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="N17509" level="4" n="7" type="chapter" type-free="capitulum">
                <p xml:id="N179FD">
                  <s xml:id="N17B0D" xml:space="preserve">
                    <pb chead="Primi tractatus" file="0078" n="78"/>
                  correlarii patet ex ſecūdo correlario ſecūde cõclu-
                    <lb/>
                  ſionis huius capitis: et ſecūda breuiter ꝓbatur ſic /
                    <lb/>
                  q2 vbicū aliqua potentia īuariata mediū īuaria­
                    <lb/>
                  tum tranſeūdo ↄ̨tinuo vniformiter remittit motū
                    <lb/>
                  ſuū ad extremū intenſius deueniendo: oīs maior
                    <lb/>
                  vel minor verſus idem extremū veniendo per ean-
                    <lb/>
                  dem lineã cõtinuo difformiter remittit motū ſuum
                    <lb/>
                  ipſa et medio continuo inuariatis / vt ptꝫ ex quarta
                    <lb/>
                  concluſione huiꝰ: et oīs potentia inuariata mediū
                    <lb/>
                  inuariatū tanſeundo ab extremo intenſiori rece-
                    <lb/>
                  dendo per eandem lineam oīno eodē modo inten-
                    <lb/>
                  dit motum ſuū ſicut remittit ab extremo remiſſiori
                    <lb/>
                  ꝓcedendo per eandē lineam verſus extremū inten­
                    <lb/>
                  ſius: ergo oīs maior ab eodē puncto intenſiori ꝓ-
                    <lb/>
                  cedendo per eandē lineã per quam ꝓcedit potētia
                    <lb/>
                  intendens motum ſuū vniformiter: ipſo medio in-
                    <lb/>
                  uariato: difformiter cõtinuo intendit motum ſuuꝫ
                    <lb/>
                  et ſimiliter oīs minor habens ad extremū intēſius
                    <lb/>
                  eiuſdem medii ꝓportionē maioris inequalitatis.
                    <lb/>
                  </s>
                  <s xml:id="N17B3A" xml:space="preserve">Et ſic patet correlariū. </s>
                  <s xml:id="N17B3D" xml:space="preserve">Et ſi fortiorē demonſtrati-
                    <lb/>
                  onē exoptas: vtaris demonſtratione adducta ad
                    <lb/>
                  quartã concluſionē paucis mutatis: que ſeſe ṗma
                    <lb/>
                  fronte intelligenti probationē illius concluſionis
                    <lb/>
                  offerūt.
                    <note position="left" xlink:href="note-0078-01a" xlink:label="note-0078-01" xml:id="N17BA7" xml:space="preserve">3. correĺ.</note>
                  </s>
                  <s xml:id="N17B4D" xml:space="preserve">¶ Sequitur tertio /  vbicū aliqua potē-
                    <lb/>
                  tia īuariata vniformiter cõtinuo ſucceſſiue intēdit
                    <lb/>
                  motū ſuū vſ ad nõ gradum: mediū īuariatū trã-
                    <lb/>
                  ſeundo ab extremo intenſiori verſus remiſſius: oīs
                    <lb/>
                  potentia maior ab eodem extremo intenſiori ꝓce-
                    <lb/>
                  dens continuo per eandē lineã in infinitū velociter
                    <lb/>
                  intendit motum ſuū. </s>
                  <s xml:id="N17B5C" xml:space="preserve">Probatur facile: qm̄ quãdo
                    <lb/>
                  ipſa potentia maior mouetur verſus extremū in-
                    <lb/>
                  tenſius cõtinuo remittendo motum ſuū .etc̈. in infi-
                    <lb/>
                  nitum velociter remittit motū ſuū / vt patet ex quin­
                    <lb/>
                  ta cõcluſione huius capitis: et oīno eadem veloci-
                    <lb/>
                  tate intendit motū ſuū retrogrado motu per ean-
                    <lb/>
                  dem lineã mouēdo ſicut antea remittebat in eiſdeꝫ
                    <lb/>
                  partibus eiuſdem linee: ergo oīs talis potentia
                    <lb/>
                  maior que ſic mouetur motu retrogrado ab extre­
                    <lb/>
                  mo intenſiori verſus remiſſius per eandē lineam
                    <lb/>
                  etc̈. in infinitū velociter intendit motum ſuū / quod
                    <lb/>
                  fuit probandū. </s>
                  <s xml:id="N17B75" xml:space="preserve">Et ſic patꝫ correlariū.
                    <note position="left" xlink:href="note-0078-02a" xlink:label="note-0078-02" xml:id="N17BAD" xml:space="preserve">4. correĺ.</note>
                  </s>
                  <s xml:id="N17B7D" xml:space="preserve">¶ Sequitur
                    <lb/>
                  quarto /  vbicun aliqua potentia īuariata me-
                    <lb/>
                  dium īuariatum tranſeundo cõtinuo ſucceſſiue in­
                    <lb/>
                  tēdit motum ſuū ad nõ gradum ſiue vniformiter
                    <lb/>
                  ſiue difformiter: oīs potentia minor habens pro-
                    <lb/>
                  portionē maioris inequalitatis ad aliquã parteꝫ
                    <lb/>
                  eiuſdē medii in infinitū tardius intendit motum
                    <lb/>
                  ſuū a puncto ad quē habet proportionē equalita­
                    <lb/>
                  tis recedendo verſus remiſſius extremū: quã data
                    <lb/>
                  potētia maior ab eodē puncto recedendo verſus
                    <lb/>
                  extremū remiſſiꝰ. </s>
                  <s xml:id="N17B94" xml:space="preserve">Ptꝫ hoc correlariū ex predictis</s>
                </p>
              </div>
              <div xml:id="N17BB3" level="4" n="8" type="chapter" type-free="capitulum">
                <head xml:id="N17BB8" xml:space="preserve">Capitulū octauū / in quo inquiritur an due
                  <lb/>
                potentie īequales idē mediū īuariatū tran-
                  <lb/>
                ſeūtes valeãt vniformiter remittere aut intē­
                  <lb/>
                dere motum ſuum per ambarū vel alterius
                  <lb/>
                earum variationem.</head>
                <p xml:id="N17BC3">
                  <s xml:id="N17BC4" xml:space="preserve">POſt̄ ſuperiori capite oſtēſū
                    <lb/>
                  eſt nullas duas potētias īequales īua-
                    <lb/>
                  riatas: id eſt quarum nulla variat̄̄ idem
                    <lb/>
                  mediū īuariatū trãſeūtes poſſe vniformiter intē-
                    <lb/>
                  dere aut remittere motū ſuū: iã īquirendū eſt an ꝑ
                    <lb/>
                  alteriꝰ eaꝝ vel ambaꝝ variationē id fieri valeat.</s>
                </p>
                <p xml:id="N17BD1">
                  <s xml:id="N17BD2" xml:space="preserve">Cuiꝰ inq̇ſitiõi p̄mittat̄̄ ꝓ baſi  fūda­
                    <lb/>
                  mēto talis ſuppoſitio. </s>
                  <s xml:id="N17BD7" xml:space="preserve">Si aliq̈ potētia vniformiṫ
                    <lb/>
                  ↄ̨tinuo ſuū motū remittēs aut ītēdēs aliq̈ potētia
                    <lb/>
                  in certa ꝓportione cõtinuo velocius mouetur: ne-
                    <lb/>
                  ceſſe eſt potentiã ipſam tardius motã cõtinuo vni­
                    <lb/>
                  formiter motū ſuū remittere aut intendere. </s>
                  <s xml:id="N17BE2" xml:space="preserve">Et ſi
                    <cb chead="Capitulū octauū."/>
                  aliqua potentia vniformiter cõtinuo ſuū motum
                    <lb/>
                  remittens aut intendens aliqua alia potentia in
                    <lb/>
                  certa ꝓportione cõtinuo tardius mouetur: neceſſe
                    <lb/>
                  eſt potentiã velocius motã vniformiter itidē con-
                    <lb/>
                  tinuo motū ſuū remittere aut intendere. </s>
                  <s xml:id="N17BF0" xml:space="preserve">Exemplū /
                    <lb/>
                  vt data potētia que incipit a gradu octauo exclu-
                    <lb/>
                  ſiue moueri cõtinuo vniformiter remittēdo motū
                    <lb/>
                  ſuū: et in dupla ꝓportione cõtinuo velocius moue­
                    <lb/>
                  do quã vna alia potētia que incipit moueri a gra­
                    <lb/>
                  du quarto excluſiue: tūc dico /  neceſſe eſt /  illa po­
                    <lb/>
                  tentia que incipit moueri a quarto gradu excluſi-
                    <lb/>
                  ue cõtinuo vniformiter remittat motum ſuū: </s>
                  <s xml:id="N17C01" xml:space="preserve">Pro­
                    <lb/>
                  batur / et ſit a. potentia remittens continuo vnifor-
                    <lb/>
                  miter motū ſuū: et ſit b. potentia que cõtinuo in f.
                    <lb/>
                  ꝓportiõe tardius mouetur quã a. potentia: et ma-
                    <lb/>
                  nifeſtū eſt /  etiã b. potentia remittit motū ſuū: q2
                    <lb/>
                  alias motus illarū potentiarū nõ cõtinuo mane-
                    <lb/>
                  rent in eadē ꝓportione. </s>
                  <s xml:id="N17C10" xml:space="preserve">Uolo igitur /  potētia a.
                    <lb/>
                  perdat in toto tēpore adequate in quo mouetur c.
                    <lb/>
                  latitudinē motus: et b.d. latitudinē motus: et tunc
                    <lb/>
                  dico /  d. latitudo motus deperdenda a b. poten-
                    <lb/>
                  tia tardius mota vniformiter cõtinuo remittetur
                    <lb/>
                  </s>
                  <s xml:id="N17C1C" xml:space="preserve">Probatur / q2 d. latitudo motus in qualibet me-
                    <lb/>
                  dietate tēporis in quo deperdetur perdet vnã me-
                    <lb/>
                  dietatē ſui, et in qualibet tertia vnã tertiam, et in
                    <lb/>
                  qualibet quarta, vnã quartã, et ſic conſequenter:
                    <lb/>
                  igitur d. latitudo deperdenda a b. potentia tar-
                    <lb/>
                  dius mota vniformiter continuo remittetur. </s>
                  <s xml:id="N17C29" xml:space="preserve">Pa-
                    <lb/>
                  tet conſequentia ex diffitione remiſſionis vnifor-
                    <lb/>
                  mis alicuius latitudinis. </s>
                  <s xml:id="N17C30" xml:space="preserve">Probatur antecedens:
                    <lb/>
                  quoniã quandocun aliqua pars aliquota c. la-
                    <lb/>
                  titudinis ab a. potentia deperdende deperdetur
                    <lb/>
                  adequate conſimilis pars aliquota et eiuſdem de­
                    <lb/>
                  nominationis deperdet d. latitudo: ſed in quali-
                    <lb/>
                  bet medietate temporis in quo ille latitudines re­
                    <lb/>
                  mittuntur c. latitudo perdit vnam medietateꝫ ſui:
                    <lb/>
                  et in qualibet tertia vnam tertiam ſui, et in quali-
                    <lb/>
                  bet quarta quartam, et ſic conſequenter: quia c. la­
                    <lb/>
                  titudo vniformiter remittitur continuo / vt patet
                    <lb/>
                  ex hypotheſi / igitur d. latitudo in qualibet medie-
                    <lb/>
                  ta temporis in quo remittitur perdit vnã medie-
                    <lb/>
                  tatem ſui, et in qualibet tertia tertiam, et in quali-
                    <lb/>
                  bet quarta quartam, et ſic cõſequenter. </s>
                  <s xml:id="N17C4D" xml:space="preserve">Patet cõ-
                    <lb/>
                  ſequentia cum minore: et probatur maior: quoniã
                    <lb/>
                  continuo latitudo motus quo mouetur a. ad lati-
                    <lb/>
                  tudinem motus quo mouetur b. eſt proportio f. ex
                    <lb/>
                  hypotheſi: et continuo motus quo mouetur a. et
                    <lb/>
                  etiam latitudo motus quo mouetur b. remittūtur /
                    <lb/>
                  ergo inter latitudinem deperditam a. motu quo
                    <lb/>
                  mouetur a. maiore, et latitudinem deperditam a
                    <lb/>
                  motu minori quo mouetur b. eſt continuo propor­
                    <lb/>
                  tio f. / vt patet ex primo correlario quinte concluſi-
                    <lb/>
                  onis ſecūdi capitis ſecunde partis: et latitudo de-
                    <lb/>
                  perdenda a motu quo mouet̄̄ a. eſt c. et latitudo de­
                    <lb/>
                  ꝑdēda a motu quo mouet̄̄ b. eſt d. / igit̄̄ inter c. et d.
                    <lb/>
                  eſt ꝓportio f. / et ex cõſequēti ſequit̄̄ /  inter partes
                    <lb/>
                  aliquotas eiuſdē denoīatiõis ipſiꝰ c. et ipſiꝰ d. pu-
                    <lb/>
                  ta īter medietatatē c. et medietatē d, et īter tertias
                    <lb/>
                  et īter quartas, et ſic cõſequēter eſt etiã ꝓportio f.
                    <lb/>
                  </s>
                  <s xml:id="N17C71" xml:space="preserve">Ptꝫ hec ↄ̨ña ex vndecima ſuppoſitiõe ſcḋi capitis
                    <lb/>
                  p̄allegati: et vltra īter ꝑtes aliq̊tas eiuſdē denoīa­
                    <lb/>
                  tionis c. latitudīs eſt ꝓportio f. et ↄ̨tinuo īter ꝑteꝫ
                    <lb/>
                  deꝑditã ab ipſo c. et deꝑditã a d. eſt f. ꝓportio / vt ꝓ­
                    <lb/>
                  batū eſt / g̊ quãdocū aliq̈ pars aliq̊ta c. latitudīs
                    <lb/>
                  ab a. potētia deꝑdēde deꝑdet̄̄: adeq̈te ↄ̨ſimilis ꝑs
                    <lb/>
                  aliq̊ta et eiuſdē denoīatiõis deꝑdet d. latitudo / qḋ
                    <lb/>
                  fuit probandum. </s>
                  <s xml:id="N17C82" xml:space="preserve">Et eodem modo probabis cum
                    <lb/>
                  vtra potentia iutendit motum ſuum altera illa-
                    <lb/>
                  rum que cotinuo in certa ꝓportione velocius mo- </s>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum