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Mathemalogiu[m] prime p[ar]tis Andree alexandri Ratisbone[n]sis mathematici su[per] nouam et veterem loycam, Aristotelis / [Beiträger: Hermann von dem Busch]
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opoꝛtet ↄſiderare vtrũ ſit in diuerſis generibꝰ generaliſſimis. ſi ſic ipm eſt multiplex qꝛ ſcðm diuerſa ſignificata ponit in diuerſis generi bus. Et ponit tria exẽpla.quoꝝ vltimũ eſt ad ꝓpoſitũ vt acuta quidã vox velox eſt ſicut dicut qui ſcom nũeros armonici ſunt q̃ᷓ in genere qlitatis eſt.Et de acuto in magnitudine.angulꝰ em acutꝰ mĩoꝛ rec to eſt. eſt in genere poſitiõis. De voce aũt quidẽ tibi diſſerẽdũ eſt

vorx eſt ſonꝰ ꝑcuſſio aeris indiſſoluta vſq; ad auditum. Motuũ do alij ſunt qᷣbus feruntur velocioꝛes.alij tardioꝛes.eoꝛũqʒ motuũ alij radioꝛes alij ſpiſſioꝛes. Ma ſi quis ↄtinuũ motũ reſpiciat. ibi aut velocitatẽ.aut tarditatẽ neceſſe eſt opᷣhendat ſi quis moueat ma aut frequẽti mouebit motu aut raro.Eẽt ſi tardꝰfuerit aut rarꝰ Fues neceſſe eſt ſonos effici. ipa tarditate raritate pellendi Sin vo lant mots celeꝛes ſpiſſi. acutos neceſſe eſt reddi ſonos. Iccirco ner⸗ uus tenuat᷑ acutũ ſonũ mittit.ſi remittat᷑ grauẽ.quãto em̃ tenſioꝛ eſt velocioꝛẽ pulſũ reddit. qui vo laxioꝛ eſt tardos ſonos Sues ef⸗ ficit.Ex hijs igi᷑ motibꝰ tãq́ᷓ pluralitate paucitate dĩa ſonoꝝ con/ ſtat. om̃is aũt talis paucitas pluralitas ita ſe vt nũerꝰ ad nũerũ

ↄpatus.eoꝝ vo m nũerũ ſunt ferũt᷑ ꝑtim ſunt eq̃les ꝑtim ineqli⸗

tate diſtãtes. qre in hijs vocibꝰ nulla ineqᷓlitate diſcoꝛdãt nulla oi no ↄſonãtia eſt. qre dixit qᷓ ſcom nũeros armonici ſunt Rabes in tẽtũ.de angulo acuto p̃us diximus de eiuſdẽ dꝛijs.

Himiliter in multũ diſtantibus vtiles ad dilti

Ponit tres vtilitates q̃̊tti inſtrumẽti qᷓ̃rũ vltima valet ad aſſignan⸗ diffinitiões qꝛ ſi eſt aligð cõmũe in quo plura ſunt ſimilia in quo cõueniũt hoc poteſt poni genere in diffinitiõibꝰ eoꝝ. hoc ſatis pa tet in hijs ſut eiuſdẽ gener? ꝓpinqui.Et huius ponit phus ſcðm ex emplũ de vnitate de pũcto ↄueniũt in hoc ſũt pᷣncipiũ qꝛ vni⸗ tas eſt p̃ncipiũ nũeri pũctꝰpncipiũ linee vnũ genꝰ hoꝝ eſt quãti tas. de hijs in pdicamẽtis ſi uftcẽter diximus. 6 5 4 Secundo thopicon. Himiliter aũt in contrarijs in puatiut t ha MHic phs oſtendit quomõ iſte ↄſequẽtie valẽt in alijs oppoſitꝭ Et p⸗ mo in puatiuis q ↄſequẽtia in ecõtrario valet in puatiue oppoſi tis niſi matererialit.ʒ in ipis valet ↄſequẽtia in ipo. Et oſequẽtia in ipo tmĩoꝝ tenetin p̃uatiue oppoſitꝭ.tꝛibꝰ ↄditiõibꝰ obruatis. in q bus ponit de hijs ſcom pᷣuationẽ habitũ oppoſitis ſunt ad ali⸗ qͥd quãtitatis.ſiue relatiuis vtẽdũ eſt.in oppoſitiõe em̃ eoꝝ ſũt ad aliqͥd eadẽ ↄſequẽtia eſtytẽdũ. hoc eſt in ipᷣo ↄſequẽtia vt in puatiõe oppoſitis vt ſi triplũ eſt multiplex. ſubtriplũ ſuu coꝛrelatiũ añcedẽ tis ſmłtiplex. dẽ aũt opponi relatiue triplũ ad ſubtriplũ multi plex ad ſubmultiplex dicunt᷑ relatiue oppoſita in ↄſequẽte. hoc qui dẽ exẽplũ eſt in hijs ſunt ʒm eſſe ſcðm dici relatiua.qᷓ relatiua ſunt ve relatiua oppoſita.ẽt qͥd multiplex ſpecies ineqᷓlitatis nue roꝝ ſubmultiplex diximus in pᷣcedẽtibꝰ de relatiuis. multiplex ðꝛ nũerus qᷓ ↄtinet minoꝛẽ plus qᷓ; ſemel.minoꝛ aũt habet vt tria ad duo dicit tripla ꝓpoꝛtio tria dicunt᷑ triplũ⁊ duo ſubtriplũ.

.*22 Trreio thomico: Vtlle aũt eſt inſpitere ſingularia in quibus in Ponit hic finalit phs aliqã documẽta ad terminãdũ ꝓbleumata pti⸗ cularia indiffinita.ẽt poͦit in vltimo documẽto. Si ĩ aliquo ꝓbleu

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