Clavius, Christoph, Geometria practica

List of thumbnails

< >
361
361 (331) 		362
362 (332)
363
363 (333) 		364
364 (334)
365
365 (335) 		366
366 (336)
367
367 (339) 		368
368 (340)
369
369 (341) 		370
370 (342)
< >
page |< < (341) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div978" type="section" level="1" n="348">
          <p>
            <s xml:id="echoid-s15850" xml:space="preserve">
              <pb o="341" file="369" n="369" rhead="LIBER OCTAVVS."/>
            ctum B, cadat neceſſariò in punctum C, vbiangulus ACF, (quem Perſpectiui
              <lb/>
            angulum incidentiæ dicunt.) </s>
            <s xml:id="echoid-s15851" xml:space="preserve">æqualis efficitur angulo BCD, quem reflexionis
              <lb/>
            appellant. </s>
            <s xml:id="echoid-s15852" xml:space="preserve">Nam ſi radius caderet in D, vel F, reflecteretur que ad B, non ageret
              <lb/>
            Natura per lineas breuiſsimas; </s>
            <s xml:id="echoid-s15853" xml:space="preserve">cum tam AD, BD, quam AF, BF, longiores ſint,
              <lb/>
            quam AC, BC vt demonſtrauimus. </s>
            <s xml:id="echoid-s15854" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s15855" xml:space="preserve">Atque ita demonſtra-
              <lb/>
            tum eſt, quod Perſpectiui aſſumunt, angulum ſcilicet incidentiæ æqualem eſſe
              <lb/>
            angulo reflexionis.</s>
            <s xml:id="echoid-s15856" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div979" type="section" level="1" n="349">
          <head xml:id="echoid-head376" xml:space="preserve">PROBL. 4. PROPOS. 8.</head>
          <p>
            <s xml:id="echoid-s15857" xml:space="preserve">SI quis numerum mente conceperit, quot ei vnitates poſttres operatio-
              <lb/>
            nes imperatas reliquæ ſint, coniicere.</s>
            <s xml:id="echoid-s15858" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15859" xml:space="preserve">
              <emph style="sc">Ivbe</emph>
            conceptum numerum per quemcunque numerum, vt per 2. </s>
            <s xml:id="echoid-s15860" xml:space="preserve">vel 3. </s>
            <s xml:id="echoid-s15861" xml:space="preserve">vel
              <lb/>
            4. </s>
            <s xml:id="echoid-s15862" xml:space="preserve">vel 10. </s>
            <s xml:id="echoid-s15863" xml:space="preserve">&</s>
            <s xml:id="echoid-s15864" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15865" xml:space="preserve">multiplicari, & </s>
            <s xml:id="echoid-s15866" xml:space="preserve">producto adde tu quemlibet numerum à numero
              <lb/>
            multiplicante numeratum. </s>
            <s xml:id="echoid-s15867" xml:space="preserve">Deinde iube ex parte aliquota ſummę totius à mul-
              <lb/>
            tiplicante numero denominata auferri ſimilem partem aliquotam numeri pro-
              <lb/>
            ducti ex multiplicante in numerum conceptum, hoc eſt, ipſum numerum
              <lb/>
            conceptum. </s>
            <s xml:id="echoid-s15868" xml:space="preserve">Ita enim reliquus numerus erit ſimilis pars aliquota numeri, quem
              <lb/>
            adiunxiſti. </s>
            <s xml:id="echoid-s15869" xml:space="preserve">Cum ergo numerus adiunctus tibi notus ſit, habeatque partem
              <lb/>
            aliquotam à numero multiplicante denominatam, ac proinde tibi cognitam:
              <lb/>
            </s>
            <s xml:id="echoid-s15870" xml:space="preserve">dices reliquas vnitates illam partem aliquotam conficere. </s>
            <s xml:id="echoid-s15871" xml:space="preserve">Exempli gratia. </s>
            <s xml:id="echoid-s15872" xml:space="preserve">
              <lb/>
            Concipiataliquis numerum 4. </s>
            <s xml:id="echoid-s15873" xml:space="preserve">iube multiplicari per 6. </s>
            <s xml:id="echoid-s15874" xml:space="preserve">fiunt 24. </s>
            <s xml:id="echoid-s15875" xml:space="preserve">iube addi nu-
              <lb/>
            merum 30. </s>
            <s xml:id="echoid-s15876" xml:space="preserve">à multiplicante 6. </s>
            <s xml:id="echoid-s15877" xml:space="preserve">numeratum, fiunt 54. </s>
            <s xml:id="echoid-s15878" xml:space="preserve">Ex ſexta parte huius ſummæ
              <lb/>
            denominata à multiplicante numero 6. </s>
            <s xml:id="echoid-s15879" xml:space="preserve">id eſt, ex 9. </s>
            <s xml:id="echoid-s15880" xml:space="preserve">fac detrahi partem quoque
              <lb/>
            ſextam prioris numeri producti 24. </s>
            <s xml:id="echoid-s15881" xml:space="preserve">nimirum 4. </s>
            <s xml:id="echoid-s15882" xml:space="preserve">videlicetipſum numerum con-
              <lb/>
            ceptum. </s>
            <s xml:id="echoid-s15883" xml:space="preserve">Ita namque remanet ſexta pars numeri adiuncti 30. </s>
            <s xml:id="echoid-s15884" xml:space="preserve">nimirum 5. </s>
            <s xml:id="echoid-s15885" xml:space="preserve">quod
              <lb/>
            in hunc modum demonſtratur.</s>
            <s xml:id="echoid-s15886" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15887" xml:space="preserve">
              <emph style="sc">Sit</emph>
            conceptus numerus A, quo ducto verbi gratia in 6. </s>
            <s xml:id="echoid-s15888" xml:space="preserve">gignatur B, & </s>
            <s xml:id="echoid-s15889" xml:space="preserve">ad-
              <lb/>
            dito F, fiat ſumma C. </s>
            <s xml:id="echoid-s15890" xml:space="preserve">Ex E, parte aliquota ſum-
              <lb/>
            mæ C, denominata à 6. </s>
            <s xml:id="echoid-s15891" xml:space="preserve">detrahatur D, pars ali-
              <lb/>
              <note position="right" xlink:label="note-369-01" xlink:href="note-369-01a" xml:space="preserve">
                <lb/>
              A # B # C # F
                <lb/>
              4 # 24 # 54 # 30
                <lb/>
              # D # E # G
                <lb/>
              # 4. # 9. # 5.
                <lb/>
              </note>
            quota prioris producti B, denominata quo-
              <lb/>
            que à 6. </s>
            <s xml:id="echoid-s15892" xml:space="preserve">hoc eſt, ipſemet numerus conceptus
              <lb/>
            A, reliquuſque fiat numerus G, quem dico par-
              <lb/>
            tem eſſe aliquotam numeri a diuncti F, à nume-
              <lb/>
            ro quoque 6. </s>
            <s xml:id="echoid-s15893" xml:space="preserve">denominatam. </s>
            <s xml:id="echoid-s15894" xml:space="preserve">Quoniam enim
              <lb/>
            ita eſt multiplex totus C, totius E, vt ablatus
              <lb/>
            B, ex C, ipſius D, ex E, ablati, quippe cum po-
              <lb/>
            natur E, talis pars ipſius C, qualis D, ipſius B,
              <lb/>
            denominata videlicet à 6. </s>
            <s xml:id="echoid-s15895" xml:space="preserve"> Igitur erit quoquereliquus F, (detracto
              <note symbol="a" position="right" xlink:label="note-369-02" xlink:href="note-369-02a" xml:space="preserve">ſchol. 7.
                <lb/>
              ſeptimi.</note>
            producto B, ex ſumma C,) ita multiplex reliqui G, (dempto ſcilicet D, ex E,)
              <lb/>
            vttotus C, totius E. </s>
            <s xml:id="echoid-s15896" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s15897" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15898" xml:space="preserve">
              <emph style="sc">Est</emph>
            autem iucundum, hoc idem coniici poſſe inter plures. </s>
            <s xml:id="echoid-s15899" xml:space="preserve">Nam ſi plures
              <lb/>
            concipiant mente numeros, ſinguli videlicet ſingulos, nullo eorum conſcio,
              <lb/>
            quem quiſq; </s>
            <s xml:id="echoid-s15900" xml:space="preserve">numerum conceperit; </s>
            <s xml:id="echoid-s15901" xml:space="preserve">& </s>
            <s xml:id="echoid-s15902" xml:space="preserve">iubeas quemlibet ſuum numerum multi-
              <lb/>
            pl@care per quemuis numerum à te electum; </s>
            <s xml:id="echoid-s15903" xml:space="preserve">deinde addere numerũ à tuo </s>
          </p>
        </div>
      </text>
    </echo>
Impressum