Alvarus, Thomas, Liber de triplici motu, 1509

Page concordance

< >
Scan Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
< >
page |< < of 290 > >|
    <echo version="1.0">
      <text xml:lang="la">
        <div xml:id="N10132" level="1" n="1" type="body">
          <div xml:id="N10136" level="2" n="1" type="other" type-free="pars">
            <div xml:id="N10E2D" level="3" n="5" type="chapter" type-free="capitulum">
              <p xml:id="N11215">
                <s xml:id="N11282" xml:space="preserve">
                  <pb chead="Prime partis" file="0015" n="15"/>
                qm̄ iuxta illam cõcluſionē reſiduū a prima parte
                  <lb/>
                ꝓportionali quauis ꝓportione rationali debet ſe
                  <lb/>
                habere vt numerꝰ minor talis ꝓportionis: et ꝑ cõ­
                  <lb/>
                ſequēs manebit ꝓ prima parte ꝓportiõali nume­
                  <lb/>
                rus ille quo numerꝰ maior talis ꝓportionis exce-
                  <lb/>
                dit minorē. </s>
                <s xml:id="N11294" xml:space="preserve">Patet hec cõſequētia / q2 ſemꝑ corpus
                  <lb/>
                debet diuidi in tot partes quotus eſt numerꝰ ma-
                  <lb/>
                ior et primus ꝓportiõis qua debet fieri diuiſio: vt
                  <lb/>
                patet ex ſecūda cõcluſione: et pro reſiduo a prima
                  <lb/>
                debent capi tot partes ex illis quotus eſt numerꝰ
                  <lb/>
                minor vt dictum eſt. </s>
                <s xml:id="N112A1" xml:space="preserve">igitur relique partes remanē­
                  <lb/>
                tes erunt prima pars. </s>
                <s xml:id="N112A6" xml:space="preserve">Patet cõſequētia ex prima
                  <lb/>
                ſuppoſitione: et ille partes remanentes ſunt nume­
                  <lb/>
                rus quo numerus maior excedit minorē, vt patet:
                  <lb/>
                igitur prima pars ꝓportionalis eſt numerus quo
                  <lb/>
                maior numerꝰ et primꝰ proportionis qua ſit diui­
                  <lb/>
                ſio excedit minorē. </s>
                <s xml:id="N112B3" xml:space="preserve">Habet ſe / igitur totū reſiduū a
                  <lb/>
                prima parte proportionali ad primã partē pro-
                  <lb/>
                portionalē in ea proportione qua numerꝰ minor
                  <lb/>
                et primus talis proportionis ſe habet ad numerū
                  <lb/>
                quo maior et primus eiuſdem proportiõis excedit
                  <lb/>
                minorem. </s>
                <s xml:id="N112C0" xml:space="preserve">quod fuit probandum </s>
                <s xml:id="N112C3" xml:space="preserve">¶ Ad habendam
                  <lb/>
                autē praxim huius correlarii in cõpoſitis propor­
                  <lb/>
                tionibus conſtituētur alique figure: quibus facile
                  <lb/>
                iudicabitur in qua proportiõe ſe habet reſiduū a
                  <lb/>
                prima parte ꝓportionali ad primã partē ꝓpor-
                  <lb/>
                tionalē. </s>
                <s xml:id="N112D0" xml:space="preserve">Ad quod facile inſpiciendū in ꝓportioni­
                  <lb/>
                bus duplis ſuperparticularibus conſtituatur na­
                  <lb/>
                turalis ſeries numeroꝝ incipiēdo a binario in īfe­
                  <lb/>
                riori linea: et in ſuperiori linea conſtituatur natu­
                  <lb/>
                ralis ordo numerorū incipiendo a ternario: tunc
                  <lb/>
                referendo primum inferioris ordinis. </s>
                <s xml:id="N112DD" xml:space="preserve">primo ſu-
                  <lb/>
                periois: habebis in qua ꝓportione ſe habet reſi-
                  <lb/>
                duū a prima parte proportiõali ad primã diuidē­
                  <lb/>
                do corpus prima ſpecie ꝓportionis duple ſuper-
                  <lb/>
                particularis: et referendo ſecundū inferioris ordi­
                  <lb/>
                nis ſecundo ſuperioris habebis illud idem in ſe-
                  <lb/>
                cunda ſpecie ꝓportionis duple ſuperparticula­
                  <lb/>
                ris. </s>
                <s xml:id="N112EE" xml:space="preserve">et ſic conſequenter vt patet in figura.</s>
              </p>
              <xhtml:table xml:id="N112FD">
                <xhtml:tr xml:id="N112FE">
                  <xhtml:td xml:id="N112FF" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <p xml:id="N11301">
                <s xml:id="N11302" xml:space="preserve">Sed ad praxim huiꝰ negocii in ſpeciebus ꝓporti­
                  <lb/>
                onis triple ſuꝑparticularis cõſtituatur in inferio­
                  <lb/>
                ri ſerie naturalis ordo numerorū incipiendo a bi­
                  <lb/>
                nario: et in ſuperiori conſtituãtur oēs numeri īpa­
                  <lb/>
                res incipiendo a quinario: et tunc referēdo primū
                  <lb/>
                inferioris ordinis primo ſuperioris: et ſecundū in­
                  <lb/>
                ferioris ſecūdo ſuperioris: et tertiū inferioris ter-
                  <lb/>
                tio ſuperioris: et ſic conſequenter. </s>
                <s xml:id="N11313" xml:space="preserve">cõſpicies in qua
                  <lb/>
                ꝓportione ſe habet reſiduum a prima parte pro­
                  <lb/>
                portionali ad primã diuiſione corporis facto pro­
                  <lb/>
                portione tripla ſuperparticulari: vt ptꝫ in figura</s>
              </p>
              <xhtml:table xml:id="N1131C">
                <xhtml:tr xml:id="N1131D">
                  <xhtml:td xml:id="N1131E" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <p xml:id="N11320">
                <s xml:id="N11321" xml:space="preserve">Ad praticandū autē ita in ſpeciebus quadruple
                  <lb/>
                ſuꝑparticularis quintuple ſuꝑparticularis .etc̈. / cõ­
                  <lb/>
                ſtituatur naturalis ſeries numerorū incipiendo a
                  <lb/>
                binario in linea inferiori: et in ſuperiori oēs nume­
                  <lb/>
                ros excedentes ſe continuo ternario incipiendo a
                  <lb/>
                ſeptenario: et ſic habebis quod queris in ſpeciebꝰ
                  <lb/>
                ꝓportionis quadruple ſuꝑparticularis </s>
                <s xml:id="N11330" xml:space="preserve">Ad quod
                  <lb/>
                inueniēdū in ſpeciebus ꝓportionis quītuple ſuꝑ­
                  <lb/>
                particularis cõſtituas in ſuperiori ordine oēs nu­
                  <lb/>
                meros excedentes ſe quaternario incipiendo a nu­
                  <lb/>
                mero nouenario: et in ſpecie ſequeuti coſtituas in
                  <lb/>
                ſuperiori ordine oēs numeros excedentes ſe qui­
                  <cb chead="Capitulum ſextū."/>
                nario incipiendo a numero vndenario: et ſic conſe­
                  <lb/>
                quenter in aliis ſpeciebus operaberis </s>
                <s xml:id="N11342" xml:space="preserve">Patet hoc
                  <lb/>
                in figuris ſequentibus.</s>
              </p>
              <xhtml:table xml:id="N11347">
                <xhtml:tr xml:id="N11348">
                  <xhtml:td xml:id="N11349" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <p xml:id="N1134B">
                <s xml:id="N1134C" xml:space="preserve">¶ Sed ad exercitiū huiꝰ vltimi correlarii in ſpecie­
                  <lb/>
                bus multipliciū ſuprapartientiū quedã etiaꝫ con-
                  <lb/>
                ſtituentur figuere. </s>
                <s xml:id="N11353" xml:space="preserve">Unde ac facile īueniendã ꝓpor­
                  <lb/>
                tionē reſidui a prima parte ꝓportionali ad ipſaꝫ
                  <lb/>
                primã in ſpeciebus ꝓportionis duple ſupraparti­
                  <lb/>
                entis cõſtituatur naturalis ſeries incipiēdo a ter­
                  <lb/>
                nario inferiori linea: in ſuperiori vero cõſtituan-
                  <lb/>
                tur oēs numeri īpares incipiēdo a quinario: et tūc
                  <lb/>
                referēdo primū inferioris ordinis primo ſuperio­
                  <lb/>
                ris: et ſcḋm ſcḋo: et tertiū tertio id quod queris fa-
                  <lb/>
                cile reperies / vt patet in figura ſequenti.</s>
              </p>
              <xhtml:table xml:id="N11366">
                <xhtml:tr xml:id="N11367">
                  <xhtml:td xml:id="N11368" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <p xml:id="N1136A">
                <s xml:id="N1136B" xml:space="preserve">¶ Ad īueniendã autē proportionē reſidui a prima
                  <lb/>
                parte ꝓportionali ad ipſam primã diuiſione cor­
                  <lb/>
                poris facta ꝓportione tripla ſuprapartiente con­
                  <lb/>
                ſtituatur ſupra naturalē ſeriē numeroꝝ incipiēdo
                  <lb/>
                a ternario vna ſeries omnium numerorum conti-
                  <lb/>
                nuo excedentium ſe ternario incipiendo ab octo-
                  <lb/>
                nario numero: vt patet in figura.</s>
              </p>
              <xhtml:table xml:id="N1137A">
                <xhtml:tr xml:id="N1137B">
                  <xhtml:td xml:id="N1137C" xml:space="preserve"/>
                </xhtml:tr>
              </xhtml:table>
              <p xml:id="N1137E">
                <s xml:id="N1137F" xml:space="preserve">¶ Ad īueniendū autē ꝓpoſitū in ſpeciebus ꝓpor-
                  <lb/>
                tionis quadruple ſuprapartiētis ſupra naturalē
                  <lb/>
                ſeriē numeroꝝ incipiendo a ternario conſtituatur
                  <lb/>
                ſeries numeroꝝ ↄ̨tinuo excedentiū ſe quaternario
                  <lb/>
                incipiendo ab vndeuario: et ſic cõſequenter ſupra
                  <lb/>
                eandē naturalē ſeriē numeroꝝ incipiendo a terna­
                  <lb/>
                rio cõſtituatur ſeries numeroꝝ cõtinuo exedentiū
                  <lb/>
                ſe numero quinario īcipiēdo a numero quarto de­
                  <lb/>
                cimo: et ſic cõſequenter operaberis in aliis. </s>
                <s xml:id="N11392" xml:space="preserve">Et hec
                  <lb/>
                de diuiſione corpoꝝ ꝓportione rationali.</s>
              </p>
            </div>
            <div xml:id="N11397" level="3" n="6" type="chapter" type-free="capitulum">
              <head xml:id="N1139C" xml:space="preserve">Capitulū ſextū / ī quo datur modus di­
                <lb/>
              uidendi corpus in partes proportiona-
                <lb/>
              les proportione irrationali.</head>
              <p xml:id="N113A3">
                <s xml:id="N113A4" xml:space="preserve">QUemadmodū quodlibet cor-
                  <lb/>
                pus diuidi poteſt ꝓportione rationali
                  <lb/>
                infinitiſ ſpeciebus eius / vt caput prece­
                  <lb/>
                dens oſtendit: ita etiã ꝓportione irrationali infi-
                  <lb/>
                nitiſ ſpeciebus eiꝰ quodlibet corpꝰ diuidi poteſt
                  <lb/>
                </s>
                <s xml:id="N113B0" xml:space="preserve">Pro cuius diuiſionis noticia ſit</s>
              </p>
              <p xml:id="N113B3">
                <s xml:id="N113B4" xml:space="preserve">Prima concluſio </s>
                <s xml:id="N113B7" xml:space="preserve">Quodlibet corpus
                  <lb/>
                diuiſū aliqua ꝓportione irrationali ſe debet ha­
                  <lb/>
                bere ad aggregatū ex oībus partibus ꝓportiona­
                  <lb/>
                bilibus tali ꝓportione ſequētibus primam in ea
                  <lb/>
                proportione qua totum diuidatur. </s>
                <s xml:id="N113C2" xml:space="preserve">Hec concluſio
                  <lb/>
                claram et euidentem ex prima precedentis capitis
                  <lb/>
                demonſtrationem ſortitur.</s>
              </p>
              <p xml:id="N113C9">
                <s xml:id="N113CA" xml:space="preserve">Secunda cõcluſio. </s>
                <s xml:id="N113CD" xml:space="preserve">Ad diuidendum
                  <lb/>
                corpus infinitis ꝓportionibꝰ irrationabilibꝰ mi­
                  <lb/>
                noribus dupla: vt puta ꝓportione diametri ad co­
                  <lb/>
                ſtam: aggregati ex medietate exceſſus quo diame­
                  <lb/>
                ter excedit coſtã et ipſa coſta ipſammet coſtam: </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum