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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                <p xml:id="N2B338">
                  <s xml:id="N2B5CC" xml:space="preserve">
                    <pb chead="De difformium intenſione" file="0267" n="267"/>
                  Et manifeſtū eſt ex diffinitiõe q̈litatis vni. diffor. / 
                    <lb/>
                  diſtãtia extremi remiſſioris ip̄us a. vel non gradꝰ a
                    <lb/>
                  ſuo gradu ſūmo eſt in g. proportiõe maior diſtãtia
                    <lb/>
                  ipſius c. ab eodē gradu ſūmo: et eadē rõne diſtantie
                    <lb/>
                  extremi remiſſioris vel nõ gradus ipſius b. a gradu
                    <lb/>
                  ſūmo ad diſtãtiã ipſius .d. ab eodē gradu ſūmo eſt
                    <lb/>
                  g. proportio. </s>
                  <s xml:id="N2B5DF" xml:space="preserve">Tunc dico /  diſtãtia ipſiꝰ c. a gradu
                    <lb/>
                  ſummo eſt in f. ꝓportione maior diſtantia ipſiꝰ d.
                    <lb/>
                  a gradu ſummo. </s>
                  <s xml:id="N2B5E6" xml:space="preserve">Quod ſic ꝓbat̄̄ / q2 ex hypotheſi ſi­
                    <lb/>
                  cut ſe hꝫ diſtãtia extremi remiſſiorꝪ in a. ab ſuo gra­
                    <lb/>
                  du ſummo ad diſtantiã ipſiꝰ c. ab eodē gradu ſūmo
                    <lb/>
                  ita ſe hꝫ diſtãtia extremi remiſſioris in b. a ſuo gra-
                    <lb/>
                  du ſummo ad diſtãtiã ipſius d. ab eodē gradu ſum­
                    <lb/>
                  mo: ergo auxilio loci a ꝑmutata ꝓportione. </s>
                  <s xml:id="N2B5F3" xml:space="preserve">ſeq̇tur
                    <lb/>
                  manifeſte probandum. </s>
                  <s xml:id="N2B5F8" xml:space="preserve">pꝫ ergo corre.</s>
                </p>
                <note position="left" xml:id="N2B685" xml:space="preserve">Calcula.</note>
                <p xml:id="N2B689">
                  <s xml:id="N2B68A" xml:space="preserve">Notandū eſt tertio circa materiam .3.
                    <lb/>
                  argumēti /  due ſunt opiniões circa difformiū q̈li-
                    <lb/>
                  tatū denoīatiões quas Cal. recitati .2. capi. prima
                    <lb/>
                  eſt  intēſio q̈litatis difformis et eiꝰ denoīatio me-
                    <lb/>
                  tiri d3 penes reductionē ad vniformitatē: quomo-
                    <lb/>
                  do autē debeat fieri talis reductio ſequēs notabi-
                    <lb/>
                  le declarabit. </s>
                  <s xml:id="N2B699" xml:space="preserve">Alia vero eſt opinio  intēſio diffor­
                    <lb/>
                  miū mēſurãda eſt gradu ſūmo. </s>
                  <s xml:id="N2B69E" xml:space="preserve">v3  ſi in pedali ſit
                    <lb/>
                  qualitas difformis ab .8. vſ ad nõ g̈dū: ſubiectuꝫ
                    <lb/>
                  eius denoīabit̄̄ intenſum vt .8. etiã ſi ꝑ .4. partē ſub­
                    <lb/>
                  iecti vel ̄tūcun paruã extendat̄̄. </s>
                  <s xml:id="N2B6A7" xml:space="preserve">Sꝫ cal. volēs im­
                    <lb/>
                  pugnare primã opinionē facit talē ↄ̨ñam. </s>
                  <s xml:id="N2B6AC" xml:space="preserve">Per ma­
                    <lb/>
                  iorem partē alicuius ſubiecti cõtinuo fit intenſio ̄
                    <lb/>
                  remiſſio eodē gradu: ergo ↄ̨tinuo totū ītēdit̄̄. </s>
                  <s xml:id="N2B6B3" xml:space="preserve">Ideo
                    <lb/>
                  ad inquirēdū an in tali reductiõe ſubiectū ſꝑ inten­
                    <lb/>
                  datur, aut ſꝑ remittat̄̄, aut aliqñ intēdatur, aliquã­
                    <lb/>
                  do vero remittat̄̄, aut maneat eque intenſum pono
                    <lb/>
                  aliq̈s ꝓpoſitiões. </s>
                  <s xml:id="N2B6BE" xml:space="preserve">¶ Prima ꝓpõ. </s>
                  <s xml:id="N2B6C1" xml:space="preserve">Iſta ↄ̨ña nichil va­
                    <lb/>
                  let ꝑ maiorē partē huiꝰ ſubiecti ↄ̨tinuo fit intenſio
                    <lb/>
                  ̄ remiſſio eodē gradu: g̊ totuꝫ ſubiectū intenditur.
                    <lb/>
                  </s>
                  <s xml:id="N2B6C9" xml:space="preserve">Probat̄̄ et ſigno vnū pedale difformiter albuꝫ cuiꝰ
                    <lb/>
                  vna medietas ſit vniformis .8. et alia vt vnū vnifor-
                    <lb/>
                  mis: et volo /  ꝑ totã horã futurã remittat̄̄ pars in-
                    <lb/>
                  tēſior et ꝑdat duos gradus adeq̈te: et totidē acq̇rat
                    <lb/>
                  pars remiſſior: et cū hoc cõdēſetur pars intēſior ad
                    <lb/>
                  ſubduplū pars vero remiſſior rarefiat: ita  quãtã
                    <lb/>
                  ̄titatē deꝑdit pars intēſior tantã acq̇rat adequa-
                    <lb/>
                  te pars remiſſior. </s>
                  <s xml:id="N2B6DA" xml:space="preserve">Quo poſito in fine hore illḋ ſub­
                    <lb/>
                  iectum erit remiſſius ꝙ̄ modo ſit. </s>
                  <s xml:id="N2B6DF" xml:space="preserve">Et tñ intēſio con-
                    <lb/>
                  tinuo fit ꝑ maiorē partē ꝙ̄ remiſſio eodē gradu: igr̄
                    <lb/>
                  in illo caſu añs illiꝰ ↄ̨ñe eſt verū / et ↄ̨ñs falſum. </s>
                  <s xml:id="N2B6E6" xml:space="preserve">Et ꝑ
                    <lb/>
                  ↄ̨ñs ↄ̨ña nõ valet / qḋ fuit ꝓbandū. </s>
                  <s xml:id="N2B6EB" xml:space="preserve">Minor ē declarat
                    <lb/>
                  coſus: et maior ꝓbat̄̄ / q2 in ṗncipio talis alteratio-
                    <lb/>
                  nis totū illud pedale eſt album vt .4. cum dimidio.
                    <lb/>
                  </s>
                  <s xml:id="N2B6F3" xml:space="preserve">Prīa em̄ medietas illius albedinis denoīat vt .4.
                    <lb/>
                  quia eſt vt .8. et alia vt dimidiū q2 eſt vt vnū. </s>
                  <s xml:id="N2B6F8" xml:space="preserve">Et in fi­
                    <lb/>
                  ne totum illud pedale eſt albuꝫ vt .3. cum .3. quartis:
                    <lb/>
                  igr̄ in fine hore illud pedale eſt remiſſius ꝙ̄ in prīci­
                    <lb/>
                  pio. </s>
                  <s xml:id="N2B701" xml:space="preserve">Mīor ꝓbat̄̄ / q2 in fine hore .3. quarte illiꝰ peda-
                    <lb/>
                  lis erunt albe vt .3. </s>
                  <s xml:id="N2B706" xml:space="preserve">Et ſic denoīabunt totuꝫ albuꝫ vt
                    <lb/>
                  duo cum vna quarta. reliq̈ o quarta intēſior cū ſit
                    <lb/>
                  vt .6. denīat vt vnū cum dimidio. </s>
                  <s xml:id="N2B70D" xml:space="preserve">Modo duo cū vna
                    <lb/>
                  quarta: et vnū cum dimidio faciunt .3. cum .3. quartꝪ:
                    <lb/>
                  igit̄̄ totuꝫ illud pedale ī fine eſt albū vt .3. cuꝫ .3. quar­
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                  tis. </s>
                  <s xml:id="N2B716" xml:space="preserve">¶ Scḋa ꝓpõ </s>
                  <s xml:id="N2B719" xml:space="preserve">Iſta ↄ̨ña nõ valet ꝑ maiorē partem
                    <lb/>
                  huiꝰ ſubiecti ↄ̨tinuo fit remiſſio ꝙ̄ intēſio eodē gra-
                    <lb/>
                  du: g̊ hoc ſubiectū remittit̄̄. </s>
                  <s xml:id="N2B720" xml:space="preserve">Probat̄̄ et ſigno vnum
                    <lb/>
                  pedale cuius vna medietas ſit alba vniformiter vt
                    <lb/>
                  8. et alia vt duo: et ꝑ horã futurã ꝑdat ſucceſſiue ꝑs
                    <lb/>
                  intenſior duos gradus albedinis: pars o remiſſi­
                    <lb/>
                  or acq̇rat illos duos adequate: et cū hoc pars intē-
                    <lb/>
                  ſior rarefiat ad ſexq̇alteruꝫ acq̇rendo .4. pedalis: et
                    <cb chead="De difformium intenſione"/>
                  tantum deꝑdat medietas remiſſior. </s>
                  <s xml:id="N2B730" xml:space="preserve">Quo poſito in
                    <lb/>
                  fine hore illud pedale erit albiꝰ ꝙ̄ mõ ſit: et tñ ma-
                    <lb/>
                  iorem partē ↄ̨tinuo fiet remiſſio ꝙ̄ intēſio eodē gra­
                    <lb/>
                  du: igr̄ illa ↄ̨ña nulla. </s>
                  <s xml:id="N2B739" xml:space="preserve">Maior ꝓbatur / q2 in ṗncipio
                    <lb/>
                  alteratiõis illud pedale ē album vt .5. / vt conſtat: et ī
                    <lb/>
                  fine eſt album vt .5. cū dimidio: igr̄ in fine hore ē al-
                    <lb/>
                  bius ꝙ̄ modo ſit. </s>
                  <s xml:id="N2B742" xml:space="preserve">minor ꝓbatur / q2 ī fine .3. quarte al­
                    <lb/>
                  be vt .6. denoīant illud pedale vt .4. cum dimidio / vt
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                  patet calculãti: et alia q̈rta vt .4. denoīat totum vt
                    <lb/>
                  vnum: igit̄̄ totum vnū pedale eſt albū vt .5. cū dimi-
                    <lb/>
                  dio: quod fuit ꝓbandū. </s>
                  <s xml:id="N2B74D" xml:space="preserve">¶ Et q̊ ſeq̇tur /  nõnū̄ in-
                    <lb/>
                  tenſio fit ꝑ maiorē partē ꝙ̄ remiſſio eodē gradu: et
                    <lb/>
                  tamē totum remittit̄̄: et aliqñ etiã intendit̄̄. </s>
                  <s xml:id="N2B754" xml:space="preserve">Et ple-
                    <lb/>
                  rū ꝑ aliqḋ tēpus intēdit̄̄: et ꝑ aliqḋ remittit̄̄. </s>
                  <s xml:id="N2B759" xml:space="preserve">Pa­
                    <lb/>
                  tent oīa iſta cum multis aliis hãc materiã tangēti-
                    <lb/>
                  bus in expoſitiõe ſupra .2. capitulū Calculatoris vi­
                    <lb/>
                  deas ea ibi. </s>
                  <s xml:id="N2B762" xml:space="preserve">Et ꝑ hoc pꝫ ſolutio .3. argumēti.</s>
                </p>
                <p xml:id="N2B765">
                  <s xml:id="N2B766" xml:space="preserve">Notandum eſt quarto pro declaratio­
                    <lb/>
                  ne materie quinti argumēti:  calculator aliter mē­
                    <lb/>
                  ſurat q̈litatis et ſiĺr q̈lificati difformis intēſionem
                    <lb/>
                  quã ꝑ reductionē ad vniformitatē: metit̄̄ em̄ diffor-
                    <lb/>
                  mis corꝑis intēſionē penes denoīationē ꝑtiū ipſiꝰ
                    <lb/>
                  qualitatis difformis: ita  vĺr cuiuſlꝫ difformis in­
                    <lb/>
                  tēſio mēſurari hꝫ penes gradū denoīatiõis q̊ talis
                    <lb/>
                  q̈litas nata eſt ſuū totale ſubiectū denoīare ſecluſa
                    <lb/>
                  ↄ̈rii ꝑmixtiõe. </s>
                  <s xml:id="N2B779" xml:space="preserve">procuiꝰ ītellectu faciliori ponit̄̄ talis
                    <lb/>
                  ſuppõ q̄ in hac mã ꝓ baſi et fundamēto hētur q̄ ta-
                    <lb/>
                  lis eſt. </s>
                  <s xml:id="N2B780" xml:space="preserve">minꝰ facit q̈litas extēſa ꝑ ꝑtē ſubiecti ad de-
                    <lb/>
                  noīationē ſui ſubiecti ꝙ̄ ſi eadē ꝑ totū extendat̄̄ ma­
                    <lb/>
                  nēte eq̈li intēſione. </s>
                  <s xml:id="N2B787" xml:space="preserve">Et ī quacū ꝓportiõe pars in
                    <lb/>
                  qua eſt talis qualitas eſt minor ſuo toto in eadē ta­
                    <lb/>
                  lis qualitas minus ſuū ſubiectū denoīant. </s>
                  <s xml:id="N2B78E" xml:space="preserve">ita  in
                    <lb/>
                  quadruplo minꝰ denoīat qualitas totū qñ eſt p̄ciſe
                    <lb/>
                  extenſa ꝑ vnam quartã ꝙ̄ qñ eſt extenſa ꝑ totū et per
                    <lb/>
                  tertiã in triplo minꝰ, et ꝑ medietatē in dupla minꝰ.
                    <lb/>
                  </s>
                  <s xml:id="N2B798" xml:space="preserve">Exemplū / vt albedo vt .4. extēſa p̄ciſe ꝑ quartã ꝑtem
                    <lb/>
                  ſubiecti denoīat totū ſubiectū albū vt vnū: q2 ſi eēt
                    <lb/>
                  extenſa ꝑ totū denoīaret totū ſubiectuꝫ vt .4. ſꝫ mo­
                    <lb/>
                  do eſt in ꝑte ī quadruplo mīori ſuo toto: g̊ in qua-
                    <lb/>
                  druplo minꝰ denoīat ſuum ſubiectū </s>
                  <s xml:id="N2B7A3" xml:space="preserve">Huiꝰ maior de­
                    <lb/>
                  claratio ponit̄̄ in expoſitiõe ſcḋi capitis calculato­
                    <lb/>
                  ris. </s>
                  <s xml:id="N2B7AA" xml:space="preserve">Ad menſurãdã aūt intēſionē alicuiꝰ difformis
                    <lb/>
                  cuiꝰ difformitas eſt īfinita aūt in īfinitū ꝓcedēs: vt
                    <lb/>
                  ſi ponat̄̄ /  prīa pars ꝓportionalis alicuiꝰ corpo-
                    <lb/>
                  ris ſit aliqualr̄ alba: et ſcḋa in ſexq̇altero magis: et
                    <lb/>
                  tertia in ſexq̇altero magis ꝙ̄ ſcḋa: et ſic ↄ̨ñter diui-
                    <lb/>
                  ſione corꝑis fctã ꝓportiõe ſexq̇tertia aut ̄uis alia
                    <lb/>
                  etc. </s>
                  <s xml:id="N2B7B9" xml:space="preserve">Aduertēda eſt q̄dã diuiſio qualitatū inherētiū
                    <lb/>
                  ꝑtibꝰ alicuiꝰ ſubiecti q̄ huic inq̇ſitiõi plurimū ē ac-
                    <lb/>
                  comoda et neceſſaria </s>
                  <s xml:id="N2B7C0" xml:space="preserve">Illã tñ abſoluã: qm̄ iam ip̄a ex­
                    <lb/>
                  poſita eſt in ſcḋo tractatu huiꝰ partis capite .6. </s>
                  <s xml:id="N2B7C5" xml:space="preserve">Di­
                    <lb/>
                  uiſio aūt eſt hec. </s>
                  <s xml:id="N2B7CA" xml:space="preserve">qualitates ꝑ diuerſas ꝑtes ſubie-
                    <lb/>
                  cti extēſe qñ ſunt equales nõnun̄ o inequales
                    <lb/>
                  intenſiue facile eſt exēpla dare. </s>
                  <s xml:id="N2B7D1" xml:space="preserve">Et ſi ſunt equales
                    <lb/>
                  aut extendunt̄̄ ſiue īherēt ꝑtibꝰ equalibꝰ aut īequa­
                    <lb/>
                  libꝰ exēpla ſunt ī prõptu. </s>
                  <s xml:id="N2B7D8" xml:space="preserve">Et ſi ſint īequales ītenſiue
                    <lb/>
                  ſiĺr valent extēdi ꝑ partes equales ſubiecti aut per
                    <lb/>
                  partes īequales. </s>
                  <s xml:id="N2B7DF" xml:space="preserve">Si qualitates īequales ī equalibꝰ
                    <lb/>
                  ptibꝰ ſubiecti īhereãt: hoc cõtīgit dupĺr / q2 aut ma­
                    <lb/>
                  ior qualitas maiori parti īheret aut mīori exēpluꝫ
                    <lb/>
                  ṗmi vt ſi albedo vt octo īhereat mediati pedalis et
                    <lb/>
                  albedo vt .4. vni tertie eiuſdē pedalis exēplū ſecū-
                    <lb/>
                  di vt ſi fiat conuerſo. </s>
                  <s xml:id="N2B7EC" xml:space="preserve">Si aūt ītenſior qualitas īhe­
                    <lb/>
                  ret parti ſubiecti mīori remiſſior qualitas maiori
                    <lb/>
                  parti ſubiecti. </s>
                  <s xml:id="N2B7F3" xml:space="preserve">hoc contīgit tripĺr: q2 aut ꝓportio
                    <lb/>
                  illarū partiū ſubiecti excedit ꝓportõem illaꝝ qua-
                    <lb/>
                  litatū: aut ꝓportio qualitatū excedit ꝓportõem il- </s>
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