Vitruvius, De architectura libri decem, 1567

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          <div xml:id="echoid-div429" type="section" level="2" n="76">
            <p>
              <s xml:id="echoid-s12256" xml:space="preserve">
                <pb o="157" file="514.01.189" n="189" rhead="QVINTVS."/>
              ceptorum late uagantes ſcripturæ, ſi non contrahantur, & </s>
              <s xml:id="echoid-s12257" xml:space="preserve">paucis, & </s>
              <s xml:id="echoid-s12258" xml:space="preserve">perlucidis ſententijs explicentur.
                <lb/>
              </s>
              <s xml:id="echoid-s12259" xml:space="preserve">ſrequentia multitudineq́; </s>
              <s xml:id="echoid-s12260" xml:space="preserve">ſermonis impediente, incertas legentium efficient cogitationes.</s>
              <s xml:id="echoid-s12261" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s12262" xml:space="preserve">Quod hic dicit {frequentia, multitudineq́; </s>
              <s xml:id="echoid-s12263" xml:space="preserve">ſermonis} declarat illud quod initio dixit. </s>
              <s xml:id="echoid-s12264" xml:space="preserve">{Qui amplioribus
                <lb/>
              uoluminibus.</s>
              <s xml:id="echoid-s12265" xml:space="preserve">} cuius oppoſitum eſt uerbum illud {Sinon contrahantur, & </s>
              <s xml:id="echoid-s12266" xml:space="preserve">paucis, & </s>
              <s xml:id="echoid-s12267" xml:space="preserve">perlucidis ſententijs
                <lb/>
              explicentur.</s>
              <s xml:id="echoid-s12268" xml:space="preserve">} Doccndo igitur eße breues oportet. </s>
              <s xml:id="echoid-s12269" xml:space="preserve">breuitas enim memoriæ opitulatur, cauendum tamen est
                <lb/>
              ne breuitati ſtudentes obſcuri ſimus. </s>
              <s xml:id="echoid-s12270" xml:space="preserve">offenderetur enim intelligentia. </s>
              <s xml:id="echoid-s12271" xml:space="preserve">quare ut breuitas, ſic intelligentiæ per-
                <lb/>
              ſpicuitas prodeſt. </s>
              <s xml:id="echoid-s12272" xml:space="preserve">utramque rem, ſcilicet & </s>
              <s xml:id="echoid-s12273" xml:space="preserve">breuitatem, & </s>
              <s xml:id="echoid-s12274" xml:space="preserve">perſpicuitatem tangit Vitr. </s>
              <s xml:id="echoid-s12275" xml:space="preserve">quæ ſi non adſunt in
                <lb/>
              ſcriptis {incertas legentium efficient cogitationes.</s>
              <s xml:id="echoid-s12276" xml:space="preserve">} intelligit autem per hoc uerbum cogitationes internas
                <lb/>
              animi partes, memoriam, & </s>
              <s xml:id="echoid-s12277" xml:space="preserve">intelligentiam. </s>
              <s xml:id="echoid-s12278" xml:space="preserve">infra dixit: </s>
              <s xml:id="echoid-s12279" xml:space="preserve">mentes.</s>
              <s xml:id="echoid-s12280" xml:space="preserve"/>
            </p>
            <note position="left" xml:space="preserve">10</note>
            <p>
              <s xml:id="echoid-s12281" xml:space="preserve">
                <emph style="sc">Itaqve</emph>
              occultas nominationes, commenſusq́;</s>
              <s xml:id="echoid-s12282" xml:space="preserve">, e membris operum pronuncians, ut memoriæ
                <lb/>
              tradantur breuiter exponam. </s>
              <s xml:id="echoid-s12283" xml:space="preserve"># Debebat dicere breuiter, & </s>
              <s xml:id="echoid-s12284" xml:space="preserve">dilucide exponam, ut utrique parti re-
                <lb/>
              ſponderet.</s>
              <s xml:id="echoid-s12285" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s12286" xml:space="preserve">
                <emph style="sc">Sic</emph>
              enim expeditius ea recipere poterunt mentes. </s>
              <s xml:id="echoid-s12287" xml:space="preserve">Non minus cum animaduertiſſem diſtentam
                <lb/>
              occupationibus ciuitatem publicis, & </s>
              <s xml:id="echoid-s12288" xml:space="preserve">priuatis: </s>
              <s xml:id="echoid-s12289" xml:space="preserve">negotijs: </s>
              <s xml:id="echoid-s12290" xml:space="preserve">paucis iudicaui ſcribendum, uti anguſto ſpa-
                <lb/>
              tio uacuitatis, ea legentes breuiter percipere poſſent. </s>
              <s xml:id="echoid-s12291" xml:space="preserve">Alia ratio cur breuis eſſe uoluerit in Archite-
                <lb/>
              ctura tradenda, & </s>
              <s xml:id="echoid-s12292" xml:space="preserve">alia item ſequitur.</s>
              <s xml:id="echoid-s12293" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s12294" xml:space="preserve">
                <emph style="sc">Etiamqvr</emph>
              Pythagorę, hisq́; </s>
              <s xml:id="echoid-s12295" xml:space="preserve">qui eius hæreſim fuerunt ſecuti, placuit cubicis rationibus præce-
                <lb/>
              ptain uoluminibus ſcribere, conſtitueruntq́; </s>
              <s xml:id="echoid-s12296" xml:space="preserve">cubum 216. </s>
              <s xml:id="echoid-s12297" xml:space="preserve">uerſuum, eosq;</s>
              <s xml:id="echoid-s12298" xml:space="preserve">non plus, quàm tres in
                <lb/>
              una conſcriptione oportere eſſe putauerunt. </s>
              <s xml:id="echoid-s12299" xml:space="preserve">Cubus autem eſt corpus ex ſex lateribus æ quali latitudi-
                <lb/>
              ne planitierum quadratum. </s>
              <s xml:id="echoid-s12300" xml:space="preserve">is cum eſt iactus, quam in partem incubuit, dum eſt intactus, immotam
                <lb/>
                <note position="left" xlink:label="note-514.01.189-02" xlink:href="note-514.01.189-02a" xml:space="preserve">20</note>
              habet ſtabilitatem: </s>
              <s xml:id="echoid-s12301" xml:space="preserve">uti ſunt etiam teſſeræ, quas in alueo ludentes iaciunt.</s>
              <s xml:id="echoid-s12302" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s12303" xml:space="preserve">Pythagoreorum præcepta breuia erant, & </s>
              <s xml:id="echoid-s12304" xml:space="preserve">in uerſiculos collecta, quemadmodum: </s>
              <s xml:id="echoid-s12305" xml:space="preserve">Gladio ignem ne fodicato:
                <lb/>
              </s>
              <s xml:id="echoid-s12306" xml:space="preserve">stater am ne tranſilito; </s>
              <s xml:id="echoid-s12307" xml:space="preserve">cerebrum ne comedito: </s>
              <s xml:id="echoid-s12308" xml:space="preserve">cor etiam ne comedito: </s>
              <s xml:id="echoid-s12309" xml:space="preserve">maluam transferto, ſed tamen ne co-
                <lb/>
              medito: </s>
              <s xml:id="echoid-s12310" xml:space="preserve">aduerſus ſolem ne loquitor: </s>
              <s xml:id="echoid-s12311" xml:space="preserve">viam regiam declinato: </s>
              <s xml:id="echoid-s12312" xml:space="preserve">cum lecto ſurges ſtragula complicato: </s>
              <s xml:id="echoid-s12313" xml:space="preserve">veſtigiumq́; </s>
              <s xml:id="echoid-s12314" xml:space="preserve">
                <lb/>
              corporis confundito: </s>
              <s xml:id="echoid-s12315" xml:space="preserve">Annulum non geſtato: </s>
              <s xml:id="echoid-s12316" xml:space="preserve">ollæ quoque uestigium turbato in cinere: </s>
              <s xml:id="echoid-s12317" xml:space="preserve">Hirundines intra
                <lb/>
              domum ne admittito: </s>
              <s xml:id="echoid-s12318" xml:space="preserve">Contra Solem ne meito: </s>
              <s xml:id="echoid-s12319" xml:space="preserve">Speculum ne ſpectate ad lucernam: </s>
              <s xml:id="echoid-s12320" xml:space="preserve">Dextrum pedem priorem
                <lb/>
              calciato, ſiniſtrum priorem lauato: </s>
              <s xml:id="echoid-s12321" xml:space="preserve">vnguium, criniumq́; </s>
              <s xml:id="echoid-s12322" xml:space="preserve">tuorum præ ſegmina ne comingito, ſed in ea conſpuito: </s>
              <s xml:id="echoid-s12323" xml:space="preserve">
                <lb/>
              a fabis abstineto. </s>
              <s xml:id="echoid-s12324" xml:space="preserve">Hæc, & </s>
              <s xml:id="echoid-s12325" xml:space="preserve">ſimilia præcepta uerſiculis concludebant, aliudq́; </s>
              <s xml:id="echoid-s12326" xml:space="preserve">innuebant, quàm uerba ſona-
                <lb/>
              bant. </s>
              <s xml:id="echoid-s12327" xml:space="preserve">Cum igitur de aliqua re una tractare uellent, uerſieulis eam certo nemero colligebant. </s>
              <s xml:id="echoid-s12328" xml:space="preserve">Summam uer-
                <lb/>
              ſiculorum a cubo ſumebant. </s>
              <s xml:id="echoid-s12329" xml:space="preserve">Cubus eſt corpus ſex quadratorum laterum, œqualiumq́; </s>
              <s xml:id="echoid-s12330" xml:space="preserve">planorum conſtans, a
                <lb/>
                <note position="left" xlink:label="note-514.01.189-03" xlink:href="note-514.01.189-03a" xml:space="preserve">30</note>
              cuius ſimilitudine cubus quoque numerus est nominatus, qui constat ex ſex planis numeris undequaq; </s>
              <s xml:id="echoid-s12331" xml:space="preserve">æqua-
                <lb/>
              libus. </s>
              <s xml:id="echoid-s12332" xml:space="preserve">Oriuntur autem cubi poſt unitatem naturali ſerie, diſpoſitis imparibus numeris, ſi primos duos im-
                <lb/>
              pares colligas, deinde tres ſequentes impares, atque ita quatuor ſequentes impares. </s>
              <s xml:id="echoid-s12333" xml:space="preserve">exempli gratia, 3, & </s>
              <s xml:id="echoid-s12334" xml:space="preserve">5,
                <lb/>
              postpoſita unitate ſunt primi impares, horum ſumma est, 8, qui numerus primus eſt cubus. </s>
              <s xml:id="echoid-s12335" xml:space="preserve">Deinde 7, 9,
                <lb/>
              11, tres ſequentes impares, reddunt, 27, qui numerus eſt ſecundus cubus. </s>
              <s xml:id="echoid-s12336" xml:space="preserve">ſic 13, 15, 17, 19, reddunt,
                <lb/>
              64, tertium cubum. </s>
              <s xml:id="echoid-s12337" xml:space="preserve">Cum igitur moto puncto efficiatur linea, & </s>
              <s xml:id="echoid-s12338" xml:space="preserve">mota linea fiat planum, & </s>
              <s xml:id="echoid-s12339" xml:space="preserve">plano moto fiat
                <lb/>
              corpus: </s>
              <s xml:id="echoid-s12340" xml:space="preserve">non est a ſimilitudine alienum, ſi continuata unitate fiat:</s>
              <s xml:id="echoid-s12341" xml:space="preserve">
                <unsure/>
              linearis numerus, quiſuo modo productus
                <lb/>
              planum efficiat numerum, a quo demum ſolidus constituatur, perinde ac ſi unitati, alia unitas adderetur, qua-
                <lb/>
              dam ſimilitudine longitudo ſola, quæ lineæ propria est ostenderetur. </s>
              <s xml:id="echoid-s12342" xml:space="preserve">Si duo tanquam linea moueãtur, perinde
                <lb/>
              est ac ſi longitudini, etiam latitudo adderetur, & </s>
              <s xml:id="echoid-s12343" xml:space="preserve">planum efficeretur, id eſt, 4, qui numerus planus eſt
                <lb/>
                <note position="left" xlink:label="note-514.01.189-04" xlink:href="note-514.01.189-04a" xml:space="preserve">40</note>
              ex quo demum eadem ratione cubus, id est ſolidus numerus conſtitueretur. </s>
              <s xml:id="echoid-s12344" xml:space="preserve">nam ſi, 4, per duo multiplicen-
                <lb/>
              tur, octo reddentur. </s>
              <s xml:id="echoid-s12345" xml:space="preserve">Vnde uana est eorum ratio, qui dicunt, ſi ſunt ſex ſuperſicies, neceſſe eſt ſex eſſe unitates.
                <lb/>
              </s>
              <s xml:id="echoid-s12346" xml:space="preserve">nam ſenarius numerus non eſt ſolidus. </s>
              <s xml:id="echoid-s12347" xml:space="preserve">Inquit igitur Vitru. </s>
              <s xml:id="echoid-s12348" xml:space="preserve">Pythagoricos rationibus cubicis numerum uerſi-
                <lb/>
              culorum, quibus aliquid tractabant, concluſiße, nec plus quàm tres cubos in una tractatione collocare uoluiſſe. </s>
              <s xml:id="echoid-s12349" xml:space="preserve">
                <lb/>
              Ideo maiorem cubum ex, 216, verſiculis constituere. </s>
              <s xml:id="echoid-s12350" xml:space="preserve">multiplicantes igitur ternarium in ſe, nouem efficiebãt,
                <lb/>
              id eſt quadratum numerum, quem per tria ducebant, & </s>
              <s xml:id="echoid-s12351" xml:space="preserve">reddebant, 27, primus eorum cubus. </s>
              <s xml:id="echoid-s12352" xml:space="preserve">Simili ratione
                <lb/>
              alium cubum ex lineari numero faciebant, 4, igitur in ſe ducta, 16, efficiunt. </s>
              <s xml:id="echoid-s12353" xml:space="preserve">Sed, 16, per, 4, ducta,
                <lb/>
              64, reddunt, & </s>
              <s xml:id="echoid-s12354" xml:space="preserve">ita efficitur ſecundus eorum cubus, cui, 27, addita, reddunt 91, inde tertium cubum ex
                <lb/>
              quinario ducunt. </s>
              <s xml:id="echoid-s12355" xml:space="preserve">nam, 5, in ſe ducta efficiunt, 25, quœ ducta per, 5, reddunt, 125, quibus additis 91,
                <lb/>
              ſumma fit, 216. </s>
              <s xml:id="echoid-s12356" xml:space="preserve">Ad hunc igitur numerum ſumma præceptorum pythagoreorum perueniebat, cubicamq́; </s>
              <s xml:id="echoid-s12357" xml:space="preserve">ra-
                <lb/>
                <note position="left" xlink:label="note-514.01.189-05" xlink:href="note-514.01.189-05a" xml:space="preserve">50</note>
              tionem adamarunt, putantes ea ſirmiter mentibus inbærere, quemadmodum cubus ſi iaciatur, in quacunque
                <lb/>
              parte inſederit, firmã habet stabilitatem. </s>
              <s xml:id="echoid-s12358" xml:space="preserve">Sed mirum qua ratione primum cubum, ideſt octo nõ admiſerint Py-
                <lb/>
              thagorei. </s>
              <s xml:id="echoid-s12359" xml:space="preserve">deinde ſecundum id eſt, 27, poſtea tertium, 64, & </s>
              <s xml:id="echoid-s12360" xml:space="preserve">non collegerint ſummam 99. </s>
              <s xml:id="echoid-s12361" xml:space="preserve">Sed forſan eo-
                <lb/>
              rum tractationes in cubos uerſiculorum numeros diuidebant, & </s>
              <s xml:id="echoid-s12362" xml:space="preserve">ſi eorum præcepta primo cubo non poterant
                <lb/>
              contineri, addebant ſecundum, qui ſi ſatis non erat, addebant tertium, qui omnis ſummæ capax erat. </s>
              <s xml:id="echoid-s12363" xml:space="preserve">Sed quia
                <lb/>
              primus, ſcilicet octo, parum est ad propoſitum aliquod unum colligendum, ideo ipſum (ut puto) reliquerunt,
                <lb/>
              & </s>
              <s xml:id="echoid-s12364" xml:space="preserve">ideo ad, 27, primo perueniebant a ternario ortum, qui numerus pythagoricis plauſibilis erat; </s>
              <s xml:id="echoid-s12365" xml:space="preserve">binarius
                <lb/>
              autem non item. </s>
              <s xml:id="echoid-s12366" xml:space="preserve">non igitur ſtatim ad, 216, uerſiculos ueniebant, ſed ſeparatim ad præcedentes cubos, qui ſi
                <lb/>
              non erant ſatis, duos colligebant, a duobus demum ad tertium perueniebant, ultra quem progredi nolebant,
                <lb/>
              ne tractationis prolixitati faſtidium afferrent, & </s>
              <s xml:id="echoid-s12367" xml:space="preserve">memoriam, cui ſeruire ſtudebant, longitudine læderent. </s>
              <s xml:id="echoid-s12368" xml:space="preserve">nam
                <lb/>
                <note position="left" xlink:label="note-514.01.189-06" xlink:href="note-514.01.189-06a" xml:space="preserve">60</note>
              </s>
            </p>
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