Alvarus, Thomas, Liber de triplici motu, 1509

Table of contents

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[4.] Capitulū q̈rtū / in quo principalr̄ q̄rit̄̄ penes quid attendi intenſio qualitatis difformis debeat.
Page: 263
[5.] Capitulum quintum inquirens penes quid gradus ſummi inductio ſit attendenda.
Page: 277
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            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <div xml:id="N17509" level="4" n="7" type="chapter" type-free="capitulum">
                <p xml:id="N179FD">
                  <s xml:id="N17B0D" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0078" n="78"/>
                  correlarii patet ex ſecūdo correlario ſecūde cõclu-
                    <lb/>
                  ſionis huius capitis: et ſecūda breuiter ꝓbatur ſic /
                    <lb/>
                  q2 vbicū aliqua potentia īuariata mediū īuaria­
                    <lb/>
                  tum tranſeūdo ↄ̨tinuo vniformiter remittit motū
                    <lb/>
                  ſuū ad extremū intenſius deueniendo: oīs maior
                    <lb/>
                  vel minor verſus idem extremū veniendo per ean-
                    <lb/>
                  dem lineã cõtinuo difformiter remittit motū ſuum
                    <lb/>
                  ipſa et medio continuo inuariatis / vt ptꝫ ex quarta
                    <lb/>
                  concluſione huiꝰ: et oīs potentia inuariata mediū
                    <lb/>
                  inuariatū tanſeundo ab extremo intenſiori rece-
                    <lb/>
                  dendo per eandem lineam oīno eodē modo inten-
                    <lb/>
                  dit motum ſuū ſicut remittit ab extremo remiſſiori
                    <lb/>
                  ꝓcedendo per eandē lineam verſus extremū inten­
                    <lb/>
                  ſius: ergo oīs maior ab eodē puncto intenſiori ꝓ-
                    <lb/>
                  cedendo per eandē lineã per quam ꝓcedit potētia
                    <lb/>
                  intendens motum ſuū vniformiter: ipſo medio in-
                    <lb/>
                  uariato: difformiter cõtinuo intendit motum ſuuꝫ
                    <lb/>
                  et ſimiliter oīs minor habens ad extremū intēſius
                    <lb/>
                  eiuſdem medii ꝓportionē maioris inequalitatis.
                    <lb/>
                  </s>
                  <s xml:id="N17B3A" xml:space="preserve">Et ſic patet correlariū. </s>
                  <s xml:id="N17B3D" xml:space="preserve">Et ſi fortiorē demonſtrati-
                    <lb/>
                  onē exoptas: vtaris demonſtratione adducta ad
                    <lb/>
                  quartã concluſionē paucis mutatis: que ſeſe ṗma
                    <lb/>
                  fronte intelligenti probationē illius concluſionis
                    <lb/>
                  offerūt.
                    <note position="left" xlink:href="note-0078-01a" xlink:label="note-0078-01" xml:id="N17BA7" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N17B4D" xml:space="preserve">¶ Sequitur tertio /  vbicū aliqua potē-
                    <lb/>
                  tia īuariata vniformiter cõtinuo ſucceſſiue intēdit
                    <lb/>
                  motū ſuū vſ ad nõ gradum: mediū īuariatū trã-
                    <lb/>
                  ſeundo ab extremo intenſiori verſus remiſſius: oīs
                    <lb/>
                  potentia maior ab eodem extremo intenſiori ꝓce-
                    <lb/>
                  dens continuo per eandē lineã in infinitū velociter
                    <lb/>
                  intendit motum ſuū. </s>
                  <s xml:id="N17B5C" xml:space="preserve">Probatur facile: qm̄ quãdo
                    <lb/>
                  ipſa potentia maior mouetur verſus extremū in-
                    <lb/>
                  tenſius cõtinuo remittendo motum ſuū .etc̈. in infi-
                    <lb/>
                  nitum velociter remittit motū ſuū / vt patet ex quin­
                    <lb/>
                  ta cõcluſione huius capitis: et oīno eadem veloci-
                    <lb/>
                  tate intendit motū ſuū retrogrado motu per ean-
                    <lb/>
                  dem lineã mouēdo ſicut antea remittebat in eiſdeꝫ
                    <lb/>
                  partibus eiuſdem linee: ergo oīs talis potentia
                    <lb/>
                  maior que ſic mouetur motu retrogrado ab extre­
                    <lb/>
                  mo intenſiori verſus remiſſius per eandē lineam
                    <lb/>
                  etc̈. in infinitū velociter intendit motum ſuū / quod
                    <lb/>
                  fuit probandū. </s>
                  <s xml:id="N17B75" xml:space="preserve">Et ſic patꝫ correlariū.
                    <note position="left" xlink:href="note-0078-02a" xlink:label="note-0078-02" xml:id="N17BAD" xml:space="preserve">4. correĺ.</note>
                  </s>
                  <s xml:id="N17B7D" xml:space="preserve">¶ Sequitur
                    <lb/>
                  quarto /  vbicun aliqua potentia īuariata me-
                    <lb/>
                  dium īuariatum tranſeundo cõtinuo ſucceſſiue in­
                    <lb/>
                  tēdit motum ſuū ad nõ gradum ſiue vniformiter
                    <lb/>
                  ſiue difformiter: oīs potentia minor habens pro-
                    <lb/>
                  portionē maioris inequalitatis ad aliquã parteꝫ
                    <lb/>
                  eiuſdē medii in infinitū tardius intendit motum
                    <lb/>
                  ſuū a puncto ad quē habet proportionē equalita­
                    <lb/>
                  tis recedendo verſus remiſſius extremū: quã data
                    <lb/>
                  potētia maior ab eodē puncto recedendo verſus
                    <lb/>
                  extremū remiſſiꝰ. </s>
                  <s xml:id="N17B94" xml:space="preserve">Ptꝫ hoc correlariū ex predictis</s>
                </p>
              </div>
              <div xml:id="N17BB3" level="4" n="8" type="chapter" type-free="capitulum">
                <head xml:id="N17BB8" xml:space="preserve">Capitulū octauū / in quo inquiritur an due
                  <lb/>
                potentie īequales idē mediū īuariatū tran-
                  <lb/>
                ſeūtes valeãt vniformiter remittere aut intē­
                  <lb/>
                dere motum ſuum per ambarū vel alterius
                  <lb/>
                earum variationem.</head>
                <p xml:id="N17BC3">
                  <s xml:id="N17BC4" xml:space="preserve">POſt̄ ſuperiori capite oſtēſū
                    <lb/>
                  eſt nullas duas potētias īequales īua-
                    <lb/>
                  riatas: id eſt quarum nulla variat̄̄ idem
                    <lb/>
                  mediū īuariatū trãſeūtes poſſe vniformiter intē-
                    <lb/>
                  dere aut remittere motū ſuū: iã īquirendū eſt an ꝑ
                    <lb/>
                  alteriꝰ eaꝝ vel ambaꝝ variationē id fieri valeat.</s>
                </p>
                <p xml:id="N17BD1">
                  <s xml:id="N17BD2" xml:space="preserve">Cuiꝰ inq̇ſitiõi p̄mittat̄̄ ꝓ baſi  fūda­
                    <lb/>
                  mēto talis ſuppoſitio. </s>
                  <s xml:id="N17BD7" xml:space="preserve">Si aliq̈ potētia vniformiṫ
                    <lb/>
                  ↄ̨tinuo ſuū motū remittēs aut ītēdēs aliq̈ potētia
                    <lb/>
                  in certa ꝓportione cõtinuo velocius mouetur: ne-
                    <lb/>
                  ceſſe eſt potentiã ipſam tardius motã cõtinuo vni­
                    <lb/>
                  formiter motū ſuū remittere aut intendere. </s>
                  <s xml:id="N17BE2" xml:space="preserve">Et ſi
                    <cb chead="Capitulū octauū."/>
                  aliqua potentia vniformiter cõtinuo ſuū motum
                    <lb/>
                  remittens aut intendens aliqua alia potentia in
                    <lb/>
                  certa ꝓportione cõtinuo tardius mouetur: neceſſe
                    <lb/>
                  eſt potentiã velocius motã vniformiter itidē con-
                    <lb/>
                  tinuo motū ſuū remittere aut intendere. </s>
                  <s xml:id="N17BF0" xml:space="preserve">Exemplū /
                    <lb/>
                  vt data potētia que incipit a gradu octauo exclu-
                    <lb/>
                  ſiue moueri cõtinuo vniformiter remittēdo motū
                    <lb/>
                  ſuū: et in dupla ꝓportione cõtinuo velocius moue­
                    <lb/>
                  do quã vna alia potētia que incipit moueri a gra­
                    <lb/>
                  du quarto excluſiue: tūc dico /  neceſſe eſt /  illa po­
                    <lb/>
                  tentia que incipit moueri a quarto gradu excluſi-
                    <lb/>
                  ue cõtinuo vniformiter remittat motum ſuū: </s>
                  <s xml:id="N17C01" xml:space="preserve">Pro­
                    <lb/>
                  batur / et ſit a. potentia remittens continuo vnifor-
                    <lb/>
                  miter motū ſuū: et ſit b. potentia que cõtinuo in f.
                    <lb/>
                  ꝓportiõe tardius mouetur quã a. potentia: et ma-
                    <lb/>
                  nifeſtū eſt /  etiã b. potentia remittit motū ſuū: q2
                    <lb/>
                  alias motus illarū potentiarū nõ cõtinuo mane-
                    <lb/>
                  rent in eadē ꝓportione. </s>
                  <s xml:id="N17C10" xml:space="preserve">Uolo igitur /  potētia a.
                    <lb/>
                  perdat in toto tēpore adequate in quo mouetur c.
                    <lb/>
                  latitudinē motus: et b.d. latitudinē motus: et tunc
                    <lb/>
                  dico /  d. latitudo motus deperdenda a b. poten-
                    <lb/>
                  tia tardius mota vniformiter cõtinuo remittetur
                    <lb/>
                  </s>
                  <s xml:id="N17C1C" xml:space="preserve">Probatur / q2 d. latitudo motus in qualibet me-
                    <lb/>
                  dietate tēporis in quo deperdetur perdet vnã me-
                    <lb/>
                  dietatē ſui, et in qualibet tertia vnã tertiam, et in
                    <lb/>
                  qualibet quarta, vnã quartã, et ſic conſequenter:
                    <lb/>
                  igitur d. latitudo deperdenda a b. potentia tar-
                    <lb/>
                  dius mota vniformiter continuo remittetur. </s>
                  <s xml:id="N17C29" xml:space="preserve">Pa-
                    <lb/>
                  tet conſequentia ex diffitione remiſſionis vnifor-
                    <lb/>
                  mis alicuius latitudinis. </s>
                  <s xml:id="N17C30" xml:space="preserve">Probatur antecedens:
                    <lb/>
                  quoniã quandocun aliqua pars aliquota c. la-
                    <lb/>
                  titudinis ab a. potentia deperdende deperdetur
                    <lb/>
                  adequate conſimilis pars aliquota et eiuſdem de­
                    <lb/>
                  nominationis deperdet d. latitudo: ſed in quali-
                    <lb/>
                  bet medietate temporis in quo ille latitudines re­
                    <lb/>
                  mittuntur c. latitudo perdit vnam medietateꝫ ſui:
                    <lb/>
                  et in qualibet tertia vnam tertiam ſui, et in quali-
                    <lb/>
                  bet quarta quartam, et ſic conſequenter: quia c. la­
                    <lb/>
                  titudo vniformiter remittitur continuo / vt patet
                    <lb/>
                  ex hypotheſi / igitur d. latitudo in qualibet medie-
                    <lb/>
                  ta temporis in quo remittitur perdit vnã medie-
                    <lb/>
                  tatem ſui, et in qualibet tertia tertiam, et in quali-
                    <lb/>
                  bet quarta quartam, et ſic cõſequenter. </s>
                  <s xml:id="N17C4D" xml:space="preserve">Patet cõ-
                    <lb/>
                  ſequentia cum minore: et probatur maior: quoniã
                    <lb/>
                  continuo latitudo motus quo mouetur a. ad lati-
                    <lb/>
                  tudinem motus quo mouetur b. eſt proportio f. ex
                    <lb/>
                  hypotheſi: et continuo motus quo mouetur a. et
                    <lb/>
                  etiam latitudo motus quo mouetur b. remittūtur /
                    <lb/>
                  ergo inter latitudinem deperditam a. motu quo
                    <lb/>
                  mouetur a. maiore, et latitudinem deperditam a
                    <lb/>
                  motu minori quo mouetur b. eſt continuo propor­
                    <lb/>
                  tio f. / vt patet ex primo correlario quinte concluſi-
                    <lb/>
                  onis ſecūdi capitis ſecunde partis: et latitudo de-
                    <lb/>
                  perdenda a motu quo mouet̄̄ a. eſt c. et latitudo de­
                    <lb/>
                  ꝑdēda a motu quo mouet̄̄ b. eſt d. / igit̄̄ inter c. et d.
                    <lb/>
                  eſt ꝓportio f. / et ex cõſequēti ſequit̄̄ /  inter partes
                    <lb/>
                  aliquotas eiuſdē denoīatiõis ipſiꝰ c. et ipſiꝰ d. pu-
                    <lb/>
                  ta īter medietatatē c. et medietatē d, et īter tertias
                    <lb/>
                  et īter quartas, et ſic cõſequēter eſt etiã ꝓportio f.
                    <lb/>
                  </s>
                  <s xml:id="N17C71" xml:space="preserve">Ptꝫ hec ↄ̨ña ex vndecima ſuppoſitiõe ſcḋi capitis
                    <lb/>
                  p̄allegati: et vltra īter ꝑtes aliq̊tas eiuſdē denoīa­
                    <lb/>
                  tionis c. latitudīs eſt ꝓportio f. et ↄ̨tinuo īter ꝑteꝫ
                    <lb/>
                  deꝑditã ab ipſo c. et deꝑditã a d. eſt f. ꝓportio / vt ꝓ­
                    <lb/>
                  batū eſt / g̊ quãdocū aliq̈ pars aliq̊ta c. latitudīs
                    <lb/>
                  ab a. potētia deꝑdēde deꝑdet̄̄: adeq̈te ↄ̨ſimilis ꝑs
                    <lb/>
                  aliq̊ta et eiuſdē denoīatiõis deꝑdet d. latitudo / qḋ
                    <lb/>
                  fuit probandum. </s>
                  <s xml:id="N17C82" xml:space="preserve">Et eodem modo probabis cum
                    <lb/>
                  vtra potentia iutendit motum ſuum altera illa-
                    <lb/>
                  rum que cotinuo in certa ꝓportione velocius mo- </s>
                </p>
              </div>
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