Alvarus, Thomas, Liber de triplici motu, 1509

List of thumbnails

< >
51
51 		52
52
53
53 		54
54
55
55 		56
56
57
57 		58
58
59
59 		60
60
< >
page |< < of 290 > >|
    <echo version="1.0">
      <text xml:lang="la">
        <div xml:id="N10132" level="1" n="1" type="body">
          <div xml:id="N1194D" level="2" n="2" type="other" type-free="pars">
            <div xml:id="N15216" level="3" n="8" type="chapter" type-free="capitulum">
              <p xml:id="N15A5B">
                <s xml:id="N15A6E" xml:space="preserve">
                  <pb chead="Secunde partis" file="0058" n="58"/>
                quam habet ad quantitatem minorem. </s>
                <s xml:id="N15A7E" xml:space="preserve">Exempluꝫ /
                  <lb/>
                vt capta proportione que eſt .12. ad .8. volo /  nu-
                  <lb/>
                merus maior puta .12. creſcat quouſ conſtituant
                  <lb/>
                16. / tūc manifeſtū eſt /  numerus maior acquiſiuit
                  <lb/>
                ſupra ſe proportionem ſexquitertiam: et tantam
                  <lb/>
                acquiſiuit ꝓportio .12. ad .8. / vt conſtat. </s>
                <s xml:id="N15A8B" xml:space="preserve">In fine em̄
                  <lb/>
                illa componitur ex ſexquialtera et ſexquitertia.
                  <lb/>
                </s>
                <s xml:id="N15A91" xml:space="preserve">Si vero .12. diminuantur vſ ad .9. ſtantibus.
                  <lb/>
                8. / tunc proportio .12. ad .8. deperdit proportio-
                  <lb/>
                nē ſexquitertiam quam deperdit numerus maior.
                  <lb/>
                </s>
                <s xml:id="N15A99" xml:space="preserve">Prima pars huius concluſionis patet ex prima
                  <lb/>
                parte quinte concluſionis: et ſecunda ex prima ſex­
                  <lb/>
                te concluſionis huius. </s>
                <s xml:id="N15AA0" xml:space="preserve">¶ Ex quo ſequitur primo / 
                  <lb/>
                ſi quantitas maior creſcat vel decreſcat manens
                  <lb/>
                maior reſpectu quantitatis minoris inuariate:
                  <lb/>
                tantam proportionem acquirit vel deperdit re-
                  <lb/>
                ſpectu quantitatis minoris quantam reſpectu ſui
                  <lb/>
                </s>
                <s xml:id="N15AAC" xml:space="preserve">Patet ex concluſione.
                  <note position="left" xlink:href="note-0058-01a" xlink:label="note-0058-01" xml:id="N15AD8" xml:space="preserve">1. correĺ.</note>
                </s>
                <s xml:id="N15AB4" xml:space="preserve">¶ Sequitur ſecundo /  ſi
                  <lb/>
                quantitas maior creſcat vel decreſcat manēs ma­
                  <lb/>
                ior reſpectu duarum quantitatum minorum ſiue
                  <lb/>
                equalium ſiue inequalium: equalem propotionē
                  <lb/>
                acquirit vel deperdit reſpectu vtriuſ quantita-
                  <lb/>
                tis ipſis inuariatis manentibus. </s>
                <s xml:id="N15AC1" xml:space="preserve">Patet hoc cor-
                  <lb/>
                relarium / quoniam aliquam proportionem acqui­
                  <lb/>
                rit vel deperdit quantitas maior reſpectu ſui: et
                  <lb/>
                quantãcun acquirit vel deperdit reſpectu ſui tã­
                  <lb/>
                tam acquirit vel deperdit reſpectu cuiuſcun quã­
                  <lb/>
                titatis minoris inuariate / vt patet ex priori: igitur
                  <lb/>
                quantam acquirit vel deperdit reſpectu ſui tantū
                  <lb/>
                reſpectu duarum quantitatum minorū ſiue equa-
                  <lb/>
                lium ſiue inequalium / quod fuit probandum.</s>
              </p>
              <p xml:id="N15ADE">
                <s xml:id="N15ADF" xml:space="preserve">Octaua concluſio. </s>
                <s xml:id="N15AE2" xml:space="preserve">Si quantitas mi­
                  <lb/>
                nor creſcat reſpectu quantitatis maioris non va-
                  <lb/>
                riate: quantam proportionem acquirit ſupra ſe
                  <lb/>
                tantam deperdit quantitas maior reſpectu mino­
                  <lb/>
                ris. </s>
                <s xml:id="N15AED" xml:space="preserve">Hoc eſt per tantam proportionem proportio
                  <lb/>
                maioris quantitatis ad minorem efficitur minor.
                  <lb/>
                </s>
                <s xml:id="N15AF3" xml:space="preserve">Si vero quantitas minor decreſcat reſpectu ma-
                  <lb/>
                ioris quantitatis inuariate: tantam proportionē
                  <lb/>
                acquirit quãtitas maior ſupra minorem per quã­
                  <lb/>
                tam ipſa minor fiet minor. </s>
                <s xml:id="N15AFC" xml:space="preserve">Hoc eſt proportio quã­
                  <lb/>
                titatis maioris ad minorē efficitur maior per pro­
                  <lb/>
                portionem quam deperdit quãtitas minor. </s>
                <s xml:id="N15B03" xml:space="preserve">Pri-
                  <lb/>
                ma pars huius concluſionis patet ex ſecūda par-
                  <lb/>
                te quinte cõcluſionis et ſecunda, ex ſecunda parte
                  <lb/>
                ſexte concluſionis huius </s>
                <s xml:id="N15B0C" xml:space="preserve">¶ Ex quo ſequitur primo /
                  <lb/>
                 ſi quantitas minor creſcat vel decreſcat reſpe-
                  <lb/>
                ctu maioris inuariate: tantam proportionem ac-
                  <lb/>
                quirit vel deperdit proportio quantitatis maio-
                  <lb/>
                ris ad minorē quãtam acquirit vel deperdit quã-
                  <lb/>
                titas minor manens minor reſpectu ſui ipſius.</s>
              </p>
              <p xml:id="N15B19">
                <s xml:id="N15B1A" xml:space="preserve">Patet hec correlarium ex concluſione.
                  <note position="left" xlink:href="note-0058-02a" xlink:label="note-0058-02" xml:id="N15BBA" xml:space="preserve">2. correĺ.</note>
                </s>
                <s xml:id="N15B22" xml:space="preserve">¶ Sequi-
                  <lb/>
                tur ſecundo /  ſi quantitas minor creſcat vel de-
                  <lb/>
                creſcat reſpectu duarum quantitatum maiorum
                  <lb/>
                ſiue equalium ſiue inequalium: tantam proporti-
                  <lb/>
                onem acquiret vel deperdet vna quantitas maior
                  <lb/>
                reſpectu quantitatis minoris ſicut altera maior
                  <lb/>
                reſpectu eiuſdem quãtitatis minoris. </s>
                <s xml:id="N15B31" xml:space="preserve">Patet hoc
                  <lb/>
                correlarium / quia vtra illarum quantitatū ean­
                  <lb/>
                dem proportionem acquiret vel deperdet: puta il­
                  <lb/>
                lam quam acquirit vĺ deperdit quantitas minor /
                  <lb/>
                vt patet ex concluſione
                  <note position="left" xlink:href="note-0058-03a" xlink:label="note-0058-03" xml:id="N15BC0" xml:space="preserve">3. correĺ.</note>
                </s>
                <s xml:id="N15B41" xml:space="preserve">¶ Sequitur tertio /  ſi due
                  <lb/>
                quãtitates maiores inequales eque velociter cre-
                  <lb/>
                ſcant vĺ decreſcant reſpectu eiuſdem quantitatis
                  <lb/>
                minoris inuariate: maiorem proportionē acqui-
                  <lb/>
                rit vel deperdit minor illarum quantitatum ma-
                  <lb/>
                iorum quam maior reſpectu eiuſdem quantitatis
                  <lb/>
                minoris inuariate. </s>
                <s xml:id="N15B50" xml:space="preserve">Probatur / quoniam quanti-
                  <cb chead="Capitulū octauū."/>
                tas minor maiorem proportioneꝫ acquirit ſupra
                  <lb/>
                ſe aut deperdit reſpectu ſui quam maior illarum
                  <lb/>
                quantitatum maiorum: igitur maiorem propor-
                  <lb/>
                tionem acquirit vĺ deperdit reſpectu quantitatis
                  <lb/>
                minoris inuariate minor illarum quantitatum
                  <lb/>
                quam maior. </s>
                <s xml:id="N15B60" xml:space="preserve">Patet conſequentia ex primo corre­
                  <lb/>
                lario ſeptime concluſionis / et antecedens patet ex
                  <lb/>
                octaua ſuppoſitione quarti capitis huius partis
                  <lb/>
                  <note position="right" xlink:href="note-0058-04a" xlink:label="note-0058-04" xml:id="N15BC6" xml:space="preserve">4. correĺ</note>
                </s>
                <s xml:id="N15B6E" xml:space="preserve">¶ Sequitur quarto /  ſi due quãtitates minores
                  <lb/>
                inequales eque velociter creſcant vel decreſcant
                  <lb/>
                reſpectu quantitatis vtra maioris inuariate:
                  <lb/>
                maiorem proportionē acquirit vel deperdit quã-
                  <lb/>
                titas illa maior reſpectu minoris quam reſpectu
                  <lb/>
                maioris. </s>
                <s xml:id="N15B7B" xml:space="preserve">Hoc correlarium ex ſecundo correlario
                  <lb/>
                huius concluſionis octaue iuncta octaua ſuppo-
                  <lb/>
                ſitione quarti capitis preallegati ſuam demon-
                  <lb/>
                ſtrationem ſortitur. </s>
                <s xml:id="N15B84" xml:space="preserve">¶ Sequitur quinto /  ſi due
                  <lb/>
                quantitates maiores ſiue equales ſiue inequales
                  <lb/>
                acquirant vel deperdant equales proportiones
                  <lb/>
                ipſis tamen manentibus maioribus reſpectu du-
                  <lb/>
                arum quantitatum minorum ſiue equalium ſiue
                  <lb/>
                inequalium: vtra illarum equalem proportionē
                  <lb/>
                acquirit vel deperdit reſpectu vtriuſ mīoris in-
                  <lb/>
                uariate. </s>
                <s xml:id="N15B95" xml:space="preserve">Patet hoc correlarium / quoniam tantaꝫ
                  <lb/>
                proportionem vtra illarum acquirit vel deper-
                  <lb/>
                dit reſpectu vtriuſ minoris quantam reſpectu
                  <lb/>
                ſui / vt patet ex primo correlario ſeptime concluſi-
                  <lb/>
                onis / ſed equalem vtra illarum acquirit vel de-
                  <lb/>
                perdit reſpectu ſui / igitur equalem reſpectu vtriuſ­
                  <lb/>
                 quantitatis minoris inuariate. </s>
                <s xml:id="N15BA4" xml:space="preserve">¶ Sequitur ſex­
                  <lb/>
                to /  ſi due quantitates minores eque proportio-
                  <lb/>
                nabiliter creſcant vel decreſcant reſpectu quanti-
                  <lb/>
                tatum vtra maiorum: equalem proportionem
                  <lb/>
                vtra illarum maiorum acquirit vel deperdit re-
                  <lb/>
                ſpectu vtriuſ minoris. </s>
                <s xml:id="N15BB1" xml:space="preserve">Patet hoc correlarium
                  <lb/>
                ex primo correlario huius octaue concluſionis.</s>
              </p>
              <p xml:id="N15BCC">
                <s xml:id="N15BCD" xml:space="preserve">¶ Multe alie cõcluſiones et correlaria ex his dua-
                  <lb/>
                bus vltimis concluſionibus auxiliantibus ceteris
                  <lb/>
                predictis poſſent facile induci ſed ſufficiãt iſte que
                  <lb/>
                ordinãtur ad infendas regulas quas ponit calcu­
                  <lb/>
                lator de motu locali </s>
                <s xml:id="N15BD8" xml:space="preserve">¶ Et hec de ſecunda parte hu­
                  <lb/>
                ius operis: in qua ſi quid ex paruitate ingenii aut
                  <lb/>
                defectu mathematice artis inculte aut rudi miner­
                  <lb/>
                ua depromptū ſit: veniam peto. </s>
                <s xml:id="N15BE1" xml:space="preserve">Uix enim hec poſ-
                  <lb/>
                ſunt leuigato ſermone exarari.
                  <note position="right" xlink:href="note-0058-05a" xlink:label="note-0058-05" xml:id="N15BFD" xml:space="preserve">Iacobi
                    <lb/>
                  primo.</note>
                </s>
                <s xml:id="N15BEB" xml:space="preserve">Si vero quid lau-
                  <lb/>
                ro dignum reperiatur: deo optimo maximo gra-
                  <lb/>
                tie reddantur a quo omne datum optimum et om-
                  <lb/>
                ne donum perfectum iacobi primo. </s>
                <s xml:id="N15BF4" xml:space="preserve">¶ Sequentem
                  <lb/>
                vero partem in quatuor tractatus diſtribuam.</s>
              </p>
              <p xml:id="N15C05">
                <s xml:id="N15C06" xml:space="preserve">Primus ad ſcribetur motui locali penes cauſam
                  <lb/>
                </s>
                <s xml:id="N15C0A" xml:space="preserve">Secundus motui locali penes effectum. </s>
                <s xml:id="N15C0D" xml:space="preserve">Tertius
                  <lb/>
                motui rarefactionis at augmentatiõis. </s>
                <s xml:id="N15C12" xml:space="preserve">Quar-
                  <lb/>
                tus autem motui alterationis.</s>
              </p>
            </div>
          </div>
          <div xml:id="N15C17" level="2" n="3" type="other" type-free="pars">
            <p xml:id="N15C1C">
              <s xml:id="N15C1D" xml:space="preserve">Sequitur liber de triplici mo­
                <lb/>
              tu huius operis tertia pars</s>
            </p>
            <div xml:id="N15C22" level="3" n="1" type="other" type-free="tractatus">
              <p xml:id="N15C27">
                <s xml:id="N15C28" xml:space="preserve">Tertie partis tractatus pri-
                  <lb/>
                mus ī quo agitur de motu quo
                  <lb/>
                ad cauſam.</s>
              </p>
              <div xml:id="N15C2F" level="4" n="1" type="chapter" type-free="capitulum"> </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum