Alvarus, Thomas, Liber de triplici motu, 1509
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            <div xml:id="N25905" level="3" n="4" type="other" type-free="tractatus">
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                    <pb chead="Quarti tractatus" file="0274" n="274"/>
                  ditas ſit vt .4. et tota frigiditas vt .2. q̄ ſunt in ſcḋa
                    <lb/>
                  ꝑte ꝓportionali a. corꝑis. </s>
                  <s xml:id="N2C289" xml:space="preserve">Uolo igr̄ /  prima pars
                    <lb/>
                  ꝓportiõalĺ a. corꝑis acq̇rat in hõ aliquã quãtitatē
                    <lb/>
                  ꝑ rarefactiõeꝫ acq̇rēdo et ꝑs hñs duplã caliditatē
                    <lb/>
                  ad caliditatē ṗme partꝪ in eadē hora acq̇rat ſubdu­
                    <lb/>
                  pla quãtitatē, et pars hñs q̈druplã caliditatem ad
                    <lb/>
                  caliditatē ṗme ꝑtis in eadē hora acq̇rat ſubq̈dru-
                    <lb/>
                  plã quãtitatē etc̈. </s>
                  <s xml:id="N2C298" xml:space="preserve">Quo poſito argr̄ ſic / a. in fine ra-
                    <lb/>
                  refactiõis nec eſt calidū nec frigidū: et aña erat ca-
                    <lb/>
                  lidū: et nullã caliditatē aut frigiditatē deperdidit
                    <lb/>
                  aut acq̇ſiuit etc̈. / igr̄ ꝓpoſitū. </s>
                  <s xml:id="N2C2A1" xml:space="preserve">Q, in fine nec eſt cali-
                    <lb/>
                  dū nec frigidū ꝓbat̄̄: q2 in fine hꝫ caliditatē ſuffici-
                    <lb/>
                  entē ip̄m denoīare īfinite calidū, et frigiditatē ſuffi­
                    <lb/>
                  entē ipſuꝫ denoīare īfinite frigidū puta illã quã hꝫ
                    <lb/>
                  in quãtitate acq̇ſita ꝑ rarefactionē: igr̄ caliditas et
                    <lb/>
                  frigiditas totalr̄ et adeq̈te ſe īpediūt: et ꝑ ↄ̨ñs illud
                    <lb/>
                  nec eſt calidū nec frigidū / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N2C2B0" xml:space="preserve">Q, autē
                    <lb/>
                  caliditas exñs in quãtitate acq̇ſita ꝑ rarefactionē
                    <lb/>
                  et ſiĺr frigiditas exñs in eadē quãtitatē ſufficiat de­
                    <lb/>
                  noīare a. infinite ſatis / ptꝫ ex his que dicta ſunt cir­
                    <lb/>
                  ca ſextam concluſionem queſtionis.</s>
                </p>
                <p xml:id="N2C2C5">
                  <s xml:id="N2C2C6" xml:space="preserve">Scḋo ad idē argr̄ ſic. </s>
                  <s xml:id="N2C2C9" xml:space="preserve">Si ꝑs affirma­
                    <lb/>
                  tiua dubii eēt a: ſeq̄ret̄̄ alicuiꝰ corꝑis certa diuiſi­
                    <lb/>
                  one quãlꝫ partē ꝓportiõalē ꝓportiõe dupla eē ca-
                    <lb/>
                  lidã: et tñ totū nõ eē calidū: ↄ̨ñs videt̄̄ īpoſſibile: igr̄
                    <lb/>
                  illud ex quo ſequit̄̄. </s>
                  <s xml:id="N2C2D4" xml:space="preserve">Seq̄la ꝓbat̄̄, et ſit a. diuiſū per
                    <lb/>
                  ꝑtes ꝓportiõales ꝓportiõe dupla, et in ṗma ꝑte ſit
                    <lb/>
                  caliditas vt .2. et frigiditas vt vnū, et in ſcḋa parte
                    <lb/>
                  ſit in duplo maior caliditas et ſiĺr frigiditas ꝙ̄ in
                    <lb/>
                  ṗma, et in tertia in duplo maior caliditas et frigi-
                    <lb/>
                  ditas ꝙ̄ in ſcḋa, et ſic deinceps ita  in qualꝫ parte
                    <lb/>
                  proportionali caliditas ſit dupla ad frigiditatē.
                    <lb/>
                  </s>
                  <s xml:id="N2C2E4" xml:space="preserve">Quo poſito manifeſtū eſt quãlꝫ partē ꝓportiõalē
                    <lb/>
                  ſcḋm illã diuiſionē eſſe calidã: </s>
                  <s xml:id="N2C2E9" xml:space="preserve">Sed  totū nõ ſit ca­
                    <lb/>
                  lidū ꝓbat̄̄ / q2 caliditas īpedit totalr̄ frigiditatē: et
                    <lb/>
                  eocõtra: igr̄ neutra illaꝝ denoīat. </s>
                  <s xml:id="N2C2F0" xml:space="preserve">Añs ꝓbat̄̄ / quia
                    <lb/>
                  vtra illaꝝ ſufficit denoīare īfinite vt ſatis ptꝫ ex
                    <lb/>
                  ſcḋa ↄ̨cluſiõe q̄ſtiõis: igr̄ ſe totalr̄ īpediūt. </s>
                  <s xml:id="N2C2F7" xml:space="preserve">¶ Itē ſe-
                    <lb/>
                  queret̄̄ alicuiꝰ corꝑis certa diuiſiõe ̄lꝫ partē ꝓpor­
                    <lb/>
                  tionalē ꝓportiõe dupla eſſe īfinite calidã: et tñ totū
                    <lb/>
                  nõ eſſe calidū / qḋ īplicat. </s>
                  <s xml:id="N2C300" xml:space="preserve">Seq̄la ꝓbat̄̄ retēto caſu ſu­
                    <lb/>
                  periori: hoc addito /  ꝑ totū a. ſit caliditas vnifor-
                    <lb/>
                  mis īfinite intenſiõis. </s>
                  <s xml:id="N2C307" xml:space="preserve">Sed  hoc ſit flm̄ ꝓbat̄̄ / q2 bñ
                    <lb/>
                  ſequit̄̄ ſcḋm hãc diuiſionē q̄lꝫ pars ꝓportiõalis
                    <lb/>
                  eiꝰ eſt calida: igr̄ ſcḋm hãc diuiſionē oēs ſunt calide
                    <lb/>
                  et oēs ſunt ip̄m totū: igr̄ totū eſt calidū / qḋ eſt nega­
                    <lb/>
                  tū.
                    <note position="left" xlink:href="note-0274-01a" xlink:label="note-0274-01" xml:id="N2C346" xml:space="preserve">ↄ̨fir̄tio.</note>
                  </s>
                  <s xml:id="N2C317" xml:space="preserve">¶ Et ↄ̨firmat̄̄ / q2 ſi intenſio mixti hñtis q̈litates
                    <lb/>
                  ↄ̈rias coextēſas ꝑ totū attendit̄̄ penes exceſſū q̈lita­
                    <lb/>
                  tis excedētis ſupra exceſſam: ſequit̄̄ /  intēſio mixti
                    <lb/>
                  hñtis q̈litates ↄ̈rias nõ coextēſas: ſed extēſas in di­
                    <lb/>
                  uerſis partibꝰ ſubiecti itidē attendit̄̄ penes exceſſū
                    <lb/>
                  q̈litatis excedētis ſupra exceſſã: ſed hoc eſt flm̄: igr̄
                    <lb/>
                  illud ex quo ſequit̄̄. </s>
                  <s xml:id="N2C326" xml:space="preserve">Seq̄la videt̄̄ nota: ſed falſitas
                    <lb/>
                  ↄ̨ñtis ꝓbat̄̄: q2 tūc ſeq̄ret̄̄ /  frigiditas nullo pacto
                    <lb/>
                  īpediret caliditatē / qḋ eſt ↄ̈ fundamentū opinionis.
                    <lb/>
                  </s>
                  <s xml:id="N2C32E" xml:space="preserve">Seq̄la ꝓbat̄̄: et pono /  ſit a. pedale in cuiꝰ vna me-
                    <lb/>
                  dietate ſic caliditas vt .8. et in alia frigiditas vt .4.
                    <lb/>
                  et b. in cuiꝰ vna medietate ſit caliditas vt .8. et alia
                    <lb/>
                  nec habeat caliditatē nec frigiditatē. </s>
                  <s xml:id="N2C337" xml:space="preserve">Quo poſito
                    <lb/>
                  a. per te eſt calidū vt .4. cū .8. excedãt .4. per .4. et b.
                    <lb/>
                  ſimiltr eſt calidum vt .4. / igr̄ frigiditas in a. nullo
                    <lb/>
                  pacto īpedit caliditatem cum oīno habeãt eandem
                    <lb/>
                  caliditatem per eandem partem.</s>
                </p>
                <p xml:id="N2C34C">
                  <s xml:id="N2C34D" xml:space="preserve">In oppoſitū tñ argit̄̄ ſic / q2 intenſio
                    <lb/>
                  mixti hñtis q̈litates ↄ̈rias coextēſas ꝑ totū nõ attē­
                    <lb/>
                  dit̄̄ penes intēſionē q̈litatis intenſioris: cū tūc ↄ̈rie
                    <lb/>
                  q̈litates nullo mõ ſe īpedirēt in denoīationibꝰ ſuis
                    <lb/>
                  nec penes ꝓportionē q̈litatis excedētis ad q̈litatē
                    <lb/>
                  exceſſū: igr̄ d3 attendi penes exceſſū q̈litatis excedē­
                    <cb chead="Capitulū quartū."/>
                  tis ſupra exceſſū cū nõ ſit aliꝰ modꝰ quo talis inten-
                    <lb/>
                  ſio poſſet mēſurari. </s>
                  <s xml:id="N2C35F" xml:space="preserve">Coña ptꝫ cū maiore: et ꝓbatur
                    <lb/>
                  mīor / q2 alias ſeq̄ret̄̄ albedinē vt .4. denoīare īfini-
                    <lb/>
                  te. </s>
                  <s xml:id="N2C366" xml:space="preserve">Seq̄la ꝓbat̄̄ / et ſit in a. pedali albedo vt .4. ꝑ totū
                    <lb/>
                  coextēſa nigredini vt .2. et remittat̄̄ vniformiṫ ni-
                    <lb/>
                  gredo vſ ad nõ gradū in hora ſtãte albedīe. </s>
                  <s xml:id="N2C36D" xml:space="preserve">Quo
                    <lb/>
                  poſito argr̄ ſic / in infinitū augebit̄̄ ꝓportio albedi­
                    <lb/>
                  nis ſupra nigredinē: igr̄ ꝑ te in īfinitū intēdet̄̄ deno­
                    <lb/>
                  minatio albedinis: et per conſequens in infinitum
                    <lb/>
                  denominabit illa albedo / quod fuit probandum.</s>
                </p>
                <p xml:id="N2C378">
                  <s xml:id="N2C379" xml:space="preserve">Pro ſolutione huiꝰ dubii. </s>
                  <s xml:id="N2C37C" xml:space="preserve">Notandum
                    <lb/>
                  eſt /  q̈litates ↄ̈rie exiſtētes in eodē ſubiecto ſe īpe-
                    <lb/>
                  diūt in ſuis denoīationibꝰ. </s>
                  <s xml:id="N2C383" xml:space="preserve">Nõ em̄ eq̄ albū et cor-
                    <lb/>
                  pus in quo ſunt ꝑ totū .6. gradꝰ albedīs cū .2. gra-
                    <lb/>
                  dibus nigredīs ſicut corpꝰ in q̊ ſūt .6. gradꝰ albedīs
                    <lb/>
                  ſine admixtiõe ↄ̈rie q̈litatis. </s>
                  <s xml:id="N2C38C" xml:space="preserve">Et nõ ſolū qualitates
                    <lb/>
                  ↄ̈rie ſe īpediūt qñ coextēdunt̄̄: verū etiã qñ in diuer-
                    <lb/>
                  ſis partibꝰ ſubiecti ponunt̄̄. </s>
                  <s xml:id="N2C393" xml:space="preserve">Nõ em̄ tm̄ denoīat al-
                    <lb/>
                  bedo vt .4. exñs in vna medietate corꝑis in cuiꝰ alia
                    <lb/>
                  medietate eſt vnꝰ gradꝰ nigredīs quantū denoīaret
                    <lb/>
                  ſi in ſubiecto nõ eſſet aliq̈ nigredo. </s>
                  <s xml:id="N2C39C" xml:space="preserve">Hoc ſuppoſito
                    <lb/>
                  aduertendū eſt /  quadruplex eſt opinio penes qḋ
                    <lb/>
                  debeat attendi inteſio mixti hñtis ↄ̈rias q̈litates
                    <lb/>
                  coextēſas: q̈s recitat calcu. in capĺo de ītēſio mixto-
                    <lb/>
                  rū. </s>
                  <s xml:id="N2C3A7" xml:space="preserve">¶ Prima eſt /  intēſio mixti d3 attēdi penes ꝓ-
                    <lb/>
                  portionē q̈litatis excedētis ad q̈litatē exceſſã. </s>
                  <s xml:id="N2C3AC" xml:space="preserve">Scḋa
                    <lb/>
                  dicit /  d3 attēdi penes q̈litatē excedentē. </s>
                  <s xml:id="N2C3B1" xml:space="preserve">Tertia di­
                    <lb/>
                  cit /  penes medietatē exceſſus q̈litatis excedentis.
                    <lb/>
                  </s>
                  <s xml:id="N2C3B7" xml:space="preserve">Quarta dicit /  penes exceſſū. </s>
                  <s xml:id="N2C3BA" xml:space="preserve">Sed ꝓ īpugnatiõe
                    <lb/>
                  3. ṗmaꝝ opinionū pono tres ꝓpõnes. </s>
                  <s xml:id="N2C3BF" xml:space="preserve">¶ Prima ꝓ-
                    <lb/>
                  poſitio </s>
                  <s xml:id="N2C3C4" xml:space="preserve">Intēſio mixti nõ attendit̄̄ penes ꝓportionē
                    <lb/>
                  q̈litatis excedētis ad exceſſam. </s>
                  <s xml:id="N2C3C9" xml:space="preserve">Probat̄̄ / q2 tūc ſeq̄-
                    <lb/>
                  ret̄̄ /  albedo vt duo īfinite poſſet denoīare ſubie-
                    <lb/>
                  ctū albū ipſa ↄ̨tinuo manēte vt duo: ſed hoc eſt flm̄:
                    <lb/>
                  igr̄ illud ex q̊ ſequit̄̄. </s>
                  <s xml:id="N2C3D2" xml:space="preserve">Seq̄la probat̄̄: et pono /  in a.
                    <lb/>
                  pedali ſit albedo vt duo: et nigredo vt vnū coextēſe
                    <lb/>
                  et remittat̄̄ nigredo vſ ad nõ gradū: ipſa albedīe
                    <lb/>
                  ↄ̨tinuo manēte vt duo. </s>
                  <s xml:id="N2C3DB" xml:space="preserve">Quo poſita manifeſtū eſt / 
                    <lb/>
                  īfinita erit ꝓportio albedīs vt duo ad nigredinem /
                    <lb/>
                  igr̄ īfinite illa albedo ſubiectū ſuū denoīabit. </s>
                  <s xml:id="N2C3E2" xml:space="preserve">¶ Se­
                    <lb/>
                  cūda ꝓpõ intēſio mixti nõ attendit̄̄ penes q̈litateꝫ
                    <lb/>
                  excedentē. </s>
                  <s xml:id="N2C3E9" xml:space="preserve">Probat̄̄ / q2 tūc ſeq̄ret̄̄ /  vna q̈litas ↄ̈ria
                    <lb/>
                  nõ īpediret alterã in ſua denoīatiõe: qḋ eſt ↄ̈ notatū
                    <lb/>
                  ptꝫ ſeq̄la: q2 albedo vt .6. ſcḋm iſtã poſitionē ad mi-
                    <lb/>
                  xta nigredini vt .2. denoīat vt .6: et tm̄ denoīaret nõ
                    <lb/>
                  admixta ↄ̈rio: igr̄. </s>
                  <s xml:id="N2C3F4" xml:space="preserve">¶ Tertia ꝓpõ. </s>
                  <s xml:id="N2C3F7" xml:space="preserve">Intēſio mixti nõ
                    <lb/>
                  attendit̄̄ penes medietatē exceſſus q̈litatis excedē-
                    <lb/>
                  tis. </s>
                  <s xml:id="N2C3FE" xml:space="preserve">Probat̄̄: q2 tūc ſeq̄ret̄̄ /  albedo vt duo īpedi-
                    <lb/>
                  ret totalr̄ .4. g̈dus nigredīs ſecū extenſe: ſed ↄ̨ñs eſt
                    <lb/>
                  flm̄: igr̄ illud ex q̊ ſequit̄̄. </s>
                  <s xml:id="N2C405" xml:space="preserve">Falſitas ↄ̨ñtis ꝓbat̄̄: et po­
                    <lb/>
                  no /  .6 g̈dus nigredīs coextēdant̄̄ duobꝰ albedīs:
                    <lb/>
                  </s>
                  <s xml:id="N2C40B" xml:space="preserve">Tūc ſcḋm iſtã poſitionē illa nigredo denoīat vt .2.
                    <lb/>
                  q2 g̈dus vt duo eſt medietas exceſſus quo .6. exce-
                    <lb/>
                  dūt .2. / igr̄ .4. g̈dus illiꝰ nigredīs vt .6. īpediūtur ab
                    <lb/>
                  illis .2. g̈dibꝰ albedīs: et ſic albedo vt .2. īpedit tota­
                    <lb/>
                  liter .4. g̈dus nigredīs: qḋ fuit ꝓbãdū. </s>
                  <s xml:id="N2C416" xml:space="preserve">Hiis p̄miſſis</s>
                </p>
                <p xml:id="N2C419">
                  <s xml:id="N2C41A" xml:space="preserve">Sit prima ↄ̨̨cluſio. </s>
                  <s xml:id="N2C41D" xml:space="preserve">Intenſio mixti in
                    <lb/>
                  quo ſunt qualitates ↄ̈rie ſiue coextēſe ſiue nõ: men-
                    <lb/>
                  ſurãda eſt penes exceſſū denoīatiõis qua vna illaꝝ
                    <lb/>
                  q̈litatū admixta ↄ̈rio nata eſt magis denoīare ſub­
                    <lb/>
                  iectū ꝙ̄ alia: ceretis paribꝰ. </s>
                  <s xml:id="N2C428" xml:space="preserve">Exēplū / vt coextēſa al-
                    <lb/>
                  bedini vt .6. nigredīe vt .2. per totū ſubiectū: qm̄ albe­
                    <lb/>
                  do vt .6. toti coextēſa ſubiecto valet ſine ↄ̈rii admix­
                    <lb/>
                  tione denoīare vt .6. et nigredo vt duo coextēſa etiã
                    <lb/>
                  ꝑ totū ſubiectū deducto īpedimēto denoīaret vt .2.
                    <lb/>
                  </s>
                  <s xml:id="N2C434" xml:space="preserve">Et .6. excedūt duo ꝑ .4. / ↄ̨ñs eſt illud ſubiectū eſſe al-
                    <lb/>
                  bū vt .4. </s>
                  <s xml:id="N2C439" xml:space="preserve">Siĺr accõmoda exēplū ↄ̈riis q̈litatibꝰ non
                    <lb/>
                  coextēſis: ſemꝑ ad denoīatiões, et nõ ad q̈litatū in-
                    <lb/>
                  tenſiões aſpiciēdo. </s>
                  <s xml:id="N2C440" xml:space="preserve">Probat̄̄ / q2 totū reſiduū deno- </s>
                </p>
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