Clavius, Christoph, Geometria practica

Page concordance

< >
Scan Original
241 211
242 212
243 213
244 214
245 215
246 216
247 217
248 218
249 219
250 220
251 221
252 222
253 223
254 224
255 225
256 226
257 227
258 228
259 229
260 230
261 231
262 232
263 233
264 234
265 235
266 236
267 237
268 238
269 239
270 240
< >
page |< < (237) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div684" type="section" level="1" n="241">
          <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>
        </div>
        <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>
          </p>
        </div>
      </text>
    </echo>
Impressum