Alvarus, Thomas, Liber de triplici motu, 1509

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                <p xml:id="N24158">
                  <s xml:id="N2418F" xml:space="preserve">
                    <pb chead="De motu augmentationis." file="0204" n="204"/>
                  vt poſtea oſtenditur. </s>
                  <s xml:id="N2419F" xml:space="preserve">Immo ſtat  infinite tarde in­
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                  cipit acq̇rere de quantitate.</s>
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                <p xml:id="N241AE">
                  <s xml:id="N241AF" xml:space="preserve">Sed cõtra / q2 tūc ſequeretur hec con­
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                  cluſio /  ſi aliqua duo inciperent augeri a non quã­
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                  to puta .a. et .b. et .a. in certa ꝓportiõe cõtinuo velo-
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                  cius augeatur ꝙ̄ .b. ip̄m .a. / qḋ in certa ꝓportione cõ­
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                  tinuo velocius augebitur ꝙ̄ .b. ꝑ magnū tempꝰ ma­
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                  nebit minus ip̄o .b. / ſed cõſequens eſt falſum: igitur
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                  illud ex quo ſequit̄̄. </s>
                  <s xml:id="N241BE" xml:space="preserve">Falſitas cõſequētis arguit̄̄ ſic.
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                  </s>
                  <s xml:id="N241C2" xml:space="preserve">quoniã ſi .a. et .b. a nõ quãto incipiēt cõtinuo eque­
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                  velociter augeri cõtinuo manerēt equalia: ſed mo-
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                  do .a. cõtinuo velocius augebit̄̄ ꝙ̄ .b. et incipiunt a
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                  nõ quãto in eodem nſtanti: ergo ſequitur /  .a. conti­
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                  nuo erit maius ipſo .b. et ꝑ cõſequens nū̄ manebit
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                  minus. </s>
                  <s xml:id="N241CF" xml:space="preserve">Sꝫ iam ꝓbo ſequelã / quoniã ſi ip̄m .a. / quod
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                  velocius augetur nõ ꝑ aliquod tēpus erit minꝰ ip̄o
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                  b. ſed ſemper maius vt dictis. </s>
                  <s xml:id="N241D6" xml:space="preserve">Detur igit̄̄ vnū inſtãs
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                  illius tēporis in quo .a. eſt maius ipſo .b. in aliqua
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                  ꝓportione: et ſemꝑ ante illud inſtans fuit maius / vt
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                  dicis: et ſit tale inſtans .c. et ſit gratia argumenti in
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                  tali inſtanti ꝓportio .a. ad .b. ſexquialtera adequa­
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                  te: et volo gr̄a exempli /  .a. cõtinuo augeatur velo-
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                  cius .b. in proportione dupla. </s>
                  <s xml:id="N241E5" xml:space="preserve">Quo poſito arguit̄̄
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                  ſic / .b. infinitas ꝓportiões ſexquialteras acquiſiuit
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                  ab inſtanti initiatīo augmētationis vſ ad inſtãs
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                  c. / vt patet ex iſto argumēto: detur igitur vnū inſtãs
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                  quod ſit .d. ante inſtans .c. inter quod et inſtans .c.b.
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                  acquiſiuit duas ſexquialteras: et arguit̄̄ ſic īter .d.
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                  inſtans et .c. inſtans acq̇ſiuit .b. duas ſexq̇alteras: et
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                  a cõtinuo in duplo velocius auget̄̄ ꝙ̄ .b. / igit̄̄ .a. inter
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                  d. inſtans et .c. inſtans acq̇ſiuit quatuor ſexq̇alteras
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                  et in .d. inſtanti erat maius ipſo .b. ꝑ te: igitur in .c.
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                  inſtanti eſt ip̄m .a. pluſ̄ in ſexquialtero maius ip̄o
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                  b. / quod eſt oppoſitū cõceſſi. </s>
                  <s xml:id="N241FE" xml:space="preserve">Dictū eſt em̄ /  in .c. in-
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                  ſtanti ſe habebãt in ꝓportione ſexq̇altera adequa­
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                  te. </s>
                  <s xml:id="N24205" xml:space="preserve">ꝓbatur ↄ̨ſia qm̄ ſi .a. et .b. in inſtãti .d. fuiſſent eq̈-
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                  lia: et acquiſiuiſſet .d. duas ſexq̇alteras: et .a.4. vſ
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                  ad inſtans .c. in ipſo inſtanti. c.a. exceſſiſſet .b. ꝑ du­
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                  as ſexquialteras: ſꝫ modo in tali inſtanti .a. eſt ad­
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                  huc maius .b. ꝑ te: et acq̇rit .4. ſexq̇alteras vſ ad ī-
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                  ſtans .c. et .b. acquirit preciſe duas vſ ad idē īſtãs
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                  c. / ergo ſeq̇tur /  in illo inſtãti .c.a. excedit .b. per du-
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                  as ſexq̇alteras ; vel ꝑ plus. </s>
                  <s xml:id="N24216" xml:space="preserve">Ptꝫ hec ↄ̨ſequētia ꝑ lo­
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                  cum a maiori: et ꝑ ↄ̨ſequēs nõ ꝑ ſexq̇alteram preci-
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                  ſe / qḋ erat inferēdū. </s>
                  <s xml:id="N2421D" xml:space="preserve">Tenet hec īductio virtute huiꝰ
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                  maxime. </s>
                  <s xml:id="N24222" xml:space="preserve">Quãdo aliqua duo ſunt equalia: et in eo­
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                  dem tēpore vnū illoruꝫ maiorē ꝓportionē acquirit
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                  ̄ reliquū: in fine tēporis illud qḋ maiorē ꝓportio­
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                  nem acq̇ſiuit eſt maius illo qḋ minorē ꝓportionem
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                  acq̇ſiuit in proportiõe ꝑ quam ꝓportio acq̇ſita illi /
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                  quod in fine eſt maius excedit ꝓportionem acquiſi­
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                  tam illi / qḋ eſt minur / vt cõſtat ex ſecūda parte: iſto
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                  modo vniuerſaliter probabis in omnibus.</s>
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                <note position="left" xml:id="N24233" xml:space="preserve">Dicitur.</note>
                <p xml:id="N24237">
                  <s xml:id="N24238" xml:space="preserve">¶ Dices et bene concedendo / quod infertur vt bene
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                  probat argumētū: et negando falſitatē ↄ̨ſequentis
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                  et ad ꝓbationē nego hanc cõditionalem ſi .a. et .b.
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                  incipiant augeri et nõ quãto ↄ̨tinuo eque velociter
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                  ipſa cõtinuo manebūt equalia. </s>
                  <s xml:id="N24243" xml:space="preserve">Immo ſtat  vnuꝫ
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                  in quacun ꝓportiõe volueris maneat minꝰ alte-
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                  ro / vt poſtea demõſtrabitur.</s>
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                <p xml:id="N2424A">
                  <s xml:id="N2424B" xml:space="preserve">Sed contra hanc ſolutionē arguitur
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                  ſic: q2 ſi illa ſolutio eſſet bona ſequeret̄̄ /  ſi .a. et .b.
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                  inciperēt augeri nõ quãto: et .a. in certa ꝓportiõe
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                  cõtinuo velocius augeret̄̄ ꝙ̄ .b. ipſum .a. / quod in cer­
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                  ta proportiõe cõtinuo velocius auget̄̄ inciperet in
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                  infinitū eſſe minus ipſo .b. / ſed cõſequēs eſt falſum:
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                  igitur illud ex quo ſeq̇tur. </s>
                  <s xml:id="N2425A" xml:space="preserve">Falſitas conſequētis ꝓ-
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                  batur: quia tunc ſequeretur /  quando aliqua duo
                    <cb chead="De motu augmentationis."/>
                  incipiunt augeri a non quãto vnū in certa ꝓpor-
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                  tione cõtinuo velocius altero illud quod tardius ī­
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                  cipit augeri incipiet in infinitū velocius acquirere
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                  de quãtitate. </s>
                  <s xml:id="N24268" xml:space="preserve">ſed hoc apparet falſum: igit̄̄ illud ex
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                  quo ſeq̇tur. </s>
                  <s xml:id="N2426D" xml:space="preserve">Seq̄la tamen ꝓbatur: quia quocū in­
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                  ſtanti dato poſt inſtans initiatiuū augmētatiõis
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                  inter illud et inſtans initiatiuū .a. erit aliquãtulum
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                  minus ip̄o .b. / vt patet ex priori replica: et in duplo
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                  minus: et in triplo: et in quadruplo: et ſic in infinitū /
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                  ergo immediate poſt illud inſtãs initiatiuū .a. erit
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                  in infinitū minus ip̄o .b. et iam nõ eſt minus: ergo in­
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                  cipit eſſe in infinitū minus ip̄o .b. et tam .a. ꝙ̄ b īci­
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                  pit a nõ ̄to acquirere quãtitatē: ergo .b. / qḋ īcipit
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                  tardius augeri incipit infinitū velocius acq̄rere de
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                  quãtitate .a. / quod in certa ꝓportione velocius inci­
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                  pit augmētari: qḋ fuit ꝓbandum. </s>
                  <s xml:id="N24286" xml:space="preserve">Sed iam probo /
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                   quocun inſtanti dato poſt illud inſtãs initia-
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                  tiuū erit .a. inter illud inſtans et inſtãs initiatiuum
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                  aliquãtulū minus ipſo .b. et in duplo: et in quadru-
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                  plo. et ſic in infinitū: q2 ſi nõ da oppoſitū: et dic /  be­
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                  ne .a. erit minus ipſo .b. / ſꝫ nun̄ in quadruplo gra­
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                  tia exēpli: et arguo ſic: capiendo vnū inſtans / qḋ ſit .c
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                  in quo .a. eſt minus .b. / vt cõcedis: et ſuperius ꝓba-
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                  tū eſt: et nun̄ ante illud inſtans erit in quadruplo
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                  minus: et cū .b. acquiret infinitas ꝓportiones qua-
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                  druplas ab inſtanti initiatiuo augmētationis vſ
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                  ad inſtans .c. capio vnū inſtans ante .c. / qḋ ſit .d. īter
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                  quod et .c. ip̄m .b. acquirit vnam quadruplã preciſe.
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                  </s>
                  <s xml:id="N242A2" xml:space="preserve">et arguo ſic / .b. inter .d. et .c. acquiret vnã quadruplã
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                  et .a. in duplo velocius augetur ꝙ̄ .b. vt ſuppono: g̊
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                  ſequitur /  a. inter .d. et .c. inſtans acq̇ret duas qua-
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                  druplas: et in .d. inſtanti .a. non erit in quadruplo
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                  minus ipſo .d. ſed in minori proportione minꝰ: igi­
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                  tur in .c. inſtanti .a. erit maius .b. / quod eſt oppoſitū
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                  conceſſi. </s>
                  <s xml:id="N242B1" xml:space="preserve">Poſitū em̄ eſt et conceſſuꝫ /  a. eſſet minus
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                  b. in .c. inſtanti: ſed nõ in quadruplo minꝰ. </s>
                  <s xml:id="N242B6" xml:space="preserve">Patꝫ tñ
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                  conſequētia / quoniã ſi in .d. inſtanti foret .a. in qua-
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                  druplo minus ipſo .b. et inter .d. inſtans et .c. inſtans
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                  acquireret .b vnã quadruplã: et .a. duas: tunc in .c. ī­
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                  ſtanti .a. eſſet equale .b. / quia acquiret illaꝫ ꝓportio­
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                  nē que deficiebat ei vt ſit equale .b. et ī ſuꝑ tãtã quãtã
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                  b. / ergo manet equale b. / ſed modo in .d. inſtanti erit
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                  a. minus ꝙ̄ tūc: et acq̇ret vſ ad .c. inſtans tantã ꝓ-
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                  portionem quãtã tunc: ergo ſeq̇tur /  in .c. inſtanti
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                  manet maius ꝙ̄ tunc et per cõſequēs maius ipſo .b. /
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                  quod fuit inferēdum. </s>
                  <s xml:id="N242CD" xml:space="preserve">Ei iſto modo ꝓbabis in qui-
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                  buſcū aliis ſpeciebus ꝓportionum. </s>
                  <s xml:id="N242D2" xml:space="preserve">Si tu em̄ di-
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                  cas /  in ſexquialtero velocius .a. cõtinuo augebit̄̄
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                  ̄ .b. et nun̄ erit in quadruplo minus: tunc ego po­
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                  ſito quod .b. inter inſtans .d. et .c. acq̇rat duas q̈dru­
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                  plas et ꝑ ↄ̨ñs ī illo tꝑe .a. acq̇ret .3. q̈druplas: et ſic ac­
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                  quiret pluſ̄ deficiebat ei vt eſſet eq̈le .b: et inſuper
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                  tantum quantum acq̇ſiuit .b. et ꝑ conſequēs in .c. in­
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                  ſtanti manebit .a. maius .b. / quod eſt oppoſitum cõ-
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                  ceſſi.</s>
                </p>
                <note position="right" xml:id="N242E5" xml:space="preserve">Confir°.</note>
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                  <s xml:id="N242EA" xml:space="preserve">Cõfirmatur / quia ſi illa poſitio eēt ve­
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                  ra ſequeretur /  .a. inciperet a nõ quãto in infinituꝫ
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                  velociter augeri: et tamen cõtinuo acq̇reret vnifor-
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                  miter de quãtitate: ſed cõſequens videtur repugna­
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                  re. </s>
                  <s xml:id="N242F5" xml:space="preserve">igitur illud ex quo ſeq̇tur. </s>
                  <s xml:id="N242F8" xml:space="preserve">Seq̄la probatur: et di­
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                  uido horã futuram ꝑ partes ꝓportionales ꝓpor-
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                  tione dupla minoribus terminatis verſus finem: et
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                  capio vnum pedale diuiſum ꝑ partes ꝓportiona-
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                  les ꝓportione dupla: et volo /  in prīa parte ꝓpor-
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                  tionali temporis deperdat vniformiter primã par­
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                  tem proportionalem ſui: et in ſecunda ſecūdam: et
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                  in tertia tertiam: et ſic cõſequēter ſemꝑ vniformiter
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                  deperdendo quãtitatem vſ ad non ̄tum: deinde
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                  volo /  in alia hora ſequenti augeatur a nõ quãta </s>
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