Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N1C8AF" level="3" n="2" type="other" type-free="tractatus">
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                <pb chead="De motu locali quo ad effectum ſubiecto difformi." file="0142" n="142"/>
                <p xml:id="N1DD9C">
                  <s xml:id="N1DD9D" xml:space="preserve">Et arguitur primo /  motus vnifor-
                    <lb/>
                  miter difformis velocitas no eſt gradn illiꝰ medio
                    <lb/>
                  ↄ̨menſurãda / q2 ſeq̄retur /  omne quod mouetur in
                    <lb/>
                  aliquo tempore vniformiter diffõrmiter a non gra­
                    <lb/>
                  du vſ ad certum gradum id eſt a non gradu vſ
                    <lb/>
                  ad duo decimum moueretur in duplo tardius quã
                    <lb/>
                  mobile motum per idem tempus gradu duo deci-
                    <lb/>
                  mo continuo / ſed conſequens eſt falſum: igitur illḋ
                    <lb/>
                  ex q̊ ſeq̇t̄̄. </s>
                  <s xml:id="N1DDB0" xml:space="preserve">Cõſeq̄ntia pꝫ / q2 in toto illo tp̄e tale mobi­
                    <lb/>
                  le motū vniformiṫ difformiṫ mouet̄̄ ita velociṫ ac ſi
                    <lb/>
                  moueretur motu vt ſex ſi talis motus debeat correſ­
                    <lb/>
                  pondere gradui medio cum ſex ſit gradus mediꝰ in­
                    <lb/>
                  ter duodecim et non gradū: ſed ſi continuo per ideꝫ
                    <lb/>
                  tempus moueretur gradu ſexto in duplo tardiꝰ mo­
                    <lb/>
                  ueretur mobili moto gradu duodecimo vniformi-
                    <lb/>
                  ter: igitur. </s>
                  <s xml:id="N1DDC1" xml:space="preserve">Sed falſitas conſequentis oſtenditur / q2
                    <lb/>
                  ſi in illo tempore moueretur in duplo tardius quaꝫ
                    <lb/>
                  mobile motum gradu duodecimo: vel igitur ī vtra­
                    <lb/>
                   medietate moueretur in duplo tardius, vel in ali­
                    <lb/>
                  qua: vel in aliqua non: ſed neutrum iſtorum eſt dicē­
                    <lb/>
                  dum: igitur. </s>
                  <s xml:id="N1DDCE" xml:space="preserve">Non primum / quia in prima mouetur
                    <lb/>
                  in quadruplo minus: igitur non in duplo minꝰ nec
                    <lb/>
                  ſecundum: quoniam in ſecunda medietate non mo-
                    <lb/>
                  uetur in duplo minus ſed in ſexquitertio </s>
                  <s xml:id="N1DDD7" xml:space="preserve">Uelocitas
                    <lb/>
                  enī ſecunde medietatis temporis correſpondet gra­
                    <lb/>
                  dui nouo: vt ptꝫ ex iſto mõ dicendi. </s>
                  <s xml:id="N1DDDE" xml:space="preserve">¶ Forte dices et be­
                    <lb/>
                  ne ad illud quod querit argumentum /  in toto tem­
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                  pore adequate mouetur in duplo minus quam mo­
                    <lb/>
                  bile motum vniformiter vt duodecim: tamē per nul­
                    <lb/>
                  lam partem temporis mouetur adequate in duplo
                    <lb/>
                  minus. </s>
                  <s xml:id="N1DDEB" xml:space="preserve">Et ideo illa conſequentia non valet: moue-
                    <lb/>
                  tur in iſto tempore in duplo minus. </s>
                  <s xml:id="N1DDF0" xml:space="preserve">ergo in vtra
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                  medietate: vel in aliqua: vel in aliqua non. </s>
                  <s xml:id="N1DDF5" xml:space="preserve">Nam in
                    <lb/>
                  prima mouetur in quadruplo minus quam mobile
                    <lb/>
                  gradu duodecimo et in ſecunda in ſexquitertio.</s>
                </p>
                <p xml:id="N1DDFC">
                  <s xml:id="N1DDFD" xml:space="preserve">Sed contra / quia tunc ſequeretur / 
                    <lb/>
                  omne mouens vniformiter a non gradu vſ ad cer­
                    <lb/>
                  tum gradum in triplo velocius moueretur in ſecun­
                    <lb/>
                  da medietate temporis quam in prima: ſed conſe-
                    <lb/>
                  quens eſt falſum: igitur. </s>
                  <s xml:id="N1DE08" xml:space="preserve">Sequela patet / quoniã ī ſe­
                    <lb/>
                  cunda medietate / vt dicis mouetur velocitate ſubſex­
                    <lb/>
                  quitertia ad gradum intenſiorem: et in prima medi­
                    <lb/>
                  etate mouetur velocitate ſubquadrupla ad eundeꝫ
                    <lb/>
                  gradum intenſiorem: ſed omne ſubſexquitertiū ad
                    <lb/>
                  aliquod eſt triplum ad quartam eius vel ad ſubqua­
                    <lb/>
                  druplum illius / quod idem eſt: igitur gradus mediꝰ
                    <lb/>
                  prime medietatis eſt triplus ad gradum medium
                    <lb/>
                  ſecunde medietatis. </s>
                  <s xml:id="N1DE1B" xml:space="preserve">¶ Dices et bene concedendo / qḋ
                    <lb/>
                  infertur / vt poſtea oſtendetur in quadam propoſi-
                    <lb/>
                  tione.</s>
                </p>
                <p xml:id="N1DE22">
                  <s xml:id="N1DE23" xml:space="preserve">Sed contra / quia ſi illa ſolutio eēt bo-
                    <lb/>
                  na ſequeretur /  in ſecunda medietate prime medie­
                    <lb/>
                  tatis in triplo velocius moueretur illud mobile quã
                    <lb/>
                  in prima eiuſdem medietatis: et diuiſa illa medieta­
                    <lb/>
                  te adhuc in duas in ſubtriplo moueretur: ſed conſequens
                    <lb/>
                  eſt falſum: igitur illud ex quo ſequitur. </s>
                  <s xml:id="N1DE30" xml:space="preserve">Falſitas con­
                    <lb/>
                  ſequentis probatur / quia tunc ſequeretur / quodlib3
                    <lb/>
                  mobile incipiens moueri a non gradu vſ ad certū
                    <lb/>
                  gradum infinita tarditate moueri per aliquod tem­
                    <lb/>
                  pus: ſed conſequens eſt falſum: igitur illud ex quo
                    <lb/>
                  ſequitur: ſequela probatur / quoniã in mediate poſt
                    <lb/>
                  inſtans initiatiuum motus tale mobile mouebitur
                    <lb/>
                  aliquantula velocitate: et in duplo minori et in tri-
                    <lb/>
                  plo minori et in quadruplo / et ſic conſequenter: igi-
                    <lb/>
                  tur infinita tarditate mouebitur / quodlibet tale mo­
                    <lb/>
                  bile: </s>
                  <s xml:id="N1DE47" xml:space="preserve">Antecedens patet ex ſolutione. </s>
                  <s xml:id="N1DE4A" xml:space="preserve">Sed falſitas cõ­
                    <cb chead="De motu locali quo ad effectum ſubiecto difformi."/>
                  ſequentis arguitur / quia alias ſequeretur mobile /
                    <lb/>
                  quod continuo infinite velociter intendit motum ſu­
                    <lb/>
                  um infinitum tarde moueri: ſed conſequens videtur
                    <lb/>
                  implicare / igitur illud ex quo ſequitur: </s>
                  <s xml:id="N1DE56" xml:space="preserve">Et ſequela
                    <lb/>
                  ꝓbatur pono caſum /  ſint īfinita mobilia .a.b.c.
                    <lb/>
                  etc. que moueantur per horaꝫ vniformiter difformi­
                    <lb/>
                  ter incipiendo a non gradu et a. moueatur per ean-
                    <lb/>
                  dem a non gradu vſ ad octauum: et b. a non gra-
                    <lb/>
                  du vſ ad ſextumdecimum: et c. a non gradu vſ ad
                    <lb/>
                  triceſimum ſecundum et conſequenter ꝓcedendo ꝑ
                    <lb/>
                  numeros duplos: et hoc in eadem hora: quo poſito
                    <lb/>
                  ſic argumentor / quodlibet iſtorum mobilium infini­
                    <lb/>
                  ta tarditate per aliquod tempus mouebitur. </s>
                  <s xml:id="N1DE6B" xml:space="preserve">ſed in
                    <lb/>
                  ta velocitate aliquod iſtorum per idem tempus in-
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                  tendet motum ſuum. </s>
                  <s xml:id="N1DE72" xml:space="preserve">ergo aliquod iſtorum quod in­
                    <lb/>
                  finita tarditate per aliquod tempus mouebitur in­
                    <lb/>
                  finita velocitate per aliquod tempus intendit mo-
                    <lb/>
                  tum ſuum / quod fuit probaudum.</s>
                </p>
                <note position="right" xml:id="N1DE7B" xml:space="preserve">cõfirma-
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                tio.</note>
                <p xml:id="N1DE81">
                  <s xml:id="N1DE82" xml:space="preserve">¶ Et confirmatur / quia ſi quilibet motus vniformi­
                    <lb/>
                  ter difformis commenſurari debeat penes graduꝫ
                    <lb/>
                  medium ſequeretur /  motus a certo gradu vſ ad
                    <lb/>
                  non gradum vt exempli gratia quo aliquod mobi­
                    <lb/>
                  le mouetur a quarto vſ ad non gradum remitten­
                    <lb/>
                  do motum ſuum in hora: et motus quo aliquod mo­
                    <lb/>
                  bile mouetur vniformiter difformiter a non gradu
                    <lb/>
                  vſ ad quartum in eadem hora eſſent omnino eq̈-
                    <lb/>
                  les / ſꝫ hoc eſt falſum: igr̄ illud ex quo ſeq̇tur. </s>
                  <s xml:id="N1DE95" xml:space="preserve">Seque-
                    <lb/>
                  la probatur vtriuſ eī motus illorū duorum motu­
                    <lb/>
                  um gradus medius eſt vt duo / et per conſequens illi
                    <lb/>
                  motus ſunt equales. </s>
                  <s xml:id="N1DE9E" xml:space="preserve">Sed iam oſtenditur falſitas
                    <lb/>
                  contequentis: quia tunc ſequeretur /  ſi aliquis mo­
                    <lb/>
                  tus intenderetur a gradu vt .4. vſ ad gradū du-
                    <lb/>
                  plum in hora et alter motus equalis illi puta vt .4.
                    <lb/>
                  ab eodem gradu quarto ln eadem hora vniformi-
                    <lb/>
                  ter et eque velociter remittatur vſ ad quietem ſiue
                    <lb/>
                  ad non gradum motus: tunc talis motus qui remit­
                    <lb/>
                  titur non dumtaxat vniformiter et eqne velociter re­
                    <lb/>
                  mitteretur ſicut alter motus equalis ei intendere-
                    <lb/>
                  tur in eodem tempore: ſed hoc eſt falſum / quia quã-
                    <lb/>
                  tam latitudineꝫ acquirit ille motus qui intenditur
                    <lb/>
                  tantam adequate deperdit ille motus qui remitti-
                    <lb/>
                  tur in eodem tempore. </s>
                  <s xml:id="N1DEB9" xml:space="preserve">Naꝫ ille q̇ intenditur cum ſit
                    <lb/>
                  vt .4. acquirit .4. gradus ſupra ſe: et in eodeꝫ tempo­
                    <lb/>
                  re ille qui remittitur vſ ad non gradum cum ſic vt
                    <lb/>
                  quatuor perdit etiam quatuor gradus in eodē tem­
                    <lb/>
                  pore. </s>
                  <s xml:id="N1DEC4" xml:space="preserve">Sed iam probo ſequelam / quoniam ille motꝰ
                    <lb/>
                  vt .4. qui remittitur in hora vſ ad non gradum re­
                    <lb/>
                  mittitur in eadem hora ad ſuum ſubduplum, et ad
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                  ſuum ſubquadruplum: et ad ſuum ſuboctuplum: et
                    <lb/>
                  ſic in infinitum </s>
                  <s xml:id="N1DECF" xml:space="preserve">Motus vero alter qui intendit̄̄ pre­
                    <lb/>
                  ciſe intenditur ad ſuum duplum. </s>
                  <s xml:id="N1DED4" xml:space="preserve">igitur in infinituꝫ
                    <lb/>
                  maiorem proportionem deperdit motus qui remit­
                    <lb/>
                  titnr quam acquirat motus qui intenditur: et ꝑ con­
                    <lb/>
                  ſequens non ita velociter ſicut vnus remittitur al-
                    <lb/>
                  ter intenditur / quod fuit probandum.</s>
                </p>
                <p xml:id="N1DEDF">
                  <s xml:id="N1DEE0" xml:space="preserve">¶ Dices forte ad punctum argumenti diſtinguen-
                    <lb/>
                  do illatum aut  in eadem hora non remittat̄̄ eque­
                    <lb/>
                  velociter vnus motus ſicut alter intenditur equali­
                    <lb/>
                  tate geometrica / et ſic conceditur / vt bene probat ar-
                    <lb/>
                  gumentum, aut equalitate arithmetica / et ſic nega-
                    <lb/>
                  tur: </s>
                  <s xml:id="N1DEED" xml:space="preserve">Ad hoc enim  eque velociter vnus motus re-
                    <lb/>
                  mittatur ſicut alter intenditur equalitate arithme­
                    <lb/>
                  tica ſufficit  quantancū latitudinem vnus acq̇-
                    <lb/>
                  rat in aliquo tempore, tantam alter deperdat ī eo­
                    <lb/>
                  dem tempore: et ita ſit in caſu poſito: ſed ad hoc 
                    <lb/>
                  aliquis motus intendatur equeuelociter geometri­
                    <lb/>
                  ce ſicut alter remittitur geometrice: oportet /  quã-
                    <lb/>
                  tãcun proportionem vnus acquirat ſupra ſe ī ali­
                    <lb/>
                  quo tempore tantaꝫ alter qui remittitur deperdat </s>
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