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="N115E7" level="3" n="7" type="chapter" type-free="capitulum">
              <p xml:id="N11668">
                <s xml:id="N1168C" xml:space="preserve">
                  <pb chead="Prime partis" file="0018" n="18"/>
                duplas: puta quattuor ad duo: et duo ad vnum:
                  <lb/>
                tunc coacerua illos numeros puta quaternarium
                  <lb/>
                binarum et vnitatem et inuenies .7. </s>
                <s xml:id="N116A2" xml:space="preserve">Diuidas igi-
                  <lb/>
                tur corpus in ſeptem ſeptimas: et pro primo ordi­
                  <lb/>
                ne capias quattuor ſeptimas: et pro ſecundo du-
                  <lb/>
                as ſeptimas: et pro vltimo vnam ſeptimam: et ſic
                  <lb/>
                comperies quot partes aliquotas continet quili-
                  <lb/>
                bet illorum ordinū. </s>
                <s xml:id="N116AF" xml:space="preserve">Et iſto modo in qualibet pro­
                  <lb/>
                portione operaberis facile autem hoc demonſtra­
                  <lb/>
                tur ex prima concluſione quoniam ſicut illi tres
                  <lb/>
                ordines cõtinuo ſe habent in proportione dupla
                  <lb/>
                et ſunt partes illius corporis: ita oprtet capere ꝑ­
                  <lb/>
                tes continuo ſe habentes in proportiõe dupla to­
                  <lb/>
                tum corpus abſoluētes eo  oꝑati ſumꝰ artificio</s>
              </p>
              <p xml:id="N116BE">
                <s xml:id="N116BF" xml:space="preserve">Tertia concluſio. </s>
                <s xml:id="N116C2" xml:space="preserve">Alicuius cõtinui
                  <lb/>
                partes aliquota proportionem aliquam rationa­
                  <lb/>
                lem acquirente: proportionē acquiſitam toti inue­
                  <lb/>
                nire. </s>
                <s xml:id="N116CB" xml:space="preserve">vt diuiſio corpore in quin partes aliquo-
                  <lb/>
                tas putas in .5. quintas vna illarum quintarum
                  <lb/>
                acquirente proportionem duplam: inuenire quan­
                  <lb/>
                tam proportionem totum illud corpus proportio­
                  <lb/>
                nē acquirat. </s>
                <s xml:id="N116D6" xml:space="preserve">In illo em̄ caſu illud corpus propor-
                  <lb/>
                tionem ſexquiquintam acquirit: cum acquirat ſu­
                  <lb/>
                pra ſe vnã quintam: hoc eſt tantuꝫ quanta eſt vna
                  <lb/>
                eius quinta. </s>
                <s xml:id="N116DF" xml:space="preserve">Probaemtur hec concluſio / et diuidatur /
                  <lb/>
                a pedale in aliquot partes aliquotas gratia exē-
                  <lb/>
                pli in .7. / et acquirat vna illarum aliquam propor­
                  <lb/>
                tionem rationalem: tunc vel illa proportio acqui­
                  <lb/>
                ſita alicui illarum partium eſt multiplex vel non
                  <lb/>
                multiplex: ſi multiplex tunc aliquotiens vel ſemel
                  <lb/>
                acquirit ſupra ſe tantum quanta ipſa pars eſt. </s>
                <s xml:id="N116EE" xml:space="preserve">et
                  <lb/>
                tot partes equales ſibi quot acquirit ſupra ſe tot
                  <lb/>
                acq̇rit ſupra oēs illas .7. partes aliquotas ī quas
                  <lb/>
                corpus erat diuiſum: et quelibet talis pars acqui­
                  <lb/>
                ſita illi parti eſt equalis cuilibet illarum partium
                  <lb/>
                aliquotarū in quas corpus eſt diuiſum: igitur ille
                  <lb/>
                partes acquiſite vel pars acquiſita eſt vel ſūt eiuſ­
                  <lb/>
                dem denominationis cū parte cui acquiruntur vĺ
                  <lb/>
                acquiritur: et ita ſi ille partes ī quas corpus diui­
                  <lb/>
                debatur ſunt ſeptime: et ille partes acquiſite ſunt
                  <lb/>
                due vel tres vel quattuor / et ſic cõſequenter: totum
                  <lb/>
                illud corpus acquiſiuit duas vel tres vel quatuor
                  <lb/>
                ſeptimas vel ſi eſt vna totum illud corpus acqui-
                  <lb/>
                ſiuit vnam ſeptimam: quo ad inuento: iam patet
                  <lb/>
                quãtam proportionē illud corpus acquiſiuit. </s>
                <s xml:id="N1170D" xml:space="preserve">Si
                  <lb/>
                em̄ acquiſiuit tres tales partes et ille ſūt ſeptime
                  <lb/>
                iam acquiſiuit totum proportionem ſupratripar­
                  <lb/>
                tientem ſeptimas / et ſic habetur propoſitum vbi
                  <lb/>
                pars aliquota proportionem multiplicē acquirit
                  <lb/>
                </s>
                <s xml:id="N11719" xml:space="preserve">Si autem acquirit rationalem nõ multiplicē ma-
                  <lb/>
                nifeſtum eſt /  illa denominatur ab aliqua parte
                  <lb/>
                aliquota vel ab aliquibꝰ partibꝰ aliquotis ade-
                  <lb/>
                quate vel inadequate (non eſt modo cura) ſicut du­
                  <lb/>
                pla ſexquitertia denominatur a numero binario
                  <lb/>
                cum tertia: et ſuprabipartiens tertias ab vnitate
                  <lb/>
                cum duabus tertiis. </s>
                <s xml:id="N11728" xml:space="preserve">Dato igitur /  aliquam talē
                  <lb/>
                proportionem rationalem non multiplicē aliqua
                  <lb/>
                talium partium aliquotarum acquiſiuerit: ad in-
                  <lb/>
                uendiendum quam proportionem acquirit totum
                  <lb/>
                diuidatur quelibet pars aliquota in partes ali-
                  <lb/>
                quotas a quibus denominatur talis proportio / et
                  <lb/>
                tunc coaceruentur omnes ille partes aliquote: et
                  <lb/>
                numerus reſultans indicabit quota pars aliquo­
                  <lb/>
                ta totius eſt aliqua īmo quelibet illarum. </s>
                <s xml:id="N1173B" xml:space="preserve">deinde
                  <lb/>
                illis omnibus addantur ille partes aliquote ac-
                  <lb/>
                quiſite equales eis. </s>
                <s xml:id="N11742" xml:space="preserve">et ſic inuenies quot partes ali­
                  <cb chead="Capitulum octauū."/>
                quotas acquiſiuit totum: et per conſequens qua-
                  <lb/>
                lem proportionem vt ſi in exemplo poſito vna il-
                  <lb/>
                larum ſeptimarum acquirat proportionē ſupra­
                  <lb/>
                bipartientem tertias: et quoniam illa proportio
                  <lb/>
                denominatur ab vno cum duabus tertiis diuida­
                  <lb/>
                tur quelibet ſeptima in tres tertias: et multipliciē­
                  <lb/>
                tur .7. per tria / et reſultabunt .12. et iam ille nume-
                  <lb/>
                rus indicat tibi quamlibet illarum partium eſſe
                  <lb/>
                vnam viceſimam primam: et partes acquiſite ſunt
                  <lb/>
                equales illis quia ſunt tertie vnius ſeptime: et ſūt
                  <lb/>
                due. </s>
                <s xml:id="N1175C" xml:space="preserve">ergo acquiſiuit duas viceſimas primas et ſic
                  <lb/>
                ꝓportionē ſuprabipartiētē viceſimas ṗmas totū
                  <lb/>
                acq̇ſiuit. </s>
                <s xml:id="N11763" xml:space="preserve">Si autē vna illarum ſeptimarū acquirat
                  <lb/>
                duplam ſexquitertiam: diuidas quamlibet ſepti­
                  <lb/>
                mam etiam in tertias: et multiplica ſeptē per tria
                  <lb/>
                et reperies / vt dictum eſt viginti vnum / et quia vna
                  <lb/>
                ſeptima acquiſiuit tantum quanta ipſa eſt puta
                  <lb/>
                vnam ſeptimam totius cuꝫ vna tertia illius ſepti­
                  <lb/>
                me: diuidas etiam illam ſeptimam acquiſitam in
                  <lb/>
                tres partes: et ille tres partes erunt tres viceſime
                  <lb/>
                prime totius / vt conſtat: et totum acquiſiuit illas
                  <lb/>
                tres et cum hoc vnam. </s>
                <s xml:id="N11778" xml:space="preserve">Acquiſiuit igitur quattuor
                  <lb/>
                viceſimas primas: et per conſequens proportionē
                  <lb/>
                ſupraquadripartiētem viceſimas primas. </s>
                <s xml:id="N1177F" xml:space="preserve">Et iſto
                  <lb/>
                modo in omni alia ſpecie proportionis operabe­
                  <lb/>
                ris. </s>
                <s xml:id="N11786" xml:space="preserve">Et ex hoc poteris inuenire proportionem quã
                  <lb/>
                acquirit totum duabus partibus eius aliquotis
                  <lb/>
                nequalibus: ſiue duabus non facientibus vnam:
                  <lb/>
                ſiue pluribus acquirentibus equalem proportio­
                  <lb/>
                nem vel etiam inequalem. </s>
                <s xml:id="N11791" xml:space="preserve">Et conſimiliter cogno­
                  <lb/>
                ſces quam proportionem deperdit totum aliqua
                  <lb/>
                parte eius vel aliquibus partibus aliquotis oli-
                  <lb/>
                quam vel aliquas proportiēes deperdente vel de­
                  <lb/>
                perdentibus.</s>
              </p>
            </div>
            <div xml:id="N1179C" level="3" n="8" type="chapter" type-free="capitulum">
              <head xml:id="N117A1" xml:space="preserve">Capitulum octauum / in quo agi-
                <lb/>
              tur de inuentione proportionis mi-
                <lb/>
              noris inequalitatis et etiam maio-
                <lb/>
              ris reſpectu cuiuſcū numeri ex re-
                <lb/>
              bus diuiſibilibus compoſiti.</head>
              <p xml:id="N117AC">
                <s xml:id="N117AD" xml:space="preserve">PLerum contingit tam in
                  <lb/>
                materia nitenionis difformis quã ꝓ­
                  <lb/>
                portiõis motuum querere proportio­
                  <lb/>
                nem ſubſequialteram vel ſubduplam vel aliquã-
                  <lb/>
                aliam minoris inequalitatis vel etiam maioris
                  <lb/>
                inequalitatis reſpectu numeri non habentis illaꝫ
                  <lb/>
                ſine fratione id eſt diuiſione vnitatis vel vnitatū
                  <lb/>
                talis numeri. </s>
                <s xml:id="N117BE" xml:space="preserve">vt ſi ponat̄̄ /  aliquod mobile per-
                  <lb/>
                tranſeat tripedale ſpacium in hora / tunc mouēs
                  <lb/>
                ſubdupla velocitate tranſit ſubduplum ſpacium
                  <lb/>
                ad tripedale in eodem tēpore. </s>
                <s xml:id="N117C7" xml:space="preserve">Modo non eſt poſ-
                  <lb/>
                ſibile dare ſubduplum ad tripedale ſine fractiõe
                  <lb/>
                vnitatis: quoniam bipedale cum dimidio eſt ſub-
                  <lb/>
                duplum tripedalis. </s>
                <s xml:id="N117D0" xml:space="preserve">Item contingit non nunquaꝫ
                  <lb/>
                querere ſexquialterum reſpectu numeri quinarii:
                  <lb/>
                et illud non poteſt dari ſine fractione vnitatis .7.
                  <lb/>
                enim cum dimidio ad .5. eſt proportio ſexquialte-
                  <lb/>
                ra. </s>
                <s xml:id="N117DB" xml:space="preserve">Quare pro inuentione talis proportionis ma­
                  <lb/>
                ioris aut minoris inequalitatis cum fractione.</s>
              </p>
              <p xml:id="N117E0">
                <s xml:id="N117E1" xml:space="preserve">Suppono primo /  duplex eſt nume­
                  <lb/>
                rus vt ad propoſitum ſufficit quidaꝫ eſt compoſi-
                  <lb/>
                tus ex vnitatibꝰ diuiſibilibꝰ .i. cuius quelibet vni­
                  <lb/>
                tas eſt res diuiſibilis: vt numerus trium pedaliū
                  <lb/>
                quattuor qualitatū .etc̈. alius vero numerus eſt cõ­ </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum