Alvarus, Thomas, Liber de triplici motu, 1509

Page concordance

< >
Scan Original
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
< >
page |< < of 290 > >|
    <echo version="1.0">
      <text xml:lang="la">
        <div xml:id="N10132" level="1" n="1" type="body">
          <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <div xml:id="N18B2D" level="4" n="9" type="chapter" type-free="capitulum">
                <p xml:id="N190B1">
                  <s xml:id="N1910E" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0093" n="93"/>
                  ſexquialtero velocius continuo moueretur quam
                    <lb/>
                  b. / vt conſtat igitur: </s>
                  <s xml:id="N1911E" xml:space="preserve">Sed minor probatur / quia a. po­
                    <lb/>
                  tentia in illo caſu c. medium tranſeundo non remit­
                    <lb/>
                  tit motum ſuum ad non gradum in puncto termi-
                    <lb/>
                  natiuo eiuſdem c. medii: igitur minor vera: </s>
                  <s xml:id="N19127" xml:space="preserve">Antece­
                    <lb/>
                  dens probatur / q2 a. potentia citius deueniet ad pū­
                    <lb/>
                  ctum terminatiuum c. medii quam b. poña: ergo cū
                    <lb/>
                  caſu ſequitur /  a. poña c. medium tranſeundo non
                    <lb/>
                  remittit motum ſuum ad non gradum in pūcto ter­
                    <lb/>
                  minatiuo c. medii etc. </s>
                  <s xml:id="N19134" xml:space="preserve">Probatur antecedens / quia ſi
                    <lb/>
                  a. poña continuo in ſexquialtero velocius mouere-
                    <lb/>
                  tur quam b. poña: eque primo a. et b. deuenirent ad
                    <lb/>
                  pnnctum terminatiuum c. medii. </s>
                  <s xml:id="N1913D" xml:space="preserve">ſed modo a. poten­
                    <lb/>
                  tia mouetur velocius quam tunc: ergo modo citius
                    <lb/>
                  deuenit ad punctum terminatiuum c. medii quaꝫ b.
                    <lb/>
                  potentia: </s>
                  <s xml:id="N19146" xml:space="preserve">Maior patet: et minor ꝓbatur / quia a. po­
                    <lb/>
                  tentia ad punctum initiatiuum c. medii habet maio­
                    <lb/>
                  rem ꝓportionem quam ſexquialteram ad ꝓportio­
                    <lb/>
                  nem b. potentie ad punctum initiatiuum ſecunde ꝑ­
                    <lb/>
                  tis ꝓportionalis c. medii diuiſi in partes ꝓportio-
                    <lb/>
                  nales ꝓportione ſexquialtera: et a. poña nõ deper-
                    <lb/>
                  dit ſubito aliquam latitudinem potentie (vt volo) /
                    <lb/>
                  igitur īmediate poſt inſtans initiatiuum motus a.
                    <lb/>
                  potentia plus quam in ſexquialtero velocius mo-
                    <lb/>
                  uebitur b. poña / quod erat ꝓbandum: </s>
                  <s xml:id="N1915B" xml:space="preserve">Conſequētia
                    <lb/>
                  patet / quia ſi a. potentia ad punctum initiatiuū etc.
                    <lb/>
                  habet maiorem ꝓportionem quam ſexquialteram
                    <lb/>
                  ad ꝓportionem b. potentie ad punctum initiatiuū
                    <lb/>
                  ſecunde partis etc. et a. poña non perdit ſubito ali-
                    <lb/>
                  quam latitudinem potentie: proportio ipſius a. ad
                    <lb/>
                  punctum initiatiuum etc. continet ꝓportionem ſex-
                    <lb/>
                  quialteram ad ꝓportionem ipſius b. ad punctuꝫ in­
                    <lb/>
                  itiatiuum ſecunde partis proportionalis etc. et ali-
                    <lb/>
                  quam proportionem vltra illam. </s>
                  <s xml:id="N19170" xml:space="preserve">quam ꝓportionē
                    <lb/>
                  vltra non ſubito deperdit: et per conſequens īmedi­
                    <lb/>
                  ate poſt inſtans initiatiuum motus a. potentia plꝰ
                    <lb/>
                  quã in ſexquialtero velocius mouebitur b. poña.</s>
                </p>
                <p xml:id="N19179">
                  <s xml:id="N1917A" xml:space="preserve">Et ſic de primo ad vltimum patet conſequentia.</s>
                </p>
                <p xml:id="N1917D">
                  <s xml:id="N1917E" xml:space="preserve">Sed maior probatur videlicet /  a. poña ad pūctuꝫ
                    <lb/>
                  initiatiuum c. medii habet maioreꝫ ꝓportionē quã
                    <lb/>
                  ſexquialteram ad proportionem b. poñe ad pūctuꝫ
                    <lb/>
                  initiatiuum ſecunde partis ꝓportionalis c. medii
                    <lb/>
                  diuiſi etc. quia a. ponã ad punctum initiatiuuꝫ c. me­
                    <lb/>
                  dii habet proportionem ſexquialteram ad ꝓportio­
                    <lb/>
                  nem quam habet b. poña ad ideꝫ punctum / vt patet
                    <lb/>
                  ex caſu: et ꝓportio ipſius b. ad punctum initiatiuuꝫ
                    <lb/>
                  c. medii eſt maior quam ꝓportio eiuſdem b. poten-
                    <lb/>
                  tie ad punctum initiatiuum ſecunde partis ꝓportio­
                    <lb/>
                  nalis: quia b. potentie inuariate minus reſiſtit pun­
                    <lb/>
                  ctum initiatiuum c. medii quam punctum initiuati­
                    <lb/>
                  uum ſecunde partis ꝓportionalis eiuſdem c. medii
                    <lb/>
                  diuiſi etc. / vt conſtat: igitur a. poña ad pūctum īitia-
                    <lb/>
                  tiuum c. medii maiorem habet ꝓportionem quam
                    <lb/>
                  ſexquialteram ad ꝓportionem b. poñe ad punctum
                    <lb/>
                  initiatiuum ſecunde partis ꝓportionalis c. medii
                    <lb/>
                  diuiſi etc. </s>
                  <s xml:id="N191A3" xml:space="preserve">Conſequentia patet / quia maior eſt ꝓpor­
                    <lb/>
                  tio alicuiꝰ tertii adminꝰ quam eiuſdem terti ad ma­
                    <lb/>
                  ius / vt patet ex ſecunda parte.</s>
                </p>
                <note position="left" xml:id="N191AA" xml:space="preserve">Dicitur.</note>
                <p xml:id="N191AE">
                  <s xml:id="N191AF" xml:space="preserve">¶ Dices forte negando ſequelam īmo / vt bene ꝓbat
                    <lb/>
                  argumentuꝫ illud eſt falſum: niſi poña a. ſubito ali­
                    <lb/>
                  quam latitudinem poñe deperderet. </s>
                  <s xml:id="N191B6" xml:space="preserve">Si enim ali-
                    <lb/>
                  qua potentia poneretur ad punctum initiatiuuꝫ c.
                    <lb/>
                  medii cuius ꝓportio ad idem punctum eſſet mille-
                    <lb/>
                  cupla ad ꝓportionē b. poñe ad punctum initiatiuū
                    <lb/>
                  ſecunde partis ꝓportionalis c. medii diuiſi per ꝑ-
                    <lb/>
                  tes ꝓportionales ꝓportione ſexquialtera etc. et illa
                    <lb/>
                  potentia ſic variaretur /  īmediate ab illo puncto ī­
                    <lb/>
                  itiatiuo recedēdo moueretur adequate in ſexquial­
                    <lb/>
                  tero velocius b. poña recedente ad puncto initiatiuo
                    <cb chead="Capitulum nonum"/>
                  ſecunde partis ꝓportionalis verſus extremum ītē-
                    <lb/>
                  ſius et continuo ſic moueretur. </s>
                  <s xml:id="N191CE" xml:space="preserve">tunc vt conſtat tam il­
                    <lb/>
                  la poña quam b. poña eque primū deuenirent ad ex­
                    <lb/>
                  tremuꝫ intenſius c. medii in quo vtra remittit mo­
                    <lb/>
                  tum ſuum ad non gradum: cõtinuo remittendo mo­
                    <lb/>
                  tum ſuum vniformiter: et hoc per illus poñe conti-
                    <lb/>
                  nuam remiſſionem. </s>
                  <s xml:id="N191DB" xml:space="preserve">Sed tunc poña illa ſubito per-
                    <lb/>
                  deret aliquam latitudinem poñe: et etiã ſubito deꝑ­
                    <lb/>
                  deret ꝓportionem quam continet vltra ꝓportiõem
                    <lb/>
                  que eſt ſexquialtera ad ꝓportionem ipſius b. poñe
                    <lb/>
                  ad punctum initiatiuum ſecunde partis ꝓportiona­
                    <lb/>
                  lis c. medii diuiſi etc. </s>
                  <s xml:id="N191E8" xml:space="preserve">Attamē alias non eſt veruꝫ (vt
                    <lb/>
                  dicis) quēadmodum bene probat argumentum.</s>
                </p>
                <p xml:id="N191ED">
                  <s xml:id="N191EE" xml:space="preserve">Sed contra / quia vbi aliqua potentia
                    <lb/>
                  inuariata aliquod medium inuariatum tranſeun-
                    <lb/>
                  do continuo vniformiter remittit motum ſuum vſ
                    <lb/>
                  ad non gradum in puncto terminatiuo eiuſdē me-
                    <lb/>
                  dii in extremo intenſiori: omnis ponã maior idem
                    <lb/>
                  medium tranſeundo adequate: vniformiter conti-
                    <lb/>
                  nuo remittit motum ſuum vſ ad nõ gradum in eo­
                    <lb/>
                  dem puncto terminatiuo per continuam ſue potētie
                    <lb/>
                  ſucceſſiuam remiſſionem: igitur ſolutio nulla. </s>
                  <s xml:id="N19201" xml:space="preserve">Ante­
                    <lb/>
                  cedens probatur ſupponendo /  īter quodlibet pū­
                    <lb/>
                  ctum intrinſecum cuiuſuis medii per quod inuaria­
                    <lb/>
                  tum aliqua poña inuariata continuo vniformiter
                    <lb/>
                  remittit motum ſuum ad non gradum in extremo ī­
                    <lb/>
                  tenſiori, et pūctum initiatiuum eiuſdem medii, me­
                    <lb/>
                  diat prima pars ꝓportionalis illius medii diuiſi
                    <lb/>
                  ꝓportione dupla ad ꝓportionem in qua ſe habet
                    <lb/>
                  ꝓportio illius poñe ad punctum initiatiuum ad ꝓ­
                    <lb/>
                  portionem eiuſdem poñe addatum pūctum intrin­
                    <lb/>
                  ſecum. </s>
                  <s xml:id="N19218" xml:space="preserve">Exemplū / vt poſito /  b. poña īuariata c. me-
                    <lb/>
                  dium īuariatum tranſeundo vniformiter continuo
                    <lb/>
                  remittat motum ſum vſ ad non gradum in extre-
                    <lb/>
                  mo intenſiori et dato vno puncto intrinſeco ad quē
                    <lb/>
                  talis poña b. habeat ꝓportionem in duplo mino-
                    <lb/>
                  rem quam ſit ꝓportio quam habeat ad punctuꝫ ini­
                    <lb/>
                  tiatiuum / tunc inter punctum īitiatiuum et illud pū-
                    <lb/>
                  ctum intrinſecum mediat prima pars ꝓportiona-
                    <lb/>
                  lis illius medii diuiſi ꝓportione quadrupla dupla
                    <lb/>
                  duple. </s>
                  <s xml:id="N1922D" xml:space="preserve">Quod ſic probatur / quia inter punctum ini-
                    <lb/>
                  tiatiuum illius c. medii et punctum intrinſecum eiuſ­
                    <lb/>
                  dem ad quod b. poña habet in duplo minorem pro­
                    <lb/>
                  portionem quam ad punctum initiatiuum: mediat
                    <lb/>
                  prima pars ꝓportionalis c. medii adequate diuiſi
                    <lb/>
                  per partes ꝓportionales proportione quadrupla
                    <lb/>
                  quia inter illa puncta mediant tres quarte que ſūt
                    <lb/>
                  prima ꝓportionalis ꝓportione quadrupla: quoni­
                    <lb/>
                  am in inſtanti medio totius temporis. </s>
                  <s xml:id="N19240" xml:space="preserve">in quo ade-
                    <lb/>
                  quate b. poña c. medium pertranſit continuo remit­
                    <lb/>
                  tendo motum ſuum vſ ad non gradum erit b. po­
                    <lb/>
                  tentia ad punctum terminatiuum trium quartarū
                    <lb/>
                  ab eadē b. ponã pertranſitarum: et in inſtanti me-
                    <lb/>
                  dio totius illius temporis habebit ad punctum in
                    <lb/>
                  quo / tunc eſt ꝓportionem ſubduplam ad ꝓportio-
                    <lb/>
                  nem quam habet ad punctum initiatiatiuum eiuſ-
                    <lb/>
                  dem c. medii quia perdit ſuam ꝓportionem vnifor­
                    <lb/>
                  miter continuo: igitur inter punctum initiatiuuꝫ c.
                    <lb/>
                  medii et punctum ad quod b. poña habet ꝓportio-
                    <lb/>
                  nem in duplo minorem ꝙ̄ habeat eadem b. potētia
                    <lb/>
                  ad punctum īitiatiuum mediant tres quarte: et per
                    <lb/>
                  conſequens prima pars ꝓportionalis c. medii pro­
                    <lb/>
                  portione quadrupla: quod fuit probandum </s>
                  <s xml:id="N1925F" xml:space="preserve">Item
                    <lb/>
                  īter punctum īitiatiuum c. medii et pūctum ad quod
                    <lb/>
                  b. poña habet in ſexquitertio minorem ꝓportioneꝫ
                    <lb/>
                  ̄ ad punctum īitiatiuum mediat prima pars pro­
                    <lb/>
                  portionalis c. medii proportione ſupraſeptipartiē­
                    <lb/>
                  te nonas que eſt dupla ad ſexquitertiam. </s>
                  <s xml:id="N1926C" xml:space="preserve">quia īter </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum