Vitruvius, De architectura libri decem, 1567

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          <div xml:id="echoid-div819" type="section" level="2" n="153">
            <p>
              <s xml:id="echoid-s26079" xml:space="preserve">
                <pb o="345" file="514.01.377" n="377" rhead="DECIMVS."/>
              loro traiecto fit una pars iugi longior, quæ imbecilliori au x iliatur iumento. </s>
              <s xml:id="echoid-s26080" xml:space="preserve">Ita in phalangis, ut
                <lb/>
              in iugis, cum in medio lora non ſunt collocata, ſed eam partem, qua progreditur lorum, a medio
                <lb/>
              centro breuiorem eſſicit, & </s>
              <s xml:id="echoid-s26081" xml:space="preserve">altera longiorem, ea ratione, ſi per id centrum, quo loci perductum eſt
                <lb/>
              lorum, utraque capita circumagentur, longior pars ampliorem, breouir minorem aget circinationem,
                <lb/>
              & </s>
              <s xml:id="echoid-s26082" xml:space="preserve">quemadmodum minores rotæ duriores, & </s>
              <s xml:id="echoid-s26083" xml:space="preserve">difficiliores habent motus, ſic phalanga, & </s>
              <s xml:id="echoid-s26084" xml:space="preserve">iuga, in qui-
                <lb/>
              bus partibus habent minora ab centro ad capita interualla, premunt duriter colla, quæ autem longio-
                <lb/>
              ra habent ab eodem centro ſpatia, leuant, oneribus extrahentes, & </s>
              <s xml:id="echoid-s26085" xml:space="preserve">ferentes. </s>
              <s xml:id="echoid-s26086" xml:space="preserve">Cum hæc ita ad centrum
                <lb/>
              porrectionibus, & </s>
              <s xml:id="echoid-s26087" xml:space="preserve">circinationibus receperint motus, tum uero etiam ploſtra, rhedæ, tympana, rotæ
                <lb/>
              cohleæ, ſcorpiones, baliſtæ, prela, cæteręq́; </s>
              <s xml:id="echoid-s26088" xml:space="preserve">machinæ ijsdem rationibus per porrectum centrum & </s>
              <s xml:id="echoid-s26089" xml:space="preserve">ro-
                <lb/>
                <note position="left" xlink:label="note-514.01.377-01" xlink:href="note-514.01.377-01a" xml:space="preserve">10</note>
              tationem circini uerſatæ, faciunt ad propoſitum effectus.</s>
              <s xml:id="echoid-s26090" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s26091" xml:space="preserve">Documentum hoc pulcherrimum reliquit Vitr. </s>
              <s xml:id="echoid-s26092" xml:space="preserve">porrectum, & </s>
              <s xml:id="echoid-s26093" xml:space="preserve">circularem motum eſſe omnium machina-
                <lb/>
              tionum principia, & </s>
              <s xml:id="echoid-s26094" xml:space="preserve">qui in eo genere internoſcet, quid oneri reſpondeat, pro quo ſit uectis, quale ſit hypomo-
                <lb/>
              chlium, unde uis mouens habeatur, eum omnibus propoſitis ea de re, quæstionibus ſatisfacturum. </s>
              <s xml:id="echoid-s26095" xml:space="preserve">Restat au-
                <lb/>
              tem, ut aliquid de rotis, & </s>
              <s xml:id="echoid-s26096" xml:space="preserve">cochleis dicamus, in quibus maximæ inſunt uirtutes, & </s>
              <s xml:id="echoid-s26097" xml:space="preserve">penè incredibiles motio-
                <lb/>
              num rationes, ut Cardanus docet. </s>
              <s xml:id="echoid-s26098" xml:space="preserve">Cochleæ ſimilibus rationibus perficiuntur. </s>
              <s xml:id="echoid-s26099" xml:space="preserve">Eſto cochlea A E. </s>
              <s xml:id="echoid-s26100" xml:space="preserve">tan-
                <lb/>
              quam fœmina, maſculus uero C D. </s>
              <s xml:id="echoid-s26101" xml:space="preserve">qui circumuertitur: </s>
              <s xml:id="echoid-s26102" xml:space="preserve">Eſto manubrium maſculo coniunctum E F. </s>
              <s xml:id="echoid-s26103" xml:space="preserve">quod
                <lb/>
              axe uertitur G H. </s>
              <s xml:id="echoid-s26104" xml:space="preserve">quàm facillime ob uectium rationem. </s>
              <s xml:id="echoid-s26105" xml:space="preserve">Appendatur ab imo maſculi onus librarum cen-
                <lb/>
              tum, quod ſit M. </s>
              <s xml:id="echoid-s26106" xml:space="preserve">verſando igitur axem G H. </s>
              <s xml:id="echoid-s26107" xml:space="preserve">Extolletur k L. </s>
              <s xml:id="echoid-s26108" xml:space="preserve">& </s>
              <s xml:id="echoid-s26109" xml:space="preserve">vnus M, ſubleuabitur. </s>
              <s xml:id="echoid-s26110" xml:space="preserve">& </s>
              <s xml:id="echoid-s26111" xml:space="preserve">contra-
                <lb/>
              rio modo uerſatione eiuſdem axis propelletur k L, inflectetq́; </s>
              <s xml:id="echoid-s26112" xml:space="preserve">ferrum obiectum immenſæ craſſitudinis. </s>
              <s xml:id="echoid-s26113" xml:space="preserve">Re-
                <lb/>
                <note position="left" xlink:label="note-514.01.377-02" xlink:href="note-514.01.377-02a" xml:space="preserve">20</note>
              liquum eſt ut ostendamus, quod onus M, moueri poſſit, & </s>
              <s xml:id="echoid-s26114" xml:space="preserve">quaratione id efficiatur. </s>
              <s xml:id="echoid-s26115" xml:space="preserve">nam cum uerbi gratia
                <lb/>
              centum millia pondo ſit in L, & </s>
              <s xml:id="echoid-s26116" xml:space="preserve">cum ſpira quæq́; </s>
              <s xml:id="echoid-s26117" xml:space="preserve">ſuam oneris partem ſuſtineat, ſi erunt decem ſpiræ in ſin-
                <lb/>
              gulis, erunt decem millia ponderis, uerum in qualibet ſpira tantum ponderant decem mille libræ, quanta est
                <lb/>
              proportio rotunditatis ad funam, cui ſuſpenditur onus M. </s>
              <s xml:id="echoid-s26118" xml:space="preserve">quanto igitur in C D, plures fuerint ſpiræ ac
                <lb/>
              circulo proximiores, tum maiores, eo M, pondus leuius reddetur, motusq́; </s>
              <s xml:id="echoid-s26119" xml:space="preserve">facilior, ac quanto facilior eo
                <lb/>
              tardior, igitur in ſpatio duorum cubitorum cochlea fieri potest, tam latis, ac humilibus ſpiris ut M. </s>
              <s xml:id="echoid-s26120" xml:space="preserve">pon-
                <lb/>
              dus a decenni puero facile ſurſum trahatur, uerum ( ut dixi ) quo facilius, eo lentius mouebitur. </s>
              <s xml:id="echoid-s26121" xml:space="preserve">cum igi-
                <lb/>
              tur tractum fuerit iuxta L K, longitudinem, oportebit M, ſuſpendi his, quæmachinam ſuſtinent in N & </s>
              <s xml:id="echoid-s26122" xml:space="preserve">
                <lb/>
              O. </s>
              <s xml:id="echoid-s26123" xml:space="preserve">& </s>
              <s xml:id="echoid-s26124" xml:space="preserve">tunc, iterum emiſſa contrario motu K L, adijcimus pondus. </s>
              <s xml:id="echoid-s26125" xml:space="preserve">Rurſumq́; </s>
              <s xml:id="echoid-s26126" xml:space="preserve">trahemus, eleuabimusq;
                <lb/>
              </s>
              <s xml:id="echoid-s26127" xml:space="preserve">ſpatio K L. </s>
              <s xml:id="echoid-s26128" xml:space="preserve">donec nectendo ſæpius e mari, uel e flumine, pondusve aliud immenſum extrahemus. </s>
              <s xml:id="echoid-s26129" xml:space="preserve">
                <lb/>
                <note position="left" xlink:label="note-514.01.377-03" xlink:href="note-514.01.377-03a" xml:space="preserve">30</note>
              Hæc cardanus. </s>
              <s xml:id="echoid-s26130" xml:space="preserve">de cochleis, qui etiam ad currus, & </s>
              <s xml:id="echoid-s26131" xml:space="preserve">rotas tranſiens dicit. </s>
              <s xml:id="echoid-s26132" xml:space="preserve">Qui currus altas habent rotas,
                <lb/>
              in molli ſolo facillime, ac celerrime mouentur, quod hærens lutum rotarum minimam occupet partem: </s>
              <s xml:id="echoid-s26133" xml:space="preserve">atque
                <lb/>
              ideo parum impediat. </s>
              <s xml:id="echoid-s26134" xml:space="preserve">Semper etiam maior rota celerius ſpatium ſuper at, ubi ferendo ſufficiat oneri. </s>
              <s xml:id="echoid-s26135" xml:space="preserve">Quin-
                <lb/>
              to etiam pauciores, eo perficitur celerius iter. </s>
              <s xml:id="echoid-s26136" xml:space="preserve">Nam plures, ſi paruæ ſunt, minore ambitu minus conficiunt
                <lb/>
              ſpatij, ſi magnæ addunt uiribus grauitatem, nec tamen plus amplectuntur ſpatij, hinc ad motiones tardæſunt,
                <lb/>
              quamobrem Imperatores Remani Eſſedæ ideſt curru duarum magnarum rotarum uehebantur, nam ubi onus
                <lb/>
              non nimis graue eſt, aut pluribus equis trahitur, aut celerius iter agitur. </s>
              <s xml:id="echoid-s26137" xml:space="preserve">Hac de cauſa noſtræ machinæpi-
                <lb/>
              robaliſtæ, quæ maxima habent onera duabus rotis trahuntur. </s>
              <s xml:id="echoid-s26138" xml:space="preserve">In ſolido uero plures rotæ eædemq́; </s>
              <s xml:id="echoid-s26139" xml:space="preserve">paruæ
                <lb/>
              ad facilitatem faciunt, diuiditur enim onus per rotas, unde additio, non multiplicatio fit earum proportio-
                <lb/>
              num. </s>
              <s xml:id="echoid-s26140" xml:space="preserve">Ecce exemplum ſi ſex duplæ inuicem multiplicentur, rationem reddunt quam habent ſexaginta qua-
                <lb/>
              tuor ad unum, eædem ſimul cunctæ duodecuplam conſtituunt, nanque magnum eſt diſcrimen, inter multipli-
                <lb/>
                <note position="left" xlink:label="note-514.01.377-04" xlink:href="note-514.01.377-04a" xml:space="preserve">40</note>
              cationem, & </s>
              <s xml:id="echoid-s26141" xml:space="preserve">additionem. </s>
              <s xml:id="echoid-s26142" xml:space="preserve">Quod igitur una rota pondus refert 64, ſex in rotis duodecim tantum æquiualet.
                <lb/>
              </s>
              <s xml:id="echoid-s26143" xml:space="preserve">Sed neſcio ego an Cardani opinio ſuos habeat numeros.</s>
              <s xml:id="echoid-s26144" xml:space="preserve"/>
            </p>
          </div>
          <div xml:id="echoid-div831" type="section" level="2" n="154">
            <head xml:id="echoid-head162" style="it" xml:space="preserve">De organorum ad aquam hauriendam generibus, & pri-
              <lb/>
            mum de tympano. # Cap. IX.</head>
            <p>
              <s xml:id="echoid-s26145" xml:space="preserve">
                <emph style="sc">Nvnc</emph>
              de organis, quæ ad hauriendam aquam inuenta ſunt, quemadmodum uarijs generi-
                <lb/>
              bus comparentur, exponam. </s>
              <s xml:id="echoid-s26146" xml:space="preserve">Et primum dicam de tympano. </s>
              <s xml:id="echoid-s26147" xml:space="preserve">Id autem non alte tollit
                <lb/>
              aquam, ſed exhaurit expeditiſsime multitudinem magnam. </s>
              <s xml:id="echoid-s26148" xml:space="preserve">Fit axis ad tornum aut ad
                <lb/>
                <note position="left" xlink:label="note-514.01.377-05" xlink:href="note-514.01.377-05a" xml:space="preserve">50</note>
              circinum fabricatus capitibus lamina ferratis, habens in medio circa ſe tympanum ex ta-
                <lb/>
              bulis inter ſe coagmentatis, collocaturq́; </s>
              <s xml:id="echoid-s26149" xml:space="preserve">in ſtipitibus habentibus in ſe ſub capite axis ferreas laminas.
                <lb/>
              </s>
              <s xml:id="echoid-s26150" xml:space="preserve">In eius tympani cauo interponuntur octo tabulæ tranſuerſæ, tangentes axem, & </s>
              <s xml:id="echoid-s26151" xml:space="preserve">extremam tympa-
                <lb/>
              ni circuitionem, quæ diuidunt æqualia in tympano ſpatia. </s>
              <s xml:id="echoid-s26152" xml:space="preserve">circa fron@em eius figuntur tabulæ, reli-
                <lb/>
              ctis ſemipedalibus aperturis ad aquam intra concipiendam. </s>
              <s xml:id="echoid-s26153" xml:space="preserve">Item ſecundum axem columbaria fiunt,
                <lb/>
              excauata in ſingulis ſpatijs ex una parte. </s>
              <s xml:id="echoid-s26154" xml:space="preserve">Id autem cum eſt nauali ratione picatum, hominibus cal-
                <lb/>
              cantibus uerſatur, & </s>
              <s xml:id="echoid-s26155" xml:space="preserve">hauriendo aquam per aperturas, quæ ſuntin frontibus tympani, reddit eam per
                <lb/>
              columbaria ſecundum axem. </s>
              <s xml:id="echoid-s26156" xml:space="preserve">Ita ſuppoſito labro ligneo, habente unà ſecum coniunctum canalem,
                <lb/>
              & </s>
              <s xml:id="echoid-s26157" xml:space="preserve">hortis ad irrigandum, & </s>
              <s xml:id="echoid-s26158" xml:space="preserve">ſalinis ad temperandum prębetur aquæ multitudo. </s>
              <s xml:id="echoid-s26159" xml:space="preserve">Cum autem altius ex-
                <lb/>
              tollendum erit, eadem ratio commutabitur ſic. </s>
              <s xml:id="echoid-s26160" xml:space="preserve">Rota fiet circum axem eadem magnitudine, ut ad al-
                <lb/>
                <note position="left" xlink:label="note-514.01.377-06" xlink:href="note-514.01.377-06a" xml:space="preserve">60</note>
              </s>
            </p>
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