Alvarus, Thomas, Liber de triplici motu, 1509

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          <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
            <div xml:id="N20F21" level="3" n="3" type="other" type-free="tractatus">
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                <pb chead="Tertii tractatus" file="0211" n="211"/>
                <p xml:id="N24C87">
                  <s xml:id="N24C88" xml:space="preserve">Probat̄̄ tñ illa ↄ̨ña: iſtud q̈dratū ꝑfectuꝫ efficit̄̄ in
                    <lb/>
                  duplo minꝰ lõgū, et in duplo minꝰ latū, et in duplo
                    <lb/>
                  minꝰ ꝓfundū. </s>
                  <s xml:id="N24C8F" xml:space="preserve">igr̄ efficit̄̄ in octuplo minꝰ: qm̄ coſta
                    <lb/>
                  illiꝰ q̈drati in fine ad coſtã illiꝰ in plīcipio diminu-
                    <lb/>
                  tiõis ſe hꝫ in ꝓportiõe ſubdupla: ita  coſte illiꝰ q̈-
                    <lb/>
                  drati in prīcipio et in fine ſe hñt in ꝓportiõe dupla
                    <lb/>
                  et illa ſunt ꝑfecta q̈drata: igr̄ illa q̈drata ſe hñt in
                    <lb/>
                  ꝓportiõe triplicata ad duplã: et illa ē octupla / vt cõ­
                    <lb/>
                  ſtat ex ſexto capite ſcḋe ꝑtis: igr̄ ꝓpoſitū. </s>
                  <s xml:id="N24C9E" xml:space="preserve">Ptꝫ hec
                    <lb/>
                  ↄ̨ña / ꝑ quãdã ↄ̨cluſiõeꝫ ſuperiꝰ ꝓbatã in tractatu de
                    <lb/>
                  motu locali peues effectū capite ſcḋo q̄ ↄ̨cĺo talṫ eſt
                    <lb/>
                  </s>
                  <s xml:id="N24CA6" xml:space="preserve">Proportio q̊dratoꝝ ꝑfectoꝝ eſt ꝓpor° coſtaꝝ tri-
                    <lb/>
                  plicata. </s>
                  <s xml:id="N24CAB" xml:space="preserve">Siĺe argumētū poteris facere de ſuꝑficie
                    <lb/>
                  cuiꝰ latitudo et lõgitudo vnifor̄iṫ diminūt̄̄ ꝑ horã.</s>
                </p>
                <p xml:id="N24CB0">
                  <s xml:id="N24CB1" xml:space="preserve">Nono prīcipalr̄ ar̄ ſic: ſi illa poſi° eſſet
                    <lb/>
                  vera ſeq̄ret̄̄: ſi hora diuidat̄̄ ꝑ partes ꝓportiõales
                    <lb/>
                  ꝓportiõe dupla: et in ṗma ꝑte ꝓportiõali īpari pe-
                    <lb/>
                  dale a. aliq̈liṫ velociṫ augeat̄̄: et in ſcḋa īpari in du­
                    <lb/>
                  plo velociꝰ: et in tertia īpari in duplo velociꝰ quã ī
                    <lb/>
                  ſcḋa īpari: et ſic ↄ̨ñter ↄ̨tinuo in q̈lꝫ īpari ſeq̄nte in
                    <lb/>
                  duplo velociꝰ̄ in īpari īmediate p̄cedēte: tūc a. pe­
                    <lb/>
                  dale īfinite velociter augeret̄̄. </s>
                  <s xml:id="N24CC2" xml:space="preserve">Cõſequēs eſt flm̄. </s>
                  <s xml:id="N24CC5" xml:space="preserve">igr̄
                    <lb/>
                  illud ex q̊ ſequit̄̄. </s>
                  <s xml:id="N24CCA" xml:space="preserve">Seq̄la ptꝫ / q2 ſi illud pedale in q̈lꝫ
                    <lb/>
                  ꝑte ꝓportiõali vniꝰ hore ꝓportiõe dupla ita aug-
                    <lb/>
                  mētaret̄̄  in q̈lꝫ ſeq̄nte in duplo velociꝰ augmēta­
                    <lb/>
                  ret̄̄̄ in īmediate p̄cedēte: ip̄m in q̈lꝫ ꝑte ꝓportiõa­
                    <lb/>
                  li tantã quãtitatē acq̇reret ſicut in ṗma / vt cõſtat: et
                    <lb/>
                  ſic in illa hora in īfinitū velociṫ augmētaret̄̄. </s>
                  <s xml:id="N24CD7" xml:space="preserve">igr̄ ſi
                    <lb/>
                  illud idē pedale in q̈lꝫ ꝑte ꝓportiõali ꝓportiõe du­
                    <lb/>
                  pla īpari ſeq̄nte in duplo velociꝰ augeat̄̄̄ in īpari
                    <lb/>
                  īmediate p̄cedēte: ipſum in q̈lꝫ ꝑte tantã quãtitatē
                    <lb/>
                  acquirit quantã in prima. </s>
                  <s xml:id="N24CE2" xml:space="preserve">Ptꝫ ↄ̨ña / q2 nõ eſt maior rõ
                    <lb/>
                  de vno ꝙ̄ de alio. </s>
                  <s xml:id="N24CE7" xml:space="preserve">Falſitas tñ ↄ̨ñtis argr̄ ſic. </s>
                  <s xml:id="N24CEA" xml:space="preserve">qm̄ ille
                    <lb/>
                  ꝑtes īpares ↄ̨tinuo ſe hñt in ꝓportiõe q̈drupla. </s>
                  <s xml:id="N24CEF" xml:space="preserve">vt
                    <lb/>
                  ptꝫ: et velocitates augmētationis in illis ꝑtibꝰ ↄ̨ti-
                    <lb/>
                  nuo ſe hñt in ꝓportiõe dupla: g̊ quãtitates acq̇ſite
                    <lb/>
                  ↄ̨tiuuo ſe hñt in ꝓportiõe ſubdupla: et ꝑ ↄ̨ñs aggre­
                    <lb/>
                  gatū ex oībꝰ illis eſt duplū ad primã illaꝝ. </s>
                  <s xml:id="N24CFA" xml:space="preserve">oīa iſta
                    <lb/>
                  ſatis patent intelligenti ea que dicta ſunt de velo-
                    <lb/>
                  citate motus localis penes effectum ſuperius.</s>
                </p>
                <p xml:id="N24D01">
                  <s xml:id="N24D02" xml:space="preserve">In oppoſitū argr̄ ſic. </s>
                  <s xml:id="N24D05" xml:space="preserve">Q2 nõ videt̄̄ alṫ
                    <lb/>
                  modus velocitatꝪ augmētatiõis ab altero illoꝝ co­
                    <lb/>
                  gnoſcende: igitur penes alterum illorum debet ve-
                    <lb/>
                  locitas motus augmentationis attendi.</s>
                </p>
                <p xml:id="N24D0E">
                  <s xml:id="N24D0F" xml:space="preserve">Pro ſolutiõe huiꝰ q̄ſtiõis quatuor ſūt
                    <lb/>
                  ordine faciēda. </s>
                  <s xml:id="N24D14" xml:space="preserve">Primo em̄ definitiones et declara-
                    <lb/>
                  tiões termīoꝝ ad hãc materiã ſpectãtiū ponētur et
                    <lb/>
                  notant̄̄. </s>
                  <s xml:id="N24D1B" xml:space="preserve">Scḋo aliq̈ inducent̄̄ ↄ̨cluſiões. </s>
                  <s xml:id="N24D1E" xml:space="preserve">Tertio po-
                    <lb/>
                  nent̄̄ dubitatiões. </s>
                  <s xml:id="N24D23" xml:space="preserve">Et poſtremo rõnes ãte oppoſitū
                    <lb/>
                  diſſoluent̄̄. </s>
                  <s xml:id="N24D28" xml:space="preserve">Aduertendū igr̄ /  augmētatio ita diffi-
                    <lb/>
                  nit̄̄ a pḣo primo de gñatiõe.
                    <note position="left" xlink:href="note-0211-01a" xlink:label="note-0211-01" xml:id="N24E19" xml:space="preserve">q̇d aug-
                      <lb/>
                    mētatio.</note>
                  </s>
                  <s xml:id="N24D32" xml:space="preserve">Augmētatio eſt p̄exi-
                    <lb/>
                  ſtētis magnitudīs additamētū.
                    <lb/>
                    <note position="left" xlink:href="note-0211-02a" xlink:label="note-0211-02" xml:id="N24E21" xml:space="preserve">q̇d dimi-
                      <lb/>
                    nutio.</note>
                  </s>
                  <s xml:id="N24D3E" xml:space="preserve">¶ Diminutio vero
                    <lb/>
                  p̄exiſtētꝪ quãtitatꝪ mīoramētū.
                    <note position="left" xlink:href="note-0211-03a" xlink:label="note-0211-03" xml:id="N24E29" xml:space="preserve">pḣs ṗmo
                      <lb/>
                    de gene.</note>
                  </s>
                  <s xml:id="N24D48" xml:space="preserve">Ex q̊ ↄ̨cludit phūs:
                    <lb/>
                   ex materia ſine magnitudīe nõ p̄t eſſe augmēta°
                    <lb/>
                    <note position="left" xlink:href="note-0211-04a" xlink:label="note-0211-04" xml:id="N24E31" xml:space="preserve">Tex. Cõ-
                      <lb/>
                    mēti .31.</note>
                  </s>
                  <s xml:id="N24D54" xml:space="preserve">Textu cõmēti triceſimi ṗmi. </s>
                  <s xml:id="N24D57" xml:space="preserve">Hec aūt augmentatio
                    <lb/>
                  duplr̄ fieri p̄t. </s>
                  <s xml:id="N24D5C" xml:space="preserve">Uno° ꝓut diſtīguit̄̄ ↄ̈ rarefactionē: et
                    <lb/>
                  ſic fit ꝑ additionē alicuiꝰ rei quãte p̄exñti
                    <lb/>
                  eiuſdē ſpecie
                    <gap/>
                  ̀ cū illa ex q̈ re cū p̄exñte fit vnū maiꝰ.
                    <lb/>
                  </s>
                  <s xml:id="N24D66" xml:space="preserve">Et hec eſt ꝓṗe illa augmētatio de q̈ phūs loquit̄̄ lo­
                    <lb/>
                  cõ p̄allegato. </s>
                  <s xml:id="N24D6B" xml:space="preserve">quãuis videat̄̄ ibi ꝓṗe de augmenta-
                    <lb/>
                  tiõe aīati loqui q̄ fit ꝑ intꝰ ſuſceptionē. </s>
                  <s xml:id="N24D70" xml:space="preserve">Alio° capit̄̄
                    <lb/>
                  augmētatio ꝓut eſt idē cū rarefactione. </s>
                  <s xml:id="N24D75" xml:space="preserve">Et iſto mõ
                    <lb/>
                  augmētatio p̄t fieri ſine additiõe alicuiꝰ alteriꝰ: ſꝫ
                    <lb/>
                  p̄ciſe ꝑ maiorē extēſionē p̄exiſtētꝪ. </s>
                  <s xml:id="N24D7C" xml:space="preserve">Et vtro iſtorū
                    <lb/>
                  modoꝝ loq̇mur in propoſito quãuis de ea ſcḋo mõ
                    <lb/>
                  peculiariṫ dictū ſit in p̄cedēti capite. </s>
                  <s xml:id="N24D83" xml:space="preserve">Tu tñ aduer-
                    <lb/>
                  te  ꝓp̄e capiēdo ṫmīos: rarefactio differt ab aug-
                    <lb/>
                  mētatiõe ſaltē diuerſa cõnotant illi duo ṫmini q̇rū
                    <cb chead="Capitulū ſecundum."/>
                  termīoꝝ ſignificãtias et ↄ̨notatiões facile ex his q̄
                    <lb/>
                  circa primū de gñatiõe dicunt̄̄ intelligere poteris.
                    <lb/>
                    <note position="right" xlink:href="note-0211-05a" xlink:label="note-0211-05" xml:id="N24E39" xml:space="preserve">pḣs ṗmo
                      <lb/>
                    de gene.</note>
                  </s>
                  <s xml:id="N24D96" xml:space="preserve">Utrū aūt augmētatio fiat ſcḋm ꝑtes formales aut
                    <lb/>
                  materiales et q̄ ſint ꝑtes for̄ales aut materiales et
                    <lb/>
                  q̊t ↄ̨ditiões req̇rant̄̄: habes ṗmo de gñatiõe capĺo
                    <lb/>
                  de augmetatiõe
                    <note position="right" xlink:href="note-0211-06a" xlink:label="note-0211-06" xml:id="N24E41" xml:space="preserve">Textu cõ­
                      <lb/>
                    mē. 36. et
                      <lb/>
                    32.</note>
                  </s>
                  <s xml:id="N24DA4" xml:space="preserve">Textu cõmēti triceſimi ſcḋi et trice­
                    <lb/>
                  ſimi ſexti videas ibi.
                    <note position="right" xlink:href="note-0211-07a" xlink:label="note-0211-07" xml:id="N24E4B" xml:space="preserve">Duplex
                      <lb/>
                    opīo de
                      <lb/>
                    augmē-
                      <lb/>
                    tatione.</note>
                  </s>
                  <s xml:id="N24DAE" xml:space="preserve">Nunc autē ſufficiat ſcire quid
                    <lb/>
                  augmētatio: et q̊tuplex eſt augmētatio: vt ītelligat̄̄
                    <lb/>
                  penes qḋ velocitas motꝰ augmētatiõis attēdi ha-
                    <lb/>
                  beat. </s>
                  <s xml:id="N24DB7" xml:space="preserve">In q̈ materia due ſūt opiniões q̈s calculator
                    <lb/>
                  recitat in capĺo de augmētatiõe: quãuis alii tertiã
                    <lb/>
                  adiiciãt.
                    <note position="right" xlink:href="note-0211-08a" xlink:label="note-0211-08" xml:id="N24E57" xml:space="preserve">Calcula.
                      <lb/>
                    Hētiſberi</note>
                  </s>
                  <s xml:id="N24DC3" xml:space="preserve">Uideas Hentiſberū cū cõmētatore ſuo in
                    <lb/>
                  tractatu de motu locali in capĺo de augmētatione
                    <lb/>
                  </s>
                  <s xml:id="N24DC9" xml:space="preserve">Nūc aūt ſufficiet dicere /  ſcḋm vnã opinionē velo­
                    <lb/>
                  citas motꝰ augmētatiõis attēdit̄̄ penes ꝓportiõa-
                    <lb/>
                  lē quãtitatꝪ acq̇ſitionē. </s>
                  <s xml:id="N24DD0" xml:space="preserve">Hoc eſt dicere. </s>
                  <s xml:id="N24DD3" xml:space="preserve"> ſi duo aug­
                    <lb/>
                  mētent̄̄ ſiue eq̈lia ſiue ineq̈lia: et eq̈lē ꝓportionē in
                    <lb/>
                  eodē tꝑe adeq̈te acq̇rãt: ipſa eq̄ velociṫ augmētant̄̄
                    <lb/>
                  et ſi minꝰ in duplo maiorē ꝓportionē acquirit quam
                    <lb/>
                  maiꝰ in eodē tꝑe: vt puta q2 minꝰ acq̇rit q̈druplã: et
                    <lb/>
                  maiꝰ duplã: minꝰ in duplo velociꝰ augmētat̄̄ quam
                    <lb/>
                  maiꝰ. </s>
                  <s xml:id="N24DE2" xml:space="preserve">Quare ↄ̨cedit hec poſitio /  ſtat aliq̇d ī q̈̈dru­
                    <lb/>
                  plo velociꝰ augmētari quã illud et in q̈druplo mīo­
                    <lb/>
                  rē quãtitatē acq̇rere adeq̈te.
                    <note position="right" xlink:href="note-0211-09a" xlink:label="note-0211-09" xml:id="N24E5F" xml:space="preserve">Calcuĺ.</note>
                  </s>
                  <s xml:id="N24DEE" xml:space="preserve">¶ Ex q̊ ſeq̇t̄̄ has ↄ̨ñas
                    <lb/>
                  ſcḋm hãc poſitionē nichil valere: iſta duo in eodem
                    <lb/>
                  tꝑe eq̈lē quãtitatē acq̇rūt: g̊ eq̄ velociṫ augent̄̄ a. in
                    <lb/>
                  duplo velociꝰ acq̇rit de quantitate ꝙ̄ b. / g̊ in duplo
                    <lb/>
                  velociꝰ augmētat̄̄: a. īfinite velociṫ acq̇rit de quãti-
                    <lb/>
                  tate: g̊ īfinite velociṫ augmētat̄̄. </s>
                  <s xml:id="N24DFB" xml:space="preserve">Scḋa autē poſitio
                    <lb/>
                  nullo pacto ↄ̨ſiderat ꝓportionē quã illud qḋ auge­
                    <lb/>
                  tur acq̇rit: ſed ſolū quãtitatē. </s>
                  <s xml:id="N24E02" xml:space="preserve">Uñ hec ↄ̨ña ſcḋ3 eã eſt
                    <lb/>
                  bona: iſta duo ſiue ſint eq̈lia ſiue inequalia equalē
                    <lb/>
                  quãtitatē acq̇rūt s̈̄titatē p̄habitã ī eodē tꝑe: g̊ eq̄
                    <lb/>
                  velociṫ augent̄̄. </s>
                  <s xml:id="N24E0B" xml:space="preserve">Hiis ãnotatiõibꝰ breuiṫ trãſcurſis:
                    <lb/>
                  reſtat aliq̈s ↄ̨cluſiões īducere. </s>
                  <s xml:id="N24E10" xml:space="preserve">Et ṗmo eas īducemꝰ
                    <lb/>
                  q̄ ex ṗori opīiõe ſequūt̄̄: q̄o ex ſcḋa poſteriꝰ ſic / igr̄</s>
                </p>
                <p xml:id="N24E65">
                  <s xml:id="N24E66" xml:space="preserve">Prima concluſio. </s>
                  <s xml:id="N24E69" xml:space="preserve">Diuiſo corpore per
                    <lb/>
                  ꝑtes ꝓportiõales q̈uis ꝓportiõe: et ṗma ꝑs ꝓpor-
                    <lb/>
                  tiõalis talis corꝑis aliq̈liṫ augmētet̄̄ acq̇rēdo talē
                    <lb/>
                  ꝓportionē q̈lis eſt inṫ ipſam et ſcḋam vel maiorē: et
                    <lb/>
                  ſcḋa in eodē tꝑe augmēter̄ in duplo velociꝰ: et ṫtia
                    <lb/>
                  in triplo velociꝰ quã ṗma: et q̈rta in q̈druplo velociꝰ
                    <lb/>
                  ̄ prima in eodē tꝑe: tale corpꝰ efficiṫ īfinitū, et īfi-
                    <lb/>
                  nitã ꝓportionē acquirit, et ſic īfinite velociꝰ augmētat̄̄
                    <lb/>
                  </s>
                  <s xml:id="N24E7B" xml:space="preserve">Probar̄ ↄ̨cĺo. </s>
                  <s xml:id="N24E7E" xml:space="preserve">q2 ī tali caſu q̄lꝫ ꝑs ꝓportiõalis illiꝰ
                    <lb/>
                  corꝑis ſeq̄ns efficit̄̄ eq̈lis vel maior ꝙ̄ ṗma. </s>
                  <s xml:id="N24E83" xml:space="preserve">g̊ ſequit̄̄ /
                    <lb/>
                   illud corpꝰ efficit̄̄ īfinite magnū. </s>
                  <s xml:id="N24E88" xml:space="preserve">Probat̄̄ añs: et
                    <lb/>
                  volo /  a. corpꝰ diuidat̄̄ ꝓportiõe h. et ṗma ꝑs ꝓpor­
                    <lb/>
                  tiõalis eiꝰ in hora acq̇rit ꝓportionē h. et ſcḋa duas
                    <lb/>
                  h. et ṫtia tres. et q̈rta q̈tuor . / et ſic ↄ̨ñter. </s>
                  <s xml:id="N24E91" xml:space="preserve">Quo poſito
                    <lb/>
                  argr̄ ſic. </s>
                  <s xml:id="N24E96" xml:space="preserve">Prima pars diſtat a ſcḋa ꝑ h. ꝓportionē
                    <lb/>
                  adeq̈te in prīcipio augmētatiõis et ip̄a p̄ma acq̇rit
                    <lb/>
                  h. ꝓportionē: et ſcḋa acq̇rit vnã h. ꝓportionē in q̈
                    <lb/>
                  ṗma excedebat eã: et īſuꝑ tãtã ꝓportiõeꝫ quãtã prīa
                    <lb/>
                  puta vnã aliã ꝓportionē h. / igr̄ efficit̄̄ eq̈lis prime.
                    <lb/>
                  </s>
                  <s xml:id="N24EA2" xml:space="preserve">Ptꝫ hec ↄ̨ña ꝑ maximã ſuperiꝰ poſitã. </s>
                  <s xml:id="N24EA5" xml:space="preserve">Quãdo due
                    <lb/>
                  quãtitates īequales creſcūt, et mīor illaꝝ acquirit
                    <lb/>
                  illã ꝓportionē q̄ eſt inter maiorē et ipſam, et inſuꝑ
                    <lb/>
                  tantaꝫ proportionē adeq̈te quantã acq̇rit maior in
                    <lb/>
                  fine augmētatiõis tales quãtitates manent eq̈les:
                    <lb/>
                  ſed ſic eſt in ꝓpoſito: igr̄. </s>
                  <s xml:id="N24EB2" xml:space="preserve">et ſic ꝓbabis /  ṫtia pars
                    <lb/>
                  effecta eſt eq̈lis ſcḋe q2 acq̇ſiuit duas ꝓportiões h.
                    <lb/>
                  ſicut ſcḋa, et inſuꝑ vnã aliã h. in qua ſcḋa excedebat
                    <lb/>
                  tertiã, et ſiĺr q̈rta acq̇ſiuit tres ꝓportiões h. ſicut et
                    <lb/>
                  tertia et īſuꝑ vnã h. in q̈ tertia excedebat illã: igr̄ ꝑ
                    <lb/>
                  illã maximã oēs ille ꝑtes manēt eq̈les qm̄ ſic ꝓba­
                    <lb/>
                  bis de quibuſcū
                    <gap/>
                  duabꝰ īmeditatis. </s>
                  <s xml:id="N24EC3" xml:space="preserve">Et eodē° ꝓba-
                    <lb/>
                  bis  tale corpꝰ acq̇rit infinitã ꝓportionē: ſi prima
                    <lb/>
                  pars eiꝰ acq̇reret maiorē ꝓportionē ꝙ̄ ſit ꝓportio </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum