Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

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        <div xml:id="echoid-div633" type="section" level="1" n="454">
          <pb o="154" file="527.01.154" n="154" rhead="A*PPENDIX*"/>
        </div>
        <div xml:id="echoid-div634" type="section" level="1" n="455">
          <head xml:id="echoid-head478" xml:space="preserve">C*APVT IV.*</head>
          <head xml:id="echoid-head479" style="it" xml:space="preserve">Demonstrationum ſupraſcriptarum nonnullas per nume@
            <lb/>
          rosinstitutas, Mathematicas eſſe.</head>
          <p>
            <s xml:id="echoid-s4581" xml:space="preserve">MAthematicæ & </s>
            <s xml:id="echoid-s4582" xml:space="preserve">Mechanicæ demonſtrationis à doctis annotatur differen-
              <lb/>
            tia, neque injuria. </s>
            <s xml:id="echoid-s4583" xml:space="preserve">Nam illa omnibus generalis eſt, & </s>
            <s xml:id="echoid-s4584" xml:space="preserve">rationem cur ita ſit
              <lb/>
            penitus demonſtrat, hæc verò in ſubjecto duntaxat paradigmate numeris de-
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            clarat. </s>
            <s xml:id="echoid-s4585" xml:space="preserve">Vt ſi demonſtraturus in rectangulo triangulo baſin recti æquè poſſe cru-
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            ribus, aſſumat triangulum cujus minimum latus ſit 3, ſecundum 4, tertium 5 pe-
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            dum, hocq́ue rectangulum eſſe deprehendatur; </s>
            <s xml:id="echoid-s4586" xml:space="preserve">tumq́ue oſtendat maximi la-
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            teris quadratum 25, æquari reliquorum laterum quadratis 16 & </s>
            <s xml:id="echoid-s4587" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4588" xml:space="preserve">Sed demon-
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            ſtratio hujuſmodi tantum eſt propoſiti exempli, unde non concluſeris omnibus
              <lb/>
            rectangulis triangulis idem contingere, neque hinc cur id fiat evidens eſt; </s>
            <s xml:id="echoid-s4589" xml:space="preserve">& </s>
            <s xml:id="echoid-s4590" xml:space="preserve">
              <lb/>
            quia opus hujuſmodi machinationein ſpeciali exemplo inſtituitur, mechanica
              <lb/>
            demonſtratio appellatur: </s>
            <s xml:id="echoid-s4591" xml:space="preserve">ſed illa quam Euclides 47 propoſ. </s>
            <s xml:id="echoid-s4592" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s4593" xml:space="preserve">uſurpat ca-
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            tholica eſt & </s>
            <s xml:id="echoid-s4594" xml:space="preserve">univerſalis, cauſam repetens ab ipſis elementis cur ita neceſſariò, & </s>
            <s xml:id="echoid-s4595" xml:space="preserve">
              <lb/>
            non aliter ſe habere poſſit: </s>
            <s xml:id="echoid-s4596" xml:space="preserve">hæc propter certitudinem in demonſtrando, & </s>
            <s xml:id="echoid-s4597" xml:space="preserve">do-
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            cendo infallibilem Mathematica dicitur; </s>
            <s xml:id="echoid-s4598" xml:space="preserve">ideoq́ue etiam ab ipſis Mathematicis
              <lb/>
            potior cenſetur & </s>
            <s xml:id="echoid-s4599" xml:space="preserve">frequentiùs uſurpatur, quam illa per numeros mechanica.
              <lb/>
            </s>
            <s xml:id="echoid-s4600" xml:space="preserve">Vnde objectionem mihi paratam intelligo, cur 4, 11, 12, 18 propoſitiones 2. </s>
            <s xml:id="echoid-s4601" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4602" xml:space="preserve">
              <lb/>
            Elem. </s>
            <s xml:id="echoid-s4603" xml:space="preserve">Statices numeris adhibitis explicarim & </s>
            <s xml:id="echoid-s4604" xml:space="preserve">demonſtrarim. </s>
            <s xml:id="echoid-s4605" xml:space="preserve">Cui occurritur,
              <lb/>
            demonſtrationem in numeris dupliciter inſtitui; </s>
            <s xml:id="echoid-s4606" xml:space="preserve">alteram ubi tanquam termini
              <lb/>
            rationem, proportionemq́ue partium expoſitæ figuræ declarant; </s>
            <s xml:id="echoid-s4607" xml:space="preserve">alteram ubi
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            quantitatem. </s>
            <s xml:id="echoid-s4608" xml:space="preserve">Illa Mathematica eſt quia univerſim ſpeciei datæ figuræ conve-
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            niat, & </s>
            <s xml:id="echoid-s4609" xml:space="preserve">in ipſis cauſam declaret; </s>
            <s xml:id="echoid-s4610" xml:space="preserve">hæc autem non item, ob rationes iſtis contra-
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            rias. </s>
            <s xml:id="echoid-s4611" xml:space="preserve">Quain re Eutochius in ſuis in Apollonium cõmentariis 11 prop. </s>
            <s xml:id="echoid-s4612" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4613" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4614" xml:space="preserve">mecum
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            facit, dum ait: </s>
            <s xml:id="echoid-s4615" xml:space="preserve">Non perturbentur qui in hæc inciderint, quodillud ex Arithmeticis de-
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            monſtretur: </s>
            <s xml:id="echoid-s4616" xml:space="preserve">antiqui enim hujuſmodi demonſtrationibus ſæpe uti conſueverunt; </s>
            <s xml:id="echoid-s4617" xml:space="preserve">quæ ta-
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            men Mathematicæ potius ſunt, quam Arithmeticæpropter analogias. </s>
            <s xml:id="echoid-s4618" xml:space="preserve">adde quod quæſi-
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            tum Arithmeticam ſit; </s>
            <s xml:id="echoid-s4619" xml:space="preserve">nam rationes & </s>
            <s xml:id="echoid-s4620" xml:space="preserve">rationum quantitates, & </s>
            <s xml:id="echoid-s4621" xml:space="preserve">multiplicationes pri-
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            mò numeris, ſecundo loco per numeros & </s>
            <s xml:id="echoid-s4622" xml:space="preserve">magnitudinibus inſunt, ex illius ſententia
              <lb/>
            qui ita ſcripſit: </s>
            <s xml:id="echoid-s4623" xml:space="preserve">Ταῦ{τα} {γὰρ} τὰ μα{θή}μα{τα} δοκ{οῦ}ν{τι} {εἶ}μεν ἀδελφά. </s>
            <s xml:id="echoid-s4624" xml:space="preserve">hoc eſt, hæ enim Ma-
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            thematicæ diſciplinæ germanæ eſſe videntur. </s>
            <s xml:id="echoid-s4625" xml:space="preserve">Inſuperautĕ objiciatur in Archimedis,
              <lb/>
            Ptolomæi, Apollonii, & </s>
            <s xml:id="echoid-s4626" xml:space="preserve">inter recentiores Comandini, Regiomontani, aliorumq́ue
              <lb/>
            ſimilium propoſitionibus ipſam rationem, non autem rationis terminos in nu-
              <lb/>
            meris nominatim proponi, quod à nobis factitatum ſit; </s>
            <s xml:id="echoid-s4627" xml:space="preserve">cui reſponſio expedita
              <lb/>
            eſt & </s>
            <s xml:id="echoid-s4628" xml:space="preserve">in promptu; </s>
            <s xml:id="echoid-s4629" xml:space="preserve">eodem jure atque ab illis citatur ratio dupla, tripla, quadru-
              <lb/>
            pla, eodem in quam jure, citari etiam rationem duodecuplam, quale illud in di-
              <lb/>
            cta 23 propoſ. </s>
            <s xml:id="echoid-s4630" xml:space="preserve">A D ad R D; </s>
            <s xml:id="echoid-s4631" xml:space="preserve">item rationem 37 ad 23 ſive ſuperquatuordecu-
              <lb/>
            partientem vigeſimastertias ipſius A R ad R D in ſupraſcripta propoſitione 11,
              <lb/>
            cum idem ſit rationem, & </s>
            <s xml:id="echoid-s4632" xml:space="preserve">rationum terminos proponere. </s>
            <s xml:id="echoid-s4633" xml:space="preserve">nam iſtarum li-
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            nearum in expoſitis figurarum illarum generibus alia ratio nulla eſt. </s>
            <s xml:id="echoid-s4634" xml:space="preserve">Cum au-
              <lb/>
            tem numerorum uſus ſit in perveſtigandis iſtiuſmodi figurarum proprietati-
              <lb/>
            bus, ut his ducibus & </s>
            <s xml:id="echoid-s4635" xml:space="preserve">commõſtratoribus facilè & </s>
            <s xml:id="echoid-s4636" xml:space="preserve">perſpicuè res ipſas pernoſca-
              <lb/>
            mus, etiam neceſſe fuit in illarum deſcriptione numeros eoſdem adſcribere, ne
              <lb/>
            aliis obſcurum ſit, quod earum autoribus & </s>
            <s xml:id="echoid-s4637" xml:space="preserve">inventoribus clarum fuerit, namq́; </s>
            <s xml:id="echoid-s4638" xml:space="preserve">
              <lb/>
            hæc ipſa eſt vera & </s>
            <s xml:id="echoid-s4639" xml:space="preserve">Mathematica demonſtratio, propoſiti veritatem ab ipſis
              <lb/>
            cauſis repetere.</s>
            <s xml:id="echoid-s4640" xml:space="preserve"/>
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