Vitruvius, De architectura libri decem, 1567

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          <div xml:id="echoid-div850" type="section" level="2" n="161">
            <p>
              <s xml:id="echoid-s26736" xml:space="preserve">
                <pb o="356" file="514.01.388" n="388" rhead="LIBER"/>
              erit in eius capitulo digitorum. </s>
              <s xml:id="echoid-s26737" xml:space="preserve">5. </s>
              <s xml:id="echoid-s26738" xml:space="preserve">ſi pondo quatuor, digitorum 6. </s>
              <s xml:id="echoid-s26739" xml:space="preserve">ſi octo, digitorum 7. </s>
              <s xml:id="echoid-s26740" xml:space="preserve">*** de-
                <lb/>
              cempondo digitorum 8. </s>
              <s xml:id="echoid-s26741" xml:space="preserve">*** uiginti pondo digitorum. </s>
              <s xml:id="echoid-s26742" xml:space="preserve">10. </s>
              <s xml:id="echoid-s26743" xml:space="preserve">*** quadraginta pondo digitorum
                <lb/>
                <emph style="sc">XII.</emph>
              S. </s>
              <s xml:id="echoid-s26744" xml:space="preserve">K. </s>
              <s xml:id="echoid-s26745" xml:space="preserve">ſexaginta pondo, digitorum
                <emph style="sc">XIII.</emph>
              & </s>
              <s xml:id="echoid-s26746" xml:space="preserve">digiti octaua parte, octuaginta pondo, digito-
                <lb/>
              rum
                <emph style="sc">XV.</emph>
              *** centum uigintipondo pedis I. </s>
              <s xml:id="echoid-s26747" xml:space="preserve">S. </s>
              <s xml:id="echoid-s26748" xml:space="preserve">& </s>
              <s xml:id="echoid-s26749" xml:space="preserve">ſeſquidigiti *** centum, & </s>
              <s xml:id="echoid-s26750" xml:space="preserve">ſexaginta pondo,
                <lb/>
              pedum
                <emph style="sc">II.</emph>
              *** centum & </s>
              <s xml:id="echoid-s26751" xml:space="preserve">octuaginta pondo pedum
                <emph style="sc">II.</emph>
              & </s>
              <s xml:id="echoid-s26752" xml:space="preserve">digitorum
                <emph style="sc">V.</emph>
              ducenta pondo pedum
                <lb/>
                <emph style="sc">II.</emph>
              & </s>
              <s xml:id="echoid-s26753" xml:space="preserve">digitorum
                <emph style="sc">VI.</emph>
              ducenta decem pondo pedum
                <emph style="sc">II.</emph>
              & </s>
              <s xml:id="echoid-s26754" xml:space="preserve">digitorum
                <emph style="sc">VII.</emph>
              ***
                <emph style="sc">Cci</emph>
              . </s>
              <s xml:id="echoid-s26755" xml:space="preserve">pon-
                <lb/>
              do
                <emph style="sc">XI.</emph>
              S.</s>
              <s xml:id="echoid-s26756" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s26757" xml:space="preserve">Quoniam balistis ingentia ſaxorum pondera torqueb antur, ideo maiori apparatu, quam in catapultis opus
                <lb/>
                <handwritten xlink:label="hd-514.01.388-1" xlink:href="hd-514.01.388-1a" number="70"/>
              erat. </s>
              <s xml:id="echoid-s26758" xml:space="preserve">Cæterum & </s>
              <s xml:id="echoid-s26759" xml:space="preserve">in ipſis haliſtis diſcrimina ſunt, licent ad unum effctum omnes comparentur. </s>
              <s xml:id="echoid-s26760" xml:space="preserve">Diſcrimina illa
                <lb/>
              ex ponderum mittendorum diuerſitate ſumuntur, hinc eſt quod aliæ uectibus, & </s>
              <s xml:id="echoid-s26761" xml:space="preserve">ſuculis, quæ ſcilicet minora
                <lb/>
                <note position="left" xlink:label="note-514.01.388-01" xlink:href="note-514.01.388-01a" xml:space="preserve">10</note>
              ſaxa mittunt, nonnullæ trochleis multorum orbiculorum, aliæ ergatis, quædam etiam tympanis tor queantur.
                <lb/>
              </s>
              <s xml:id="echoid-s26762" xml:space="preserve">Balista igitur omnis ad propoſitam magnitudinem ponderis ſaxi, quod id organum mittere debet, perficienda
                <lb/>
              est. </s>
              <s xml:id="echoid-s26763" xml:space="preserve">Verum ea tatio non eſt omnibus expedita, niſi enim Geometria, & </s>
              <s xml:id="echoid-s26764" xml:space="preserve">Arithmetica adfuerit, uanus erit
                <lb/>
              labor, quoniam periculum eſt ne in eum errorem incidamus, quem illi incidere, qui cum cubum duplicare in-
                <lb/>
              stituiſſent, octuplum ſecere. </s>
              <s xml:id="echoid-s26765" xml:space="preserve">ita enim ſi ex hoc principio, quod experientia, & </s>
              <s xml:id="echoid-s26766" xml:space="preserve">obſeruatione inualuit, ut ſi dua-
                <lb/>
              pondo ſaxum quinum digitum ſoramen quærat, quis ratiocinetur quatuorpondo ſaxum denum digitum fora-
                <lb/>
              men habere debere, falletur demum ut pluſquam centum pedum ſunis, ſeu foraminis diametrum ſiciat, ſi ſa-
                <lb/>
              xum ducentorum & </s>
              <s xml:id="echoid-s26767" xml:space="preserve">quinquaginta pondo uelit torquere. </s>
              <s xml:id="echoid-s26768" xml:space="preserve">Cum neceſſe ſit ( ut ait Eratoſthenes ad Ptolomæum
                <lb/>
              regem in epiſtola, ſuperiori libro citata ) omnia proportione augeri, craſſitudines, magnitudines, foramina,
                <lb/>
              modtolos, & </s>
              <s xml:id="echoid-s26769" xml:space="preserve">neruos ingredientes, quæ ſine mediarum comparabilium inuentione fieri non poſſunt. </s>
              <s xml:id="echoid-s26770" xml:space="preserve">Atque
                <lb/>
                <note position="left" xlink:label="note-514.01.388-02" xlink:href="note-514.01.388-02a" xml:space="preserve">20</note>
              hæc nos iuuabunt, ſi Geometricis rationibus uti uelimus. </s>
              <s xml:id="echoid-s26771" xml:space="preserve">Sumatur enim diameter funis, ſeu ſoramiuis baliſtæ
                <lb/>
              quæ duapondo ſaxum mittere debet, & </s>
              <s xml:id="echoid-s26772" xml:space="preserve">ſit linea a b. </s>
              <s xml:id="echoid-s26773" xml:space="preserve">& </s>
              <s xml:id="echoid-s26774" xml:space="preserve">ſumatur linea c d. </s>
              <s xml:id="echoid-s26775" xml:space="preserve">dupla ipſi a b. </s>
              <s xml:id="echoid-s26776" xml:space="preserve">& </s>
              <s xml:id="echoid-s26777" xml:space="preserve">iuxta
                <lb/>
              aliquem modum ex ſupradictis in nono libro mediarum inueniendarum, capiantur mediæ comparabiles, & </s>
              <s xml:id="echoid-s26778" xml:space="preserve">ha
                <lb/>
              bebitur diameter funis baliſtæ, quæ quatuor pondo ſaxum mittere debet. </s>
              <s xml:id="echoid-s26779" xml:space="preserve">Verum ſinumeris ea ratio quærenda
                <lb/>
              eſt, ut Græci monent, ita erit ſciendum ut etiam animaduertit Ioannes Buteo qui ſic ait. </s>
              <s xml:id="echoid-s26780" xml:space="preserve">Cum lapis duapon-
                <lb/>
              do foramen habe at digitorum quinque, quæritur ad lapidem quatuor pondo quot digitorum debeat eſſe ſora-
                <lb/>
              men? </s>
              <s xml:id="echoid-s26781" xml:space="preserve">ad cubum redige 5. </s>
              <s xml:id="echoid-s26782" xml:space="preserve">hoc est ducas in ſe, postea in productum, fit cubus 125. </s>
              <s xml:id="echoid-s26783" xml:space="preserve">cum itaque uideas ad
                <lb/>
              duapondo diametrum ſoraminis dari, quæ ſua cubicatione producat 125. </s>
              <s xml:id="echoid-s26784" xml:space="preserve">ratione ſequitur, ut ad quatuor
                <lb/>
              pondo, quod eſt duplum 2. </s>
              <s xml:id="echoid-s26785" xml:space="preserve">tanta diametros adhibeatur, quæ ſua etiam cubicatione compleat numerum 250.
                <lb/>
              </s>
              <s xml:id="echoid-s26786" xml:space="preserve">qui duplus eſt cubi 125. </s>
              <s xml:id="echoid-s26787" xml:space="preserve">Sed quia 250 non eſt cubus ipſius, quod quæritur ad diametron, latus perfecte
                <lb/>
                <note position="left" xlink:label="note-514.01.388-03" xlink:href="note-514.01.388-03a" xml:space="preserve">30</note>
              dari non potest in numeris, cum non ſit in rerum natura. </s>
              <s xml:id="echoid-s26788" xml:space="preserve">Supereſt igitur ut huic propinquum numerum ra-
                <lb/>
              tiocinando diſquiras, quem inuenies eſſe maiorem quam 6. </s>
              <s xml:id="echoid-s26789" xml:space="preserve">quod eſt latus cubi 216. </s>
              <s xml:id="echoid-s26790" xml:space="preserve">maiorem etiam quam
                <lb/>
              ſex & </s>
              <s xml:id="echoid-s26791" xml:space="preserve">parte quarta, minorem autem, quàm ſex, & </s>
              <s xml:id="echoid-s26792" xml:space="preserve">tertia. </s>
              <s xml:id="echoid-s26793" xml:space="preserve">Ex his particulis tertia ſcilicet, & </s>
              <s xml:id="echoid-s26794" xml:space="preserve">quarta ſum-
                <lb/>
              pto dimidio, quod eſt ſeptem quartædecimæ, iunctoq; </s>
              <s xml:id="echoid-s26795" xml:space="preserve">ad ſex numerum habetis ſenarium, cum ſeptem uigeſimis
                <lb/>
              quartis, adeo ueritati propinquum, ut inde nullus, de quo ſit curandum, error oriri poſſit. </s>
              <s xml:id="echoid-s26796" xml:space="preserve">nam cubus lateris
                <lb/>
              ſex & </s>
              <s xml:id="echoid-s26797" xml:space="preserve">ſeptem uigeſimæ quartæ, est 249. </s>
              <s xml:id="echoid-s26798" xml:space="preserve">& </s>
              <s xml:id="echoid-s26799" xml:space="preserve">ex particulis 13824. </s>
              <s xml:id="echoid-s26800" xml:space="preserve">775. </s>
              <s xml:id="echoid-s26801" xml:space="preserve">dicimus itaque in balista, quæ
                <lb/>
              quatuor pondo mittere debet, ſoramen in eius capitulo fieri debere digitorum ſex, &</s>
              <s xml:id="echoid-s26802" xml:space="preserve">digiti ſeptem uigeſimiſ-
                <lb/>
              quartis. </s>
              <s xml:id="echoid-s26803" xml:space="preserve">Inquiramus autem lapidis decempondo foramen: </s>
              <s xml:id="echoid-s26804" xml:space="preserve">cum igitur hoc pondus ad duapondo ſit quincuplũ
                <lb/>
              ita & </s>
              <s xml:id="echoid-s26805" xml:space="preserve">cubum ſoraminis ipſius, ad cubum foraminis alterius, quincuplum eſſe oportet. </s>
              <s xml:id="echoid-s26806" xml:space="preserve">neque enim aliter in-
                <lb/>
              stituta proportio conſtat. </s>
              <s xml:id="echoid-s26807" xml:space="preserve">propterea iam poſitum cubum 125. </s>
              <s xml:id="echoid-s26808" xml:space="preserve">multiplico per 5. </s>
              <s xml:id="echoid-s26809" xml:space="preserve">& </s>
              <s xml:id="echoid-s26810" xml:space="preserve">colligo 625. </s>
              <s xml:id="echoid-s26811" xml:space="preserve">poſſum
                <lb/>
                <note position="left" xlink:label="note-514.01.388-04" xlink:href="note-514.01.388-04a" xml:space="preserve">40</note>
              etiam ad hoc ratiocinando regulam adhibere dicendo ſi pondo 2. </s>
              <s xml:id="echoid-s26812" xml:space="preserve">fiat 10. </s>
              <s xml:id="echoid-s26813" xml:space="preserve">quid 125. </s>
              <s xml:id="echoid-s26814" xml:space="preserve">Age multiplicando
                <lb/>
              125. </s>
              <s xml:id="echoid-s26815" xml:space="preserve">in 10. </s>
              <s xml:id="echoid-s26816" xml:space="preserve">& </s>
              <s xml:id="echoid-s26817" xml:space="preserve">productum. </s>
              <s xml:id="echoid-s26818" xml:space="preserve">1250. </s>
              <s xml:id="echoid-s26819" xml:space="preserve">partireper 2. </s>
              <s xml:id="echoid-s26820" xml:space="preserve">idemq; </s>
              <s xml:id="echoid-s26821" xml:space="preserve">quod prius inuenies, ſcilicet. </s>
              <s xml:id="echoid-s26822" xml:space="preserve">625. </s>
              <s xml:id="echoid-s26823" xml:space="preserve">Huius
                <lb/>
              cubitum latus, ad uerem accedens proxime eſt 8. </s>
              <s xml:id="echoid-s26824" xml:space="preserve">& </s>
              <s xml:id="echoid-s26825" xml:space="preserve">undecim uigeſimæ, unde prouenit cubus 625. </s>
              <s xml:id="echoid-s26826" xml:space="preserve">& </s>
              <s xml:id="echoid-s26827" xml:space="preserve">
                <lb/>
              211. </s>
              <s xml:id="echoid-s26828" xml:space="preserve">octomilenas. </s>
              <s xml:id="echoid-s26829" xml:space="preserve">Inuentum igitur ad lapidem pondo decem aptandum eſſe foramen digitorum octo, cum
                <lb/>
              undecim uigeſimis. </s>
              <s xml:id="echoid-s26830" xml:space="preserve">Quæ quidem particula digiti ſemiſſem excedit una uigeſima. </s>
              <s xml:id="echoid-s26831" xml:space="preserve">& </s>
              <s xml:id="echoid-s26832" xml:space="preserve">ſic ad omne datum pon-
                <lb/>
              dus rationibus cubicis ſoramina inueſtigari poſſunt. </s>
              <s xml:id="echoid-s26833" xml:space="preserve">Sed in his, quæ ab authore ponutur, demptis primo, & </s>
              <s xml:id="echoid-s26834" xml:space="preserve">
                <lb/>
              ultimo non niſi ſecundum proximitatem inuentio procedit quod & </s>
              <s xml:id="echoid-s26835" xml:space="preserve">intelligentiæ difficultatem, & </s>
              <s xml:id="echoid-s26836" xml:space="preserve">ratiocina-
                <lb/>
              tioni moleſtiam affert. </s>
              <s xml:id="echoid-s26837" xml:space="preserve">In multis tamen numeri for aminum perſecte conuniunt, ut pote ſi detur lapis pondo
                <lb/>
              ſexdecim for amen erit digitorum decem. </s>
              <s xml:id="echoid-s26838" xml:space="preserve">Quoniam cubus lateris 10. </s>
              <s xml:id="echoid-s26839" xml:space="preserve">quieſt 1000. </s>
              <s xml:id="echoid-s26840" xml:space="preserve">ad cubum lateris 5.
                <lb/>
              </s>
              <s xml:id="echoid-s26841" xml:space="preserve">qui est 125. </s>
              <s xml:id="echoid-s26842" xml:space="preserve">rationem habet, quam pondo ſesxdecim, ad duapondo, ideſt octuplam. </s>
              <s xml:id="echoid-s26843" xml:space="preserve">Item ad pondo 54. </s>
              <s xml:id="echoid-s26844" xml:space="preserve">ſo-
                <lb/>
                <note position="left" xlink:label="note-514.01.388-05" xlink:href="note-514.01.388-05a" xml:space="preserve">50</note>
              ramen erit digitorum quindecim ad pondo, 128. </s>
              <s xml:id="echoid-s26845" xml:space="preserve">digitorum 20. </s>
              <s xml:id="echoid-s26846" xml:space="preserve">hoc eſt pedis nuius, cum quadrante. </s>
              <s xml:id="echoid-s26847" xml:space="preserve">Ad
                <lb/>
              pondo 250. </s>
              <s xml:id="echoid-s26848" xml:space="preserve">quod eſt maximum in Vitruuio, pedis unius cum nouem digitis. </s>
              <s xml:id="echoid-s26849" xml:space="preserve">Docet præterea idem author,
                <lb/>
              quod datis quibuſlibet for aminum numeris, omne etiam pondus ipſorum in numeris dabitur abſolutè. </s>
              <s xml:id="echoid-s26850" xml:space="preserve">quorum
                <lb/>
              aliquot exempla ſubijcit. </s>
              <s xml:id="echoid-s26851" xml:space="preserve">Eſto foramen in balista digitorum ſex, cujus lapidem oporteat inuentire. </s>
              <s xml:id="echoid-s26852" xml:space="preserve">Accipe duos
                <lb/>
              cubos laterum 5. </s>
              <s xml:id="echoid-s26853" xml:space="preserve">& </s>
              <s xml:id="echoid-s26854" xml:space="preserve">6. </s>
              <s xml:id="echoid-s26855" xml:space="preserve">qui ſunt. </s>
              <s xml:id="echoid-s26856" xml:space="preserve">125. </s>
              <s xml:id="echoid-s26857" xml:space="preserve">& </s>
              <s xml:id="echoid-s26858" xml:space="preserve">216. </s>
              <s xml:id="echoid-s26859" xml:space="preserve">& </s>
              <s xml:id="echoid-s26860" xml:space="preserve">ita rationcinare. </s>
              <s xml:id="echoid-s26861" xml:space="preserve">Si 125. </s>
              <s xml:id="echoid-s26862" xml:space="preserve">fit 216. </s>
              <s xml:id="echoid-s26863" xml:space="preserve">quid duapon-
                <lb/>
              do? </s>
              <s xml:id="echoid-s26864" xml:space="preserve">& </s>
              <s xml:id="echoid-s26865" xml:space="preserve">productum partiens in 125. </s>
              <s xml:id="echoid-s26866" xml:space="preserve">prouenietq́; </s>
              <s xml:id="echoid-s26867" xml:space="preserve">357. </s>
              <s xml:id="echoid-s26868" xml:space="preserve">dicemus igitur foramini digitorum ſex deberi da-
                <lb/>
              pidem trapondo cum particula 125. </s>
              <s xml:id="echoid-s26869" xml:space="preserve">quæ quidem paulo maior eſt quincunce. </s>
              <s xml:id="echoid-s26870" xml:space="preserve">& </s>
              <s xml:id="echoid-s26871" xml:space="preserve">hoc modo datis foramini-
                <lb/>
              bus lapidum grauitatem ſemper habebis: </s>
              <s xml:id="echoid-s26872" xml:space="preserve">ut in ſemipedali foramine lapis erit octopondo cum 24. </s>
              <s xml:id="echoid-s26873" xml:space="preserve">centeſi-
                <lb/>
              mis uigeſimis quintis. </s>
              <s xml:id="echoid-s26874" xml:space="preserve">Inſemipedali, & </s>
              <s xml:id="echoid-s26875" xml:space="preserve">unius digiti pondo 11. </s>
              <s xml:id="echoid-s26876" xml:space="preserve">cum 83. </s>
              <s xml:id="echoid-s26877" xml:space="preserve">centum uigeſimis quintis in peda-
                <lb/>
              li pondo 65. </s>
              <s xml:id="echoid-s26878" xml:space="preserve">cum 67. </s>
              <s xml:id="echoid-s26879" xml:space="preserve">centum uigeſimis quintis, in palmo pedali centum uiginit octo, in ſeſquipedali pon-
                <lb/>
                <note position="left" xlink:label="note-514.01.388-06" xlink:href="note-514.01.388-06a" xml:space="preserve">60</note>
              </s>
            </p>
          </div>
        </div>
      </text>
    </echo>
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