Alvarus, Thomas, Liber de triplici motu, 1509

Table of figures

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                  <s xml:id="N24ACD" xml:space="preserve">
                    <pb chead="De motu augmentationis." file="0210" n="210"/>
                  falſum: igr̄ ex illud quo ſequit̄̄. </s>
                  <s xml:id="N24AD9" xml:space="preserve">Seq̄la ptꝫ / q2 tantã
                    <lb/>
                  quãtitatē ſupra totã p̄habitã acq̇rit medietas: ſic
                    <lb/>
                  totū: igr̄ medietas, et totū eq̄ velociṫ augent̄̄. </s>
                  <s xml:id="N24AE0" xml:space="preserve">Ptꝫ
                    <lb/>
                  ↄ̨ña expoſitiõe. </s>
                  <s xml:id="N24AE5" xml:space="preserve">Sed ꝓbo falſitatē ↄ̨ñtis. </s>
                  <s xml:id="N24AE8" xml:space="preserve">Tū ṗmo
                    <lb/>
                  q2 tūc ſeq̄ret̄̄ /  eq̄ velociṫ augeret̄̄ totū ſicut in īfi-
                    <lb/>
                  nitū modica eiꝰ pars. </s>
                  <s xml:id="N24AEF" xml:space="preserve">Sꝫ hoc vr̄ abſurdū: igr̄ illud
                    <lb/>
                  ex q̊ ſequit̄̄. </s>
                  <s xml:id="N24AF4" xml:space="preserve">Seq̄la ptꝫ / q2 qñ totū acq̇rit vnū ſemipe­
                    <lb/>
                  dale, medietas eiꝰ acq̇rit tm̄, et octaua et ſexdecima
                    <lb/>
                  termīata ad illã quantitatē acq̇ſitã, et ſic ↄ̨ñter: igr̄.
                    <lb/>
                  </s>
                  <s xml:id="N24AFC" xml:space="preserve">Tū ſcḋo q2 ſtat /  medietas alicuiꝰ intēdat̄̄ aliq̈liṫ
                    <lb/>
                  velociṫ acq̇rēdo aliquã intēſionē: tñ totū nõ acq̇rit
                    <lb/>
                  tantã. </s>
                  <s xml:id="N24B03" xml:space="preserve">ergo eodē mõ ſtat in motu augmētatiõis 
                    <lb/>
                  medietas aliqualiṫ velociṫ augeat̄̄, et totū nõ: et ꝑ
                    <lb/>
                  ↄ̨ñs illatū flm̄. </s>
                  <s xml:id="N24B0A" xml:space="preserve">¶ Dices et bene ↄ̨cedēdo illatū in ta­
                    <lb/>
                  li caſu: et ad ꝓbationē falſitatꝪ eiꝰ ↄ̨cedēdo illḋ ↄ̨ñs
                    <lb/>
                  vcꝫ /  ita velociter auget̄̄ totū ſicut īfinite modica
                    <lb/>
                  eiꝰ pars ſignãter ſi hoc fiat ꝑ additionē quãtitatis
                    <lb/>
                  alicui medietati: ſicut ſit qñ aliq̇d addit̄̄ parti aīaĺ:
                    <lb/>
                  et augmētat̄̄ aīal. </s>
                  <s xml:id="N24B17" xml:space="preserve">¶ Ad ſcḋam īprobationē cõcedo
                    <lb/>
                    <gap/>
                  q2 ſtat  medietas
                    <lb/>
                  alicꝰ ītēdat̄̄ et nõ totū: et ſtat  totū ītēdat̄̄ et vna eiꝰ
                    <lb/>
                  medietas nõ intēdat̄̄. </s>
                  <s xml:id="N24B21" xml:space="preserve">Nõ tñ ſtat  pars augmētet̄̄
                    <lb/>
                  ſine diminutiõe aliq̈ quī totū augmētet̄̄. </s>
                  <s xml:id="N24B26" xml:space="preserve">Cõtra tūc
                    <lb/>
                  ſeq̄ret̄̄ /  ſēꝑ eq̄ velociter augmētaret̄̄ aliqua pars
                    <lb/>
                  ſicut totū. </s>
                  <s xml:id="N24B2D" xml:space="preserve">Sed ↄ̨ñs eſt flm̄: igr̄ illud ex q̊ ſequit̄̄. </s>
                  <s xml:id="N24B30" xml:space="preserve">Fal­
                    <lb/>
                  ſitas ↄ̨ñtis ꝓbat̄̄. </s>
                  <s xml:id="N24B35" xml:space="preserve">Et volo /  vtri medietati vnius
                    <lb/>
                  pedalis addat̄̄ ſemipedale in extremis oppoſitis:
                    <lb/>
                  tūc manifeſtū eſt  totū acq̇rit pedalē quãtitatem
                    <lb/>
                  et nulla ꝑs eiꝰ acq̇rit pedalē quãtitatē: igr̄ nulla ꝑs
                    <lb/>
                  ibi auget̄̄ ita velociṫ ſicut totū: et ꝑ ↄ̨ñs nõ ſēꝑ eque­
                    <lb/>
                  velociṫ etc̈. </s>
                  <s xml:id="N24B42" xml:space="preserve">Seq̄la tñ ꝓbat̄̄: q2 ſi nõ ſēꝑ augmētaret̄̄
                    <lb/>
                  aliq̈ pars ita velociṫ ſicut totū: maxīe eſſet in caſu
                    <lb/>
                  in q̊ ꝓbat̄̄ falſitas ↄ̨ñtis: ſed in illo caſu eque velo-
                    <lb/>
                  citer augetur aliqua pars ſicut totum puta pars
                    <lb/>
                  que cõponitur ex duabꝰ quartis extremis cū parti-
                    <lb/>
                  bus extremalibꝰ q̄ ꝑtes extreme circūferētiales cõ-
                    <lb/>
                  ſtituūt vnū quadratū inṫ qḋ manet aliud vt ptꝫ in
                    <lb/>
                    <figure xlink:href="fig-0210-01a" xlink:label="fig-0210-01" xml:id="N24B9E" number="12">
                      <image file="0210-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YHKVZ7B4/figures/0210-01"/>
                    </figure>
                  figura iã ſequenti: igr̄. </s>
                  <s xml:id="N24B58" xml:space="preserve">¶ Dices et bñ
                    <lb/>
                  negãdo ſeq̄lã: et ad punctū ꝓbatiõis
                    <lb/>
                  dr̄  etiã in illo caſu eq̄ velociṫ au-
                    <lb/>
                  get̄̄ aliq̈ ꝑs ſicut totū / vt ꝓbat argu-
                    <lb/>
                  mētū: et ſic negat̄̄ /  maxīe eſſet ī illo
                    <lb/>
                  caſu: ſed dico /  eſt in caſu vbi totuꝫ
                    <lb/>
                  ꝑ totū rarefit: tūc em̄ nulla ꝑs ita velociṫ auget̄̄ ſi-
                    <lb/>
                  cut totū / vt ſatꝪ ptꝫ / quī ſi totū aliqḋ qḋ ꝑ totū rare-
                    <lb/>
                  fit rarefiat ad duplū: ipſū totū acq̇rit tantã quãti-
                    <lb/>
                  tatē ſicut ipſū eſt: et nulla ꝑs acq̇rit quãtitatē
                    <lb/>
                  ſicut illud totū eſt. </s>
                  <s xml:id="N24B6F" xml:space="preserve">¶ Sed ↄ̈: q2 tūc ſeq̄ret̄̄ /  qñ ali-
                    <lb/>
                  quid augmētaret̄̄ ꝑ rarefactionē q̄ rarefactio eſt ꝑ
                    <lb/>
                  totū ſubiectū quãtitas quã adeq̈te acq̇rit totū eſſet
                    <lb/>
                  mīma quã nõ acq̇rit aliq̄ ꝑs. </s>
                  <s xml:id="N24B78" xml:space="preserve">Sed hoc vr̄ flm̄: igr̄ il-
                    <lb/>
                  lud ex quo ſequit̄̄. </s>
                  <s xml:id="N24B7D" xml:space="preserve">Seq̄la pꝫ. </s>
                  <s xml:id="N24B80" xml:space="preserve">q2 dato /  totū acq̇rat
                    <lb/>
                  pedalē quãtitatē: manifeſtū eſt /  vna medietas eiꝰ
                    <lb/>
                  acq̇ſiuit aliquã partē illiꝰ: et aggregatū ex illa me-
                    <lb/>
                  dietate et ṗma ꝑte ꝓportiõali alteriꝰ medietatꝪ acq̇­
                    <lb/>
                  ſiuit maiorē: et aggregatū ex illa et duabus primis
                    <lb/>
                  ꝑtibꝰ ꝓportiõabilibꝰ alteriꝰ adhuc acq̇ſiuit maiorē /
                    <lb/>
                  et ſic ↄ̨ñter calculando. </s>
                  <s xml:id="N24B8F" xml:space="preserve">Ptꝫ /  quãtitas acq̇ſita ipſi
                    <lb/>
                  toti eſt minima quã nõ acquiſiuit aliqua pars.</s>
                </p>
                <p xml:id="N24BA4">
                  <s xml:id="N24BA5" xml:space="preserve">Octauo contra eandē partē q̄ſtionis
                    <lb/>
                  argr̄ ſic. </s>
                  <s xml:id="N24BAA" xml:space="preserve">Qm̄ ſi velocitas augmētatiõis attēderet̄̄
                    <lb/>
                  penes abſolutã acq̇ſitionē quãtitatꝪ: ſeq̄ret̄̄ /  qḋlꝫ
                    <lb/>
                  iſtoꝝ īciperet īfinite velociṫ augeri: et tñ īciperet in-
                    <lb/>
                  finitū tarde augeri aliqḋ iſtoꝝ: ſed ↄ̨ñs videt̄̄ re-
                    <lb/>
                  pugnare: igr̄ illud ex quo ſequit̄̄. </s>
                  <s xml:id="N24BB5" xml:space="preserve">Seq̄la ptꝫ et volo /
                    <lb/>
                   ſint īfinita ↄ̨tinuo ſe habētia in ꝓportiõe ſubdu­
                    <lb/>
                  pla: ita  primū ſit pedale, ſcḋ3 ſemipedale, tertiū
                    <lb/>
                  q̈rta pedalis / et ſic ↄ̨ñter: et diuidat̄̄ hora ꝑ ꝑtes ꝓ-
                    <lb/>
                  portiõales ꝓportione dupla qḋlibet o illoꝝ diu­
                    <cb chead="De motu augmentationis."/>
                  dat̄̄ ꝑ partes ꝓportiõales ꝓportiõe ſexquialtera: et
                    <lb/>
                  qḋlꝫ illoꝝ in q̈libet ꝑte ꝓportiõali hore ꝑdat vnaꝫ
                    <lb/>
                  partē ꝓportionalē ſui ꝓportiõe ſexq̇altera quouſ
                    <lb/>
                  in fine hore deueniat ad nõ quantū: deinde īcipiant
                    <lb/>
                  illa a nõ quãto augeri oīno ſicut diminuebant̄̄ pu-
                    <lb/>
                  ta in q̈libet ꝑte ꝓportiõali hore ꝓportiõe dupla ac­
                    <lb/>
                  quirēdo vna ꝑte ꝓportiõalē ſui ꝓportiõe ſexq̇alte-
                    <lb/>
                  ra q̊ poſito argr̄ ſic: qḋlꝫ illoꝝ īmediate poſt illud
                    <lb/>
                  inſtãs augmētatiõis a nõ quãto in īfinitū velociter
                    <lb/>
                  augmētabit̄̄: et īmediate poſt tale inſtãs in infinitū
                    <lb/>
                  tarde augebit̄̄ aliqḋ illoꝝ: et mõ nullum illoꝝ aug-
                    <lb/>
                  mentat̄̄ igr̄ ꝓpoſitū. </s>
                  <s xml:id="N24BD9" xml:space="preserve">Probat̄̄ maior: q2 qḋlꝫ illoꝝ
                    <lb/>
                  īcipit a nõ quãto in qualꝫ ꝑte ꝓportiõali ꝓportiõe
                    <lb/>
                  dupla acq̇rere ꝓportionē ſexq̇alterã: g̊ qḋlꝫ illoꝝ in­
                    <lb/>
                  cipit in īfinitū velociṫ acq̇rere de quãtitate / vt ptꝫ ex
                    <lb/>
                  ſcḋa ↄ̨firmatiõe ſcḋi argumēti huiꝰ q̄ſtiõis et ꝑ ↄ̨ñs
                    <lb/>
                  qḋlꝫ illoꝝ īcipit in īfinitū velociṫ augeri qñ in īfini­
                    <lb/>
                  tū velox augmētatio eſt in īfinitū velox acq̇ſitio quã­
                    <lb/>
                  titatꝪ / vt ptꝫ ex hac poſitionē. </s>
                  <s xml:id="N24BEA" xml:space="preserve">Probat̄̄ minor vcꝫ / 
                    <lb/>
                  īmediate poſt hoc in īfinitū tarde acq̇ret aliqḋ iſto­
                    <lb/>
                  rū de quãtitate q2 ↄ̨tinuo in īfinitū minꝰ primo erit
                    <lb/>
                  aliqḋ illoꝝ: ſicut fuit in via diminutiõis: et incipiunt
                    <lb/>
                  oīa illa a nõ quãto in eodē inſtãti augeri: g̊ quocū
                    <lb/>
                  inſtãti dato poſt hoc īter hoc et illud īfinite modicū
                    <lb/>
                  quãtitatē acq̇ſiuit aliqḋ illoꝝ: et ꝑ ↄ̨ñs īfinite tarde
                    <lb/>
                  auget̄̄ aliqḋ illoꝝ. </s>
                  <s xml:id="N24BFB" xml:space="preserve">¶ Dices et bñ ↄ̨cedēdo illatū nec
                    <lb/>
                  illud eſt incõueniēs: ſed ſequēs / vt ꝓbat argumentū.
                    <lb/>
                  </s>
                  <s xml:id="N24C01" xml:space="preserve">Sed ↄ̈ / q2 pari rõne ↄ̨cedendū eſſet / qḋ vnū et idem a
                    <lb/>
                  nõ quãto īciperet in īfinitū velociṫ augmētari: et il-
                    <lb/>
                  lud idē īciperet a nõ quãto in īfinitū tarde augmē-
                    <lb/>
                  tari. </s>
                  <s xml:id="N24C0A" xml:space="preserve">ſed ↄ̨ñs eſt flm̄: igr̄ illud ex quo ſequit̄̄. </s>
                  <s xml:id="N24C0D" xml:space="preserve">Falſi-
                    <lb/>
                  tas ↄ̨ñtis ptꝫ / q2 detur illud et ſit a. / et argr̄ ſic / a. inci­
                    <lb/>
                  pit in īfinitū velociṫ augmētari: g̊ īcipit in infinitū
                    <lb/>
                  velociter acq̇rere de quãtitate: et ꝑ ↄ̨ñs nõ īcipit in
                    <lb/>
                  infinitū velociṫ acq̇rere de quãtitate: et ſic habet̄̄ 
                    <lb/>
                  īcipit ī īfinitū velociṫ acq̇rere de quantitate: et nõ
                    <lb/>
                  īcipit ī īfinitū velociṫ acq̇rē de quãtitate / qḋ īplicat
                    <lb/>
                  </s>
                  <s xml:id="N24C1D" xml:space="preserve">Seq̄la tū ꝓbat̄̄ et volo /  a. īcipiat augeri a nõ quã­
                    <lb/>
                  to in aliqua hora diuiſa ꝑ partes ꝓportiõales ꝓ-
                    <lb/>
                  portiõe dupla ſiĺr  vna medietas eiꝰ in qualꝫ ꝑte
                    <lb/>
                  ꝓportiõali pari acq̇rat ꝓportionē ſexq̇alterã: et al­
                    <lb/>
                  tera medietas in q̈libet īpari acq̇rat octuplã quo
                    <lb/>
                  poſito argr̄ ſic / illud in tali caſu īcipit in īfinitū ve-
                    <lb/>
                  lociter augeri et etiã īcipit in īfinitū tarde augeri et
                    <lb/>
                  hoc a nõ quãto: igr̄ ꝓpoſitū. </s>
                  <s xml:id="N24C2E" xml:space="preserve">Argr̄ maior / q2 incipit
                    <lb/>
                  in ꝑtibꝰ ꝓportiõalibꝰ paribꝰ īfinite velociṫ acq̇rere
                    <lb/>
                  de quãtitate / vt ptꝫ ex ſcḋa ↄ̨firmatiõe ſcḋi argumē­
                    <lb/>
                  ti p̄allegati: igr̄ incipit in īfinitū velociter augeri.
                    <lb/>
                  </s>
                  <s xml:id="N24C38" xml:space="preserve">Probat̄̄ mīor: q2 illud īcipit in īfinitū tarde acq̇re­
                    <lb/>
                  re de quantitate in partibꝰ īparibꝰ / vt ptꝫ ex dedu-
                    <lb/>
                  ctione ṗme ↄ̨firmatiõis ſcḋi argumēti preallegati:
                    <lb/>
                  igr̄ īcipit illud īfinite tarde augeri in ꝑtibꝰ īparibꝰ
                    <lb/>
                    <note position="right" xlink:href="note-0210-01a" xlink:label="note-0210-01" xml:id="N24C7B" xml:space="preserve">Confir-
                      <lb/>
                    matio.</note>
                  </s>
                  <s xml:id="N24C48" xml:space="preserve">¶ Confirmat̄̄. </s>
                  <s xml:id="N24C4B" xml:space="preserve">Q2 ſi illn poſito eſſet vera ſeq̇ret̄̄ / 
                    <lb/>
                  nullū quadratū ꝑfectū poſſet vniformiṫ diminui
                    <lb/>
                  ad nõ quãtū qñ trina eiꝰ dimēſio puta lõgitudo la­
                    <lb/>
                  titudo et ꝓfūditas vniformiṫ a nõ quãto diminuūt̄̄ /
                    <lb/>
                  ſed ↄ̨ñs eſt flm̄ / q2 nõ videt̄̄ repugnare tale quadra­
                    <lb/>
                  tū vniformiter ſic diminui ad nõ quantū: igit̄̄ illud
                    <lb/>
                  ex quo ſequit̄̄. </s>
                  <s xml:id="N24C5A" xml:space="preserve">Sequela tñ ꝓbatur: quia ſi aliquod
                    <lb/>
                  ſic poteſt diminui detur aliquod quadratū pedalr̄
                    <lb/>
                  lõgū, pedaliṫ latū, pedaliṫ ꝓfūdū, qḋ ſit a. </s>
                  <s xml:id="N24C61" xml:space="preserve">Tūc ar̄
                    <lb/>
                  ſic / ↄ̨tinuo lõgitudo latitudo et ēt ꝓfūditas huiꝰ q̈-
                    <lb/>
                  drati a. vniformiṫ ī hora diminuit̄̄ vſ ad nõ ̄tū:
                    <lb/>
                  igr̄ in ṗma ꝑte ꝓportiõali hore ꝓportiõe dupla il-
                    <lb/>
                  lud q̈dratū efficit̄̄ in duplo minꝰ logū ī duplo minꝰ
                    <lb/>
                  latū. </s>
                  <s xml:id="N24C6E" xml:space="preserve">in duplo minꝰ ꝓfundū: et ſic ꝑ ↄ̨ñs efficit̄̄ ī octu­
                    <lb/>
                  plo minꝰ: et ꝑ ↄ̨ñs in ṗma medietate ꝑdit ſeptē octa­
                    <lb/>
                  uas: et in ſcḋa medietate vnã tm̄: et ꝑ ↄ̨ñs in illa hõ
                    <lb/>
                  cõtinuo diminuit̄̄ vniformiṫ / qḋ fuit probandū</s>
                </p>
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