Alvarus, Thomas, Liber de triplici motu, 1509

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            <div xml:id="N25905" level="3" n="4" type="other" type-free="tractatus">
              <div xml:id="N2C8AE" level="4" n="5" type="chapter" type-free="capitulum">
                <p xml:id="N2CDA1">
                  <s xml:id="N2CE93" xml:space="preserve">
                    <pb chead="Inductionis gradus ſūmi cõſideratio." file="0280" n="280"/>
                  locitas inducti. g. ſ. cum ſubiectum rarefit aut condē-
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                  ſatur debet attendi penes totam quantitatem ſubie­
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                  cti dempta illa quam acquirunt aut deperdunt par­
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                  tes poſt̄ ſunt ſūme. </s>
                  <s xml:id="N2CEA1" xml:space="preserve">vt ſi totū erat pedale in princi-
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                  pio: et in fine manet tripedale: et partes poſt̄ erant
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                  ſumme acquiſiuerunt pedale preciſe tūc velocitas in­
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                  ductionis debet attendi penes bipedale preciſe. </s>
                  <s xml:id="N2CEAA" xml:space="preserve">Ui-
                    <lb/>
                  deas cal. in .2. ca. de inductione grad. ſum. </s>
                  <s xml:id="N2CEAF" xml:space="preserve">Et hic mo­
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                  dus cal. michi placat: quãuis alter poſſit ſuſtineri</s>
                </p>
                <p xml:id="N2CEE8">
                  <s xml:id="N2CEE9" xml:space="preserve">Notandum eſt tertio /  cum gradus
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                  ſummus inducitur per duo vnifor. difformia ter-
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                  minata ad ſum. mediante alteratione vniformi per
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                  totum extenſa illa poſſunt multipliciter ſe habere.
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                  </s>
                  <s xml:id="N2CEF3" xml:space="preserve">quia aut illa ſunt equalia in quantitate et quali-
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                  tate omnino, aūt in quantitate tãtum, aut inequa­
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                  lia in qualitate et quãtitate ſiĺ. </s>
                  <s xml:id="N2CEFA" xml:space="preserve">¶ Si ſunt inequa-
                    <lb/>
                  lia in quantitate et qualitate ſimul: hoc contingit
                    <lb/>
                  dupliciter quia aut maius excedit in quantitate et
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                  qualitate, aut in quantitate ſolum. </s>
                  <s xml:id="N2CF03" xml:space="preserve">Et hic exceſſus
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                  venit ſumendus extremo remiſſiori / vt conſtat. </s>
                  <s xml:id="N2CF08" xml:space="preserve">¶ Si
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                  autem illa ſunt equalia in quanti. et quali. aut al-
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                  terantur per totum equali alteratione aut non.
                    <lb/>
                  </s>
                  <s xml:id="N2CF10" xml:space="preserve">¶ Si autem ſunt equalia quantitatiue tantum aut
                    <lb/>
                  alterantur alteratione equali. </s>
                  <s xml:id="N2CF15" xml:space="preserve">aut inequali. </s>
                  <s xml:id="N2CF18" xml:space="preserve">¶ Si
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                  inequali aut intenſius alteratur maiori, aut mino-
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                  ri. </s>
                  <s xml:id="N2CF1F" xml:space="preserve">Si minori aut minori in ea proportione qua ſe
                    <lb/>
                  habent exceſſus quibꝰ gra. ſum. excedit extrema re-
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                  miſſiora. </s>
                  <s xml:id="N2CF26" xml:space="preserve">aut in maiori, aut in minori. </s>
                  <s xml:id="N2CF29" xml:space="preserve">¶ Si vero
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                  ſunt equalia in qualitantum. </s>
                  <s xml:id="N2CF2E" xml:space="preserve">aut alterantur equa­
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                  li alteratione, aut non. </s>
                  <s xml:id="N2CF33" xml:space="preserve">¶ Sed ſi ſint inequalia in
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                  quãti. et quali. et maiꝰ vtro modo excedit aut al­
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                  terantur equali alteratione, aut non. </s>
                  <s xml:id="N2CF3A" xml:space="preserve">Si non, aut
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                  maius alteratur maiori aut minori. </s>
                  <s xml:id="N2CF3F" xml:space="preserve">Si minori aut
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                  in ea proportiõe minori qua ſe habet exceſſus quo
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                  gra. ſum. excedit extremum remiſſioris ad exceſſum
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                  quo excedit extremum remiſſius intenſioris aut in
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                  maiori, aut in minori. </s>
                  <s xml:id="N2CF4A" xml:space="preserve">¶ Si autem ſunt inequalia
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                  vtro modo et minus excedit in qualitate tunc aut
                    <lb/>
                  equali alteratione alterantur aut non. </s>
                  <s xml:id="N2CF51" xml:space="preserve">Si non aut
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                  minus alteratur maiori, aut minori: </s>
                  <s xml:id="N2CF56" xml:space="preserve">Si minori aut
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                  in ea proportione minori qua ſe habet exceſſus q̊
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                  gradus ſum. excedit extremum remiſſioris ad exceſ­
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                  ſum quo excedit extremū remiſſius intenſioris aut
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                  in maiori aut in minori. </s>
                  <s xml:id="N2CF61" xml:space="preserve">Exempla nõ poſui gratia
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                  breuitatis. </s>
                  <s xml:id="N2CF66" xml:space="preserve">Hac diuiſione conſummata pono ali­
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                  quas concluſiones.</s>
                </p>
                <note position="left" xml:id="N2CF6B" xml:space="preserve">2. pars q̄­
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                ſtionis.</note>
                <p xml:id="N2CF71">
                  <s xml:id="N2CF72" xml:space="preserve">Prima concluſio. </s>
                  <s xml:id="N2CF75" xml:space="preserve">Si aliquod vni. dif­
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                  for. terminatum ad ſummum alteretur latitudine
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                  alterationis vniformi per totum in ipſum vnifor-
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                  miter continuo inducitur gradus ſummus. </s>
                  <s xml:id="N2CF7E" xml:space="preserve">hec con­
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                  cluſio patet ex primo argumento ante oppoſitum</s>
                </p>
                <p xml:id="N2CF83">
                  <s xml:id="N2CF84" xml:space="preserve">Secunda concluſio. </s>
                  <s xml:id="N2CF87" xml:space="preserve">Si duo vni. dif­
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                  for. terminata ad ſum. equalia omnino in quanti. et
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                  quali. alterentur eadem latitu. alterationis vnifor­
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                  mi per totum in ipſa equeuelociter continuo indu-
                    <lb/>
                  citur gradus ſumus. </s>
                  <s xml:id="N2CF92" xml:space="preserve">Probatur / quia equeuelociter
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                  continuo gradus ſum. deueniet ad punctum vnius
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                  ſicut ad punctum correſpondens alterius et pūcta
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                  correſpondentia equaliter diſtant a puncto initia­
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                  tiuo motus / vt conſtat / quia ſūt equalia / igitur eque­
                    <lb/>
                  uelociter gradus ſummus in ipſa inducetur.</s>
                </p>
                <p xml:id="N2CF9F">
                  <s xml:id="N2CFA0" xml:space="preserve">Tertia concluſio. </s>
                  <s xml:id="N2CFA3" xml:space="preserve">Si in caſu prioris
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                  concluſionis vnū illorum alteretur alteratione vni.
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                  per totum minori ſiue remiſſiori ꝙ̄ aliud: in ea pro­
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                  portione qua alteratio vnius excedit olterationem
                    <lb/>
                  alterius in ea velocius continuo inducitur in ipſū
                    <lb/>
                  gradus ſūmus. </s>
                  <s xml:id="N2CFB0" xml:space="preserve">Probatur / et ſit proportio altera-
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                  tiouum f. et a. alteratū velocius et b. tardius. </s>
                  <s xml:id="N2CFB5" xml:space="preserve">Et ar­
                    <cb chead="Inductionis gradus ſūmi cõſideratio."/>
                  guo ſic / ad punctum extremum ipſius a. in f. propor­
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                  tione citius deueniet gra. ſum. ꝙ̄ ad correſpondēs
                    <lb/>
                  in b. quia illa puncta extrema equaliter diſtant a
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                  ſummo, et illa diſtantia in .f. proportione citius a-
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                  quiritur in extremo ipſius a. ꝙ̄ ipſius b. cum altera­
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                  tio continuo ſit in f. proportione maior in extremo
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                  ipſius a. ꝙ̄ ipſius b. ex caſu. </s>
                  <s xml:id="N2CFC7" xml:space="preserve">igitur cõtinuo in f. pro-
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                  portiõe velociꝰ inducitur gradus ſūmus in a. ꝙ̄ in
                    <lb/>
                  b. / quod fuit probandū </s>
                  <s xml:id="N2CFCE" xml:space="preserve">Patet conſequentia / quia in
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                  vtrū illoꝝ vniformiter continuo inducit̄̄ gra. ſū.
                    <lb/>
                  ex prima concluſione.</s>
                </p>
                <p xml:id="N2CFD5">
                  <s xml:id="N2CFD6" xml:space="preserve">Quarta cõcluſio. </s>
                  <s xml:id="N2CFD9" xml:space="preserve">Si equalia in quã-
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                  titate tm̄ vni, diff. termi. ad ſū. alterētur equali al-
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                  ratiõe vniformi ꝑ totū per intenſius illoꝝ ↄ̨tinuo
                    <lb/>
                  velocius inducit̄̄ gra. ſū in ea ꝓportiõe qua ſe hñt
                    <lb/>
                  exceſſus q̇bus gradus ſū. excedit extrema remiſſio-
                    <lb/>
                  ra illoꝝ. </s>
                  <s xml:id="N2CFE6" xml:space="preserve">Probat̄̄ / ſit a. intēſius et b. remiſſius: et ſit f.
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                  ꝓportio exceſſus quo gra. ſū. excedit extremū remiſ­
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                  ſius b. ad exceſſū quo excedit extremū remiſſiꝰ ip̄iꝰ
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                  a. </s>
                  <s xml:id="N2CFEF" xml:space="preserve">Et arguit̄̄ ſic / in .f. ꝓportiõe gra. ſū. citius erit ad
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                  extremū ip̄iꝰ a. ꝙ̄ ip̄ius b. cū alteratlo ad illa extre­
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                  ma ſit equalis: et in .f. ꝓportione minꝰ diſtat extre-
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                  mū .a. a ſū. ꝙ̄ extremū ipſiꝰ b. / ergo in .f. ꝓportiõe ve­
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                  locius ↄ̨tinuo inducitur gra. ſū. in a. ꝙ̄ in b. / qḋ fuit
                    <lb/>
                  ꝓbãdū. </s>
                  <s xml:id="N2CFFC" xml:space="preserve">pꝫ ↄ̨ña / q2 ex prima concluſio gradus ſū. in
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                  vtrum illorum continuo vnifor. inducitur.</s>
                </p>
                <p xml:id="N2D001">
                  <s xml:id="N2D002" xml:space="preserve">Quinta concluſio. </s>
                  <s xml:id="N2D005" xml:space="preserve">Si in caſu quar.
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                  conclu. intenſius alteretur maiori alteratione ꝙ̄ re-
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                  miſſius. </s>
                  <s xml:id="N2D00C" xml:space="preserve">Tunc in ipſum velocius inducitur gra. ſum.
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                  ̄ in aliud in proportione compoſita ex proportione
                    <lb/>
                  exceſſum quibus gra. ſum. excedit extrema remiſſio-
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                  ra i lorum: et proportione alterationum. </s>
                  <s xml:id="N2D015" xml:space="preserve">Ponatur
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                  prior hypoteſis. </s>
                  <s xml:id="N2D01A" xml:space="preserve">et ſit g. proportio alterationum: et al­
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                  teretur a maiori altera. </s>
                  <s xml:id="N2D01F" xml:space="preserve">Et arguitur ſic / ſi alteraren-
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                  tur equali alteratione in f. proportione gra. ſum. in­
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                  duceretur velocius in a. ꝙ̄ in b. ex priori conclu. </s>
                  <s xml:id="N2D026" xml:space="preserve">Sed
                    <lb/>
                  adhuc modo in a. in g. proportione velocius īducitur
                    <lb/>
                  gradus ſummꝰ ꝙ̄ tunc: igitur modo in a. inducit̄̄ gra­
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                  dus ſummi velociuſ in b. in proportione compoſi-
                    <lb/>
                  ta ex f. et g. / quod fuit probandum. </s>
                  <s xml:id="N2D031" xml:space="preserve">Probatur minor /
                    <lb/>
                  quia in g. proportione quilꝫ punctus velocius altera­
                    <lb/>
                  tur ꝙ̄ tunc: et equaliter a principio alteratiõis diſtat
                    <lb/>
                  a ſūma ſicut tunc: et vniformi. continuo in a. inducitur
                    <lb/>
                  gradus ſummꝰ et ſimiliter in b. ex prima conſiõe / igi-
                    <lb/>
                  tur modo in g. proportione velocius inducitur gra-
                    <lb/>
                  dus ſummꝰ.</s>
                </p>
                <p xml:id="N2D040">
                  <s xml:id="N2D041" xml:space="preserve">Sexta concluſio. </s>
                  <s xml:id="N2D044" xml:space="preserve">Si predicta a.b. al­
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                  terentur vniformi alteratione per totum. </s>
                  <s xml:id="N2D049" xml:space="preserve">et b. in f.
                    <lb/>
                  proportione maiori alteratione alteretur: equeuelo-
                    <lb/>
                  citer in ipſa inducitur gradus ſummꝰ. </s>
                  <s xml:id="N2D050" xml:space="preserve">Probatur q̇a
                    <lb/>
                  ſi a. et b. equali alteratione alterarentur in b.f. ꝓpor­
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                  tione tardius induceretur gradus ſummꝰ ꝙ̄ in a. ex
                    <lb/>
                  quarta concluſione. </s>
                  <s xml:id="N2D059" xml:space="preserve">Sed modo in f. proportione ve-
                    <lb/>
                  locius inducitur in b. ꝙ̄ tunc: ergo modo equeueloci­
                    <lb/>
                  ter inducitur gradus ſummꝰ in b. ſicut in a. </s>
                  <s xml:id="N2D060" xml:space="preserve">Similis
                    <lb/>
                  minor in precedenti concluſione arguta eſt.</s>
                </p>
                <p xml:id="N2D065">
                  <s xml:id="N2D066" xml:space="preserve">Septima concluſio. </s>
                  <s xml:id="N2D069" xml:space="preserve">Si predicta a.b.
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                  alterentur alte. vni. per totum et b. alteretur in maio­
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                  ri proportione ꝙ̄ f. maiori alteratione ꝙ̄ a. tunc in b.
                    <lb/>
                  inducitur velocius gradus ſummꝰ in ea proportione
                    <lb/>
                  per quam proportio alterationum excedit f. propor­
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                  tionem. </s>
                  <s xml:id="N2D076" xml:space="preserve">Et ſi b. alteretur maiori alteratione que ta-
                    <lb/>
                  men ſit in minori proportione maior ꝙ̄ ſit f. propor-
                    <lb/>
                  tio: tunc in b. tardius inducitur gradus ſummꝰ ꝙ̄ in
                    <lb/>
                  a. in proportione per quã proportio f. excedit ꝓpor­
                    <lb/>
                  tionem illarum alterationum. </s>
                  <s xml:id="N2D081" xml:space="preserve">Hoc ex iam dictis au-
                    <lb/>
                  xiliantibus hiis que dicta ſunt in tertia concluſiõe .2.
                    <lb/>
                  tractatus ſuam ſortitur oſtenſionem.</s>
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