Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s11078" xml:space="preserve">
              <pb o="237" file="267" n="267" rhead="LIBER SEXTVS."/>
            nerefertiſſimus. </s>
            <s xml:id="echoid-s11079" xml:space="preserve">Idem verò poſtea argumentum alia via aggreſſus eſt,
              <lb/>
            & </s>
            <s xml:id="echoid-s11080" xml:space="preserve">meo certè iudicio, faciliori & </s>
            <s xml:id="echoid-s11081" xml:space="preserve">magis generali, Simon Steuinius
              <lb/>
            Brugenſis: </s>
            <s xml:id="echoid-s11082" xml:space="preserve">ſed in qua aliquid deſiderari videatur, vt omnibus ſuper-
              <lb/>
            ficiebus rectilineis (quodipſe velle videtur) conuenire poſſit. </s>
            <s xml:id="echoid-s11083" xml:space="preserve">quod
              <lb/>
            facilè iudicabunt, qui illius problemata Geometrica attentè perlege-
              <lb/>
            rint. </s>
            <s xml:id="echoid-s11084" xml:space="preserve">Res enim propoſita nulla ratione confici poteſt, niſi prius duæ
              <lb/>
            propoſitiones demonſtrentur, quarum priorem ipſe ſine demonſtra-
              <lb/>
            tione aſſumit pro principio, poſterioris verò ne meminit quidem,
              <lb/>
            cum tamen admodum ſit neceſſaria, & </s>
            <s xml:id="echoid-s11085" xml:space="preserve">quam Machometus Bagdedi-
              <lb/>
            nus demonſtrauit paulò aliter, quam nos. </s>
            <s xml:id="echoid-s11086" xml:space="preserve">Has ergo duas propoſitiones
              <lb/>
            ad initium huius lib. </s>
            <s xml:id="echoid-s11087" xml:space="preserve">demonſtrabimus, & </s>
            <s xml:id="echoid-s11088" xml:space="preserve">poſteriorem quidem longè
              <lb/>
            generalius, quam à Machometo factum eſt. </s>
            <s xml:id="echoid-s11089" xml:space="preserve">quod beneuolo Lecto-
              <lb/>
            ri iudicandum relinquo. </s>
            <s xml:id="echoid-s11090" xml:space="preserve">Deindè
              <unsure/>
            ſuperficierum rectilinearum diui-
              <lb/>
            ſionem aggrediemur, inſiſtentes eiuſdem Steuinii veſtigiis, niſi quan-
              <lb/>
            do generalius rem oportebit demonſtrare. </s>
            <s xml:id="echoid-s11091" xml:space="preserve">Nihil autem deratione Ma-
              <lb/>
            chometi, & </s>
            <s xml:id="echoid-s11092" xml:space="preserve">Federici Commandini dicemus: </s>
            <s xml:id="echoid-s11093" xml:space="preserve">tum quia libellus ipſo-
              <lb/>
            rum in manibus omnium eſt, ac propterea eum, quicunque vo-
              <lb/>
            let, legere poterit: </s>
            <s xml:id="echoid-s11094" xml:space="preserve">tum quia propoſita aliqua figura multorum an-
              <lb/>
            gulorum, non ſine difficultate, ac labore eam ſtudioſus diuidet, ni-
              <lb/>
            ſi diuiſionis omnium præcedentium figurarum memor ſit, quod in
              <lb/>
            noſtra ratione non accidit: </s>
            <s xml:id="echoid-s11095" xml:space="preserve">tum denique quia illorum ratio ſolum fi-
              <lb/>
            guris ordinariis conuenit, quæ videlicet omnes angulos habent intror-
              <lb/>
            ſum, tot nimirũ, quotlatera figura ipſa continet, noſtra autem via figuras
              <lb/>
            etiamillas complectitur, quæ angulos habent partim introrſum, & </s>
            <s xml:id="echoid-s11096" xml:space="preserve">par-
              <lb/>
            tim extrorſum vergentes.</s>
            <s xml:id="echoid-s11097" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div686" type="section" level="1" n="242">
          <head xml:id="echoid-head267" xml:space="preserve">THOREMA 1. PROPOSITIO 1.</head>
          <p>
            <s xml:id="echoid-s11098" xml:space="preserve">SI magnitudo in quotuis partes ſecetur vtcunque, & </s>
            <s xml:id="echoid-s11099" xml:space="preserve">alia quæpiam ma-
              <lb/>
            gnitudo in totidem partes ordine illis proportionales: </s>
            <s xml:id="echoid-s11100" xml:space="preserve">habebunt
              <lb/>
            quotlibet partes prioris magnitudinis ſimul ad reliquas omnes par-
              <lb/>
            tes ſimul eandem proportionem, quam totidem partes poſterioris
              <lb/>
            magnitudinis ſimul ad reliquas omnes partes ſimul. </s>
            <s xml:id="echoid-s11101" xml:space="preserve">Et ſi quælibet
              <lb/>
            pars prioris magnitudinis ſecetur in duas partes vtcunque, ſecetur
              <lb/>
            autem & </s>
            <s xml:id="echoid-s11102" xml:space="preserve">pars poſterioris magnitudinis illi parti reſpondens in alias
              <lb/>
            duas partes
              <unsure/>
            duabus illis proportionales: </s>
            <s xml:id="echoid-s11103" xml:space="preserve">erunt quoque ibidem to-
              <lb/>
            tæ magnitudines ſectæ proportionaliter.</s>
            <s xml:id="echoid-s11104" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11105" xml:space="preserve">
              <emph style="sc">Sit</emph>
            magnitudo A B, ſecta in quotuis partes vtcunque A C, C D, D E, EF,
              <lb/>
            F B: </s>
            <s xml:id="echoid-s11106" xml:space="preserve">& </s>
            <s xml:id="echoid-s11107" xml:space="preserve">alia magnitudo qualiſcunque G H, etiamſi diuerſi ſit generis, ſecta </s>
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