Alvarus, Thomas, Liber de triplici motu, 1509

Table of Notes

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                <p xml:id="N17642">
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                    <pb chead="Primi tractatus" file="0075" n="75"/>
                  ſione: et moueatur per illud potentia vt .8. nõ va-
                    <lb/>
                  riata. </s>
                  <s xml:id="N1765F" xml:space="preserve">ſecundum vero per quod mouetur alia po-
                    <lb/>
                  tentia vt .8. non variata taliter diſponatur /  qñ
                    <lb/>
                  in priori medio fuerit aliqua reſiſtentia per totū:
                    <lb/>
                  in ſolo puncto vbi eſt mobile in ſecundo medio ſit
                    <lb/>
                  adequate tanta reſiſtentia ceteris inuariatis ita­
                    <lb/>
                   poſtquã alicui puncto aliqua latitudo reſiſten-
                    <lb/>
                  tie addita eſt nulla ei vlteriꝰ addatur aut remouea­
                    <lb/>
                  tur ita  manet per totum difforme in fine quo po­
                    <lb/>
                  ſito mobile motum in ſecundo medio remittet mo­
                    <lb/>
                  tum ſuum vniformiter primo ad gradum et dein-
                    <lb/>
                  de ad non gradum / igitur concluſio vera. </s>
                  <s xml:id="N17676" xml:space="preserve">Antece-
                    <lb/>
                  dens probatur / quia mobile motum in primo me-
                    <lb/>
                  dio vniformiter remittit motum ſuū / vt ptꝫ ex prio­
                    <lb/>
                  ri concluſione: et ſecundum mobile motū in ſecun-
                    <lb/>
                  do medio in quolibet inſtãti temporis / quo ſic mo-
                    <lb/>
                  uetur eſt motum equali velocitate adequate cū pri­
                    <lb/>
                  mo: igitur ſecundum mobile etiam vniformiter re­
                    <lb/>
                  mittet motū ſuum. </s>
                  <s xml:id="N17687" xml:space="preserve">Patet conſequentia / quia ſi il-
                    <lb/>
                  la duo continuo equaliter mouentur et vnum illo­
                    <lb/>
                  rum in medietate temporis perdit aliquam velo-
                    <lb/>
                  citatem et in quarta. et in quinta. / et ſic conſequēter /
                    <lb/>
                  igitur et alterū in medietate temporis tantã velo-
                    <lb/>
                  citateꝫ deperdit adequate ſicut ṗmū et in q̈rta tan­
                    <lb/>
                  tã: et in quinta tantã: et ſic conſequenter: igitur ſi
                    <lb/>
                  vnum vniformiter remittit motū ſuū etiam alterū
                    <lb/>
                  motū ſuū vniformiter remittet / quod fuit proban-
                    <lb/>
                  dum.
                    <note position="left" xlink:href="note-0075-01a" xlink:label="note-0075-01" xml:id="N176D0" xml:space="preserve">1. correl.
                      <lb/>
                    triceſīa
                      <lb/>
                    ſeptīa cõ­
                      <lb/>
                    cluſio cal­
                      <lb/>
                    cu.</note>
                  </s>
                  <s xml:id="N176A1" xml:space="preserve">¶ Ex quo ſequitur /  aliqua potentia nõ va-
                    <lb/>
                  riata tranſeundo medium difforme inuariatū: va­
                    <lb/>
                  let vniformiter remittere motum ſuum. </s>
                  <s xml:id="N176A8" xml:space="preserve">Proba-
                    <lb/>
                  tur hoc correlarium et volo /  illud ſecundum mo-
                    <lb/>
                  bile quod mouetur per medium difforme poſtquã
                    <lb/>
                  ſemel tale ſecundum medium difforme pertranſie­
                    <lb/>
                  rit / quando idem medium variabatur: ipſo medio
                    <lb/>
                  quieſcente mobile inuariatum pertranſeat idem
                    <lb/>
                  medium eo modo quo antea pertranſibat: hoc eſt
                    <lb/>
                  incipiendo ab eodem puncto verſus idem pūctuꝫ:
                    <lb/>
                  quo poſito illud mobile tranſeundo illud mediuꝫ
                    <lb/>
                  inuariatum remittit motū ſuū vniformiter / igitur
                    <lb/>
                  correlarium verum. </s>
                  <s xml:id="N176BF" xml:space="preserve">Probatur antecedens / q2 ta-
                    <lb/>
                  le mobile continuo eque velociter pertranſit illud
                    <lb/>
                  medium inuariatum ſicut pertranſibat illud quã­
                    <lb/>
                  do medium variabatur: ſed quando variabatur
                    <lb/>
                  vniformiter remittit motū ſuū: ergo et quando nõ
                    <lb/>
                  variatur etiam vniformiter remittit motū ſuum.</s>
                </p>
                <p xml:id="N176DE">
                  <s xml:id="N176DF" xml:space="preserve">Patet maior / quoniam continuo partes medii il­
                    <lb/>
                  lius inuariati et intenſiue et extenſiue tantum reſi-
                    <lb/>
                  ſtunt ipſi mobili quantum conſimiles partes me-
                    <lb/>
                  dii variati cum illa media ſint oīno equalia exten­
                    <lb/>
                  ſiue: et continuo partes conſimiles que pertranſe-
                    <lb/>
                  untur equaliter reſiſtunt omnino. </s>
                  <s xml:id="N176EC" xml:space="preserve">In punctis em̄
                    <lb/>
                  correſpondentibus equalem omnino reſiſtentiaꝫ
                    <lb/>
                  habent.
                    <note position="left" xlink:href="note-0075-02a" xlink:label="note-0075-02" xml:id="N17719" xml:space="preserve">2. confir.</note>
                  </s>
                  <s xml:id="N176F8" xml:space="preserve">¶ Sequitur ſecundo /  aliqua potentia ī­
                    <lb/>
                  uariata mediū inuariatum tranſeundo: vniformi­
                    <lb/>
                  ter continuo intendit motum ſuum. </s>
                  <s xml:id="N176FF" xml:space="preserve">Probat̄̄ hoc
                    <lb/>
                  correlarium poſito /  potentia que pertranſit ali­
                    <lb/>
                  quod medium inuariatum a pūcto remiſſiori mo-
                    <lb/>
                  uendo verſus punctum intenſius remittendo vni-
                    <lb/>
                  formiter continuo motum ſuum: iterum motu re-
                    <lb/>
                  trogrado moneatur a puncto intenſiori verſus re­
                    <lb/>
                  miſſius. </s>
                  <s xml:id="N1770E" xml:space="preserve">quo poſito talis potentia vniformiter in­
                    <lb/>
                  tendit motum ſuum quē antea vniformiter remit­
                    <lb/>
                  tebatur igitur.</s>
                </p>
                <p xml:id="N1771F">
                  <s xml:id="N17720" xml:space="preserve">Tertia concluſio </s>
                  <s xml:id="N17723" xml:space="preserve">Nulla potentia nõ
                    <lb/>
                  variata tranſeundo mediuꝫ vniformiter difforme
                    <lb/>
                  non variatum: poteſt vniformiter remittere aut ī­
                    <lb/>
                  tendere motū ſuum. </s>
                  <s xml:id="N1772C" xml:space="preserve">Patet hec concluſio ex trige-
                    <lb/>
                  ſima nona et quadrageſima concluſionibus quin­
                    <lb/>
                  ti capitis huius tractatꝰ. </s>
                  <s xml:id="N17733" xml:space="preserve">¶ Ex quo ſequitur /  ali­
                    <cb chead="Capitulum ſeptimum"/>
                    <note position="right" xlink:href="note-0075-03a" xlink:label="note-0075-03" xml:id="N17789" xml:space="preserve">1. correl.</note>
                  qua potentia non variata tranſeundo mediū vni­
                    <lb/>
                  formiter difforme non variatum taliter poteſt ip­
                    <lb/>
                  ſum pertranſire:  vniformiter continuo mouea-
                    <lb/>
                  tur. </s>
                  <s xml:id="N17744" xml:space="preserve">Probatur / quoniam ſi moueatur ab vno ex-
                    <lb/>
                  tremo laterali ad aliud extremum ſibi correſpon­
                    <lb/>
                  dens ſemper vniformiter mouebitur / igitur corre-
                    <lb/>
                  larium verum. </s>
                  <s xml:id="N1774D" xml:space="preserve">Probatur antecedens / quoniã ſem­
                    <lb/>
                  per mouebitur cum equali reſiſtentia. </s>
                  <s xml:id="N17752" xml:space="preserve">cum omnia
                    <lb/>
                  puncta in linea recta laterali exiſtentia in tali me­
                    <lb/>
                  dio equalis ſunt reſiſtentie. </s>
                  <s xml:id="N17759" xml:space="preserve">Et hoc ſiue mobile ſit
                    <lb/>
                  diuiſibile ſiue indiuiſibile.
                    <note position="right" xlink:href="note-0075-04a" xlink:label="note-0075-04" xml:id="N1778F" xml:space="preserve">2: correl.</note>
                  </s>
                  <s xml:id="N17763" xml:space="preserve">¶ Iam ex hoc ſequitur /
                    <lb/>
                   tribus modis poteſt ſpacium vniformiter dif-
                    <lb/>
                  forme pertranſiri a potentia non variata: </s>
                  <s xml:id="N1776A" xml:space="preserve">Uno
                    <lb/>
                  modo ipſa continuo remittente motum. </s>
                  <s xml:id="N1776F" xml:space="preserve">Alio mo-
                    <lb/>
                  do ipſa continuo intendente motã. </s>
                  <s xml:id="N17774" xml:space="preserve">Tertio modo
                    <lb/>
                  ipſa continuo vniformiter mota. </s>
                  <s xml:id="N17779" xml:space="preserve">Non excludo ta­
                    <lb/>
                  men alios modos. </s>
                  <s xml:id="N1777E" xml:space="preserve">Si enim moueretur in circulo ī
                    <lb/>
                  tali ſpacio aliquando intenderet motuꝫ et aliquã­
                    <lb/>
                  do remitteret.</s>
                </p>
                <note position="right" xml:id="N17795" xml:space="preserve">Triceſīa­
                  <lb/>
                octaua ↄ̨­
                  <lb/>
                cluſio cal­
                  <lb/>
                cu.</note>
                <p xml:id="N1779F">
                  <s xml:id="N177A0" xml:space="preserve">Quarta concluſio </s>
                  <s xml:id="N177A3" xml:space="preserve">Si aliqua poten-
                    <lb/>
                  tia non variata tranſeundo aliquod medium non
                    <lb/>
                  variatum vniformiter remittit motū ſuum ad gra­
                    <lb/>
                  dum vel ad non gradū: nulla maior vel minor idē
                    <lb/>
                  medium tranſeundo medio et ipſa inuariatis vni­
                    <lb/>
                  formiter motū ſuū remittit. </s>
                  <s xml:id="N177B0" xml:space="preserve">Probatur / ſit b. potē­
                    <lb/>
                  tia minor que inuariata in d. tempore pertranſit
                    <lb/>
                  c. medium inuariatū: continuo vniformiter remit­
                    <lb/>
                  tendo motum ſuum. </s>
                  <s xml:id="N177B9" xml:space="preserve">et ſit a. poña maior que iuua-
                    <lb/>
                  riata in e. tempore c. medium inuariatū tranſit. </s>
                  <s xml:id="N177BE" xml:space="preserve">et
                    <lb/>
                  dico /  a. potentia maior c. mediuꝫ tranſeundo nõ
                    <lb/>
                  continuo vniformiter remittit motū ſuū </s>
                  <s xml:id="N177C5" xml:space="preserve">Quod ſic
                    <lb/>
                  probatur / ſit g. ſpacium quod pertranſitur in me-
                    <lb/>
                  dietate d. temporis a b. potentia minore perden-
                    <lb/>
                  do medietatē velocitatis deperdende: et ſit h. ſpa-
                    <lb/>
                  cium pertranſitum ab eadē potentia in ſcḋa me-
                    <lb/>
                  dietate eiuſdē temporis adequate ad quod h. ſpa­
                    <lb/>
                  cium habeat g. proportionē f. que proportio f. eſt
                    <lb/>
                  ꝓportio velocitatis qua mouetur b. potētia ī pri­
                    <lb/>
                  ma medietate d. tēporis ad velocitatē qua moue-
                    <lb/>
                  tur eadē potentia in ſecunda medietate eiuſdē tē-
                    <lb/>
                  poris. </s>
                  <s xml:id="N177DC" xml:space="preserve">quo poſito ꝓbo /  a. potentia maior c. medi­
                    <lb/>
                  um tranſeundo non continuo vniformiter remit-
                    <lb/>
                  tit motū ſuū. </s>
                  <s xml:id="N177E3" xml:space="preserve">quia ſi non: detur oppoſitum videli­
                    <lb/>
                  cet /  in caſu a. potentia maior inuariata c. mediū
                    <lb/>
                  inuariatū in e. tempore adequate tranſeundo. </s>
                  <s xml:id="N177EA" xml:space="preserve">vni­
                    <lb/>
                  formiter remittit motū ſuū / et arguo ſic / a. potētia
                    <lb/>
                  maior et c. vniformiter remittit motū ſuū in e. tem­
                    <lb/>
                  pore / igitur in prima medietate eiuſdē e. temporis
                    <lb/>
                  pertranſit g. ſpaciū et in ſecunda h. ſpacium inter
                    <lb/>
                  que ſpacia eſt proportio f. ex hypotheſi: et vltra in
                    <lb/>
                  prima medietate e. temporis a. pertranſit g. ſpa-
                    <lb/>
                  cium et in ſecunda h. inter que eſt proportio f. / ergo
                    <lb/>
                  velocitatis qua a. mouetur in prima medietate
                    <lb/>
                  e. temporis ad velocitatem qua mouetur in ſecun­
                    <lb/>
                  da eſt f. proportio: conſequens eſt contra ſecundū
                    <lb/>
                  correlarium ſuppoſitionis huius capitis / igitur et
                    <lb/>
                  antecedens: et per conſequens contradictorum an­
                    <lb/>
                  tecedentis eſt verum / quod fuit probandum </s>
                  <s xml:id="N17807" xml:space="preserve">Secū­
                    <lb/>
                  da conſequentia patet per hanc maximam </s>
                  <s xml:id="N1780C" xml:space="preserve">Eadē
                    <lb/>
                  eſt proportio velocitatū equalibus temporibꝰ co­
                    <lb/>
                  extenſarum: et ſpaciorum ab eiſdē pertranſitoruꝫ
                    <lb/>
                  </s>
                  <s xml:id="N17814" xml:space="preserve">Et prima conſequentia probatur in qua eſt vis ꝓ­
                    <lb/>
                  bationis / q2 ſi a. potentia maior et c. in e. tempore
                    <lb/>
                  vniformiter remittit motum ſuum. </s>
                  <s xml:id="N1781B" xml:space="preserve">ipſa a. potētia
                    <lb/>
                  in prima medietate e. temporis medietatē veloci-
                    <lb/>
                  tatis deperdende adequate deperdit: et ipſa a. po­
                    <lb/>
                  tentia illam medietatem velocitatis deperdende
                    <lb/>
                  deperdendo adequate, g. ſpacium adequate per­
                    <lb/>
                  tranſit / igitur a. potentia in prima medietate: tē­ </s>
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