

ticoꝝ applicatōe efficit̉ vna ſuꝑficies cū duabꝰ. ⁊ ideo tangentia ſe mathematice nō hn̄t vltīa ſil̓. ſꝫ vnū Sꝫ tāgētiaet applicata ſibi phyſice retinēt eē diſtinctū. ⁊ ideo nō vniūtur nec idē fiūt ſua vltima. ſꝫ ſil̓ ſtꝭ mō p̄dc̄o. Mediuꝫ qd̓grece intermediū vocat̉ ē illud in qd̓ ip̄m qd̓ mutat mobile aptu natū ē pͥmū dimittere id qd̓ mouet̉ qͣꝫ in qd̓ mouetvt vltimū. Cū em̄ ꝓbatū ē ſupra ꝙ mutatōis nō eſt mutatio. neqꝫ motꝰ ſit motꝰ nec p̄t eē motꝰ ex motu. neqꝫ mōtus ad motū. oꝫ ꝙ in eo ex qͦeſt motꝰ nō ſit motꝰ. qm̄ alit̓motꝰ eſſꝫ ex motu. Eodē mō oꝫ ꝙ in vltimo ad qd̓ ē motus nō ſit motꝰ. cū motꝰ nō ſit ad motū. ideo ncc̄ariū ē ꝙin int̓mēdio qd̓ ē int̓ terminū a qͦ ⁊ terminū ad quē ſit motus. ideo intermediū in phyſicis ē in qd̓ pͥmū id qd̓ mouetur dimittit. hͦ eſt extendit id qd̓ mouet̉ ẜm qd̓ mouet̉. ⁊ hͦeſt in iſto ꝯtinue pͥus qͣꝫ veniat ad terminū vltimū motꝰin qͦ eſt motꝰ in motū eē. ⁊ hͦ ẜm naturā ꝯtinue mutatōisꝙ ſi mutatio ſit int̓rupta. tūc nō ncc̄ario veniet ad vltimūſꝫ ſiſtet in aliqͦ medioꝝ. Eſt gͦ ẜm ꝙ in phyſicis accipit̉ intermediū ad qd̓ pͥmū nata eſt ire trāſmutatio aliqͣ anteqͣꝫveniat ad illud ad qd̓ poſtremo trāſmutat̉ in qͦ tranſmutatio ē in trāſmutatū eē. Intermediū aūt ſicut pꝫ in phyſicis ẜᵐ ꝙ in phyſicis accipit̉ ad minꝰ ē in tribꝰ. qꝛ oīs mōtus ē int̓ duo ꝯtraria. ⁊ iō vnū ꝯtrarioꝝ ē pͥmū pͥncipiū ⁊alterū finis motꝰ. ⁊ intermediū eſt in qͦ eſt motus de vnoin aliud. qd̓ hꝫ quodā mō vtrūqꝫ ꝯtrarioꝝ¶ Cōtinue aūt mouet̉ qd̓ nihil aūt pauciſſimūdeficit rei nō tꝑis nihil em̄ ꝓhibet deficiētē reiet nō tꝑis. ⁊ ſtatim aut poſt ypatim. id eſt pͥmāſonare vltimā. ſꝫ rei ī qͣ mouet̉. hoc āt ⁊ ī his q̄ſunt ẜm locū ⁊ ī alijs mutatōibꝰ manifeſtū eſtHic. p. on̄dit qͥd ſit ꝯtinue moueri. qꝛ ponit̉ in definitōemedij. Et d̓t ꝙ ꝯtinue moueri ē. qn̄ ī motu nihil aut pauciſſimū deficit rei ⁊ nō tꝑis. ⁊ hͦ ſic on̄dit̉. qꝛ aliqͥs ē motꝰ īqͦ nihil ꝓhibet mouēs aliqͣꝫtulū deficere rei mote. vt clarepꝫ in motu ꝓgreſſiuo qͦrūdā aīaliū. ſꝫ ſi ꝯtinuꝰ eē dēat neceſſariū eſt ꝙ ī nullo deficiat tꝑe. Eſt em̄ motꝰ qͦrūdā aīaliū ſicut armonia cithare in qͣ faciēs armoniā ꝑcutiēdo citharā aliquātulū deficit chorde. qꝛ pͥus ꝑcutit pͥmā ī acumine q̄ d̓r grece ypatim. ⁊ poſtea ſine interruptōe tꝑis dimiſſis intermedijs ꝑcutit vltimā in grauitate. ⁊ qͣꝫuis nōſit ibi ꝯtinuꝰ trāſitꝰ ꝑcuſſionis a pͥma chorda. ſꝫ ꝑcutiensdeficit rei ꝑcuſſe tn̄ ſonꝰ iſtaꝝ chordaꝝ ẜm armoniā ē indiſtās ⁊ ꝯtinuꝰ. ⁊ gͦ ē vna ꝯtinua armoīa ẜᵐ tp̄s Ita etiāin ꝓnūciatōe lrāꝝ in ſyllaba. qꝛ ſyllaba ē lr̄aꝝ ꝯphēſio indiſtāter ꝓlata. ⁊ ſic etꝭ motꝰ qͦrūdā aīaliū. ſicut eoꝝ q̄ ābulant. Manifeſtū em̄ eſt ꝙ nō ſil̓ innitūt̉ pedibꝰ vtriuſqꝫ lateris. ſꝫ pͥus fixa vna ꝑte pedū leuat̉ altera ꝑs ſi plures qͣꝫduos habeāt pedes. ⁊ ſi hn̄t duos pedes tūc eleuato vnofigit̉ alter. tn̄ qꝛ ſine interruptiōe tꝑis ꝟtꝰ mouēs mouetvnū pꝰ alterū. ideo ꝯtinua d̓r ambulatio. Uolātia eūt ⁊natātia nec rei mote deficiūt nec tꝑi. qꝛ oꝑtꝫ ꝙ ſil̓ ⁊ ſemelꝟtus mouēs alas ad volādū aut pēnas ad natādū ſimnitat̉ inſtrumētis vtriuſqꝫ lateris Et ideo etiā ars natādi in hoībꝰ nulla alia ē niſi ꝙ ſil̓ ꝯtrahit ⁊ extēdit vtrāqꝫmanū ⁊ vtrūqꝫ crus vel ſaltē crus vtrūqꝫ Qn̄ em̄ motꝰnaturalis eſt nō aīalis. tūc eſt oīno ꝯtinuꝰ. ⁊ ideo nō deficit rei. hoc eſt ꝙ nō deficit ei qd̓ mouet̉ ẜm rem illā in quāmouet̉. et hoc eſt manifeſtū in om̄ibꝰ motibꝰ. Eſt em̄ ꝯtinua loci mutatio in qua mouens nō deficit mobili ẜm rēin qua eſt motus. hoc eſt ẜm vbi. ⁊ eſt ꝯtinua alteratio in

qua mouens nō deficit mobili ẜm qualitatē ad quā eſt alteratio. Et ſil̓iter intelligendū eſt de augmento ⁊ decremento. Et illud qd̓ dictū eſt de intermedio. qd̓ eſt in quoeſt pͥmo ꝯtinuꝰ motus qui eſt inter ꝯtraria. hoc maximeapparet verum in his q̄ ſunt ẜm locū ꝯtrariaCōtrariū aūt ẜm locū ē ẜm rectitudinē diſtāsplurimū Minima em̄ finita. metꝝ aūt finitū ē¶ Fric ph̓us definit ꝯtraria ẜm locū. ⁊ hoc ideo. qm̄ ſi in (ter loca nō eſſet ꝯtrarietas. ſic nō eſſet motus localis. cūmotus ſit inter ꝯtraria. ⁊ tollit̉ ip̄m qd̓ eſt ꝯtinue moueriDicit ergo ph̓us ꝙ ꝯtraria ẜm locū dicūtur que plurimū hoc eſt maxime diſtāt ẜᵐ lineam rectam. non em̄ poteſt mēſurari diſtantia niſi per lineam rectaꝫ. qꝛ iſta vnitaeſt inter extrema Curue aūt ſunt infinite. recta aūt eſt minima ⁊ breuiſſima. ⁊ ideo notiſſima nobis ⁊ ẜm rōnem. ꝓpter qd̓ ꝑ ipſam menſuratur diſtantia. ⁊ ideo illa ſola ẜmnaturam eſt media ꝓpter quod illa eſt inter medium perquod eſt motus leuis aſcendendo ⁊ motus grauis deſcēdendo. Sic aūt eſt ⁊ in alijs motibꝰ naturalibꝰ. quia natura procedens ab extremitate in extremuꝫ ſemper mouetper intermediū breuiſſimū. ⁊ hoc eſt rectum. ⁊ ideo rectuꝫeſt iudex ſui ⁊ obliqui. qm̄ per rectum cognoſcitur vtrūqꝫ ſcꝫ rectum ⁊ curuū.¶ Conſequēter āt ꝙ cū poſt principiū ſoluꝫ ſitaut poſitione aut ſpecie aut aliquo ſit determinatorū. nullum mediū eſt eorum que ſunt ineodem genere. ⁊ cuius cōſequēter eſt. Dico autem in linea linee ẜm ꝙ ſunt linee. aut vnitatisvnitas. ẜm ꝙ ſunt vnitates aut domus domꝰAliud autē nihil ꝓhibet eſſe mediū. ꝯſequēterautem eſt alicui. cuꝫ poſterius aliquid eſt. Nōem̄ vnū ꝯſequenter eſt duobꝰ. neqꝫ noua lunaſecūde ꝯſequenter. licet hec illi.Hic. p. definit ꝯn̄ter. Et d̓t ꝙ ꝯn̄ter d̓r qn̄ vnuꝫ eſt poſtaliud. tta ꝙ nihil mediat eiuſdē gn̄is. Aut ꝯn̄ter ẜm ꝙ inphyſicis ⁊ in alijs cōiter ſumit̉ eſt. ꝙ cū ſit ſolū poſt id qd̓eſt eius pͥncipiū aut pōne. ſicut vnū corpꝰ poſt aliud. autſpē ſicut vnꝰ nūerus eſt poſt aliū. aut ordine. ſicut milespoſt regē. aut aliqͦ mō ſic determinato. ſcꝫ ꝙ aliqͥd ſit pͥncipiū ⁊ aliqͥd poſt ip̄m nullū hꝫ mediū qd̓ ſit de nūero eorū q̄ ſunt eiuſdē generis cū ip̄o pͥncipio ſuo reſpectu cuiusd̓r ip̄m eſſe ꝯn̄ter. ſicut dicimꝰ ꝙ linea ſeqͥtur lineā pōne.ſi nulla ſit linea inter eas. vnitas ſeqͥtur vnitateꝫ ſi nullaſit eaꝝ media vnitas. ⁊ domꝰ domū ſi nulla ſit domꝰ intermedia. Et ſil̓r ẜm ſpēm aīal bipes ſequit̉ hominem ⁊hmōi. ſꝫ nō ꝓhibet quin res alteriꝰ generis poſſit eē interea que ſunt ꝯſequēter. vt ſi ſtat canis aut equus inter duas domos adhuc habent ſe ille due domus ꝯſequēter. qꝛom̄e illud qd̓ eſt alicui ꝯn̄ter ⁊ ẜm aliquē modū ꝯn̄ter eſtet oꝫ ꝙ ſit poſterius illo ex quo accipit ꝯn̄ter eē. ⁊ ideo nōd̓r in ordine numeri ꝙ vnū ſit ꝯn̄ter ad duo. nec in acceſſionibꝰ lune d̓r ꝙ pͥma luna ſit ꝯn̄s ſecūdā ſed ecōuerſo.Habitū aūt eſt qd̓ ꝯſequenter eſt cuꝫ tangatqm̄ autē oīs mutatio in oppoſitis eſt. oppoſitaaūt ꝯtraria. ⁊ q̄ ẜm ꝯtradictōem ſunt: ꝯtradictionis aūt nihil medium. manifeſtum eſt ꝙ inꝯtrarijs erit medium

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