Vitruvius, De architectura libri decem, 1567

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            <pb o="87" file="514.01.119" n="119" rhead="TERTIVS."/>
            <p style="it">
              <s xml:id="echoid-s8236" xml:space="preserve">Reliquæ rationes, quæ inter eoſdem terminos cadunt, quæ ſunt, primi ad quartum uel ſextum, ſecundi ad
                <lb/>
              tertium uel quintum, tertij ad quintum, & </s>
              <s xml:id="echoid-s8237" xml:space="preserve">quarti ad ſextum, ex reliquorum numerorum rationibus minime
                <lb/>
              componi poſſunt. </s>
              <s xml:id="echoid-s8238" xml:space="preserve">Reſtat ut huiuſmodi compoſitiones experientia dirigamus , ſuisq́; </s>
              <s xml:id="echoid-s8239" xml:space="preserve">regulis exerceamus, Fin-
                <lb/>
              gamus igitur ſextum ignorari numerum, quem uolumus inuenire. </s>
              <s xml:id="echoid-s8240" xml:space="preserve">duc ſecundum in tertium, & </s>
              <s xml:id="echoid-s8241" xml:space="preserve">productum par
                <lb/>
              tire per primum, & </s>
              <s xml:id="echoid-s8242" xml:space="preserve">quartum rurſus ex partitione terminorum duces in quintum, productumq́; </s>
              <s xml:id="echoid-s8243" xml:space="preserve">partire per quar
                <lb/>
              tum, habebis quæſitum numerum . </s>
              <s xml:id="echoid-s8244" xml:space="preserve">eſto in eo primo ordine. </s>
              <s xml:id="echoid-s8245" xml:space="preserve">9. </s>
              <s xml:id="echoid-s8246" xml:space="preserve">ignoratus numerus. </s>
              <s xml:id="echoid-s8247" xml:space="preserve">ducito 2. </s>
              <s xml:id="echoid-s8248" xml:space="preserve">in 3. </s>
              <s xml:id="echoid-s8249" xml:space="preserve">fient
                <lb/>
              6. </s>
              <s xml:id="echoid-s8250" xml:space="preserve">quæ per. </s>
              <s xml:id="echoid-s8251" xml:space="preserve">1. </s>
              <s xml:id="echoid-s8252" xml:space="preserve">partita ſex ſimiliter erunt, hæc ducito in 6. </s>
              <s xml:id="echoid-s8253" xml:space="preserve">quintum uidelicet numerum, reddentur. </s>
              <s xml:id="echoid-s8254" xml:space="preserve">36.
                <lb/>
              </s>
              <s xml:id="echoid-s8255" xml:space="preserve">quæ partita per 4. </s>
              <s xml:id="echoid-s8256" xml:space="preserve">dabunt. </s>
              <s xml:id="echoid-s8257" xml:space="preserve">9. </s>
              <s xml:id="echoid-s8258" xml:space="preserve">qui erat quæſitus , & </s>
              <s xml:id="echoid-s8259" xml:space="preserve">ignoratus numerus. </s>
              <s xml:id="echoid-s8260" xml:space="preserve">Quod ſi quintus ignotus fuerit
                <lb/>
              ducito primum in quartum, & </s>
              <s xml:id="echoid-s8261" xml:space="preserve">quod inde prouenit partire per tertium , & </s>
              <s xml:id="echoid-s8262" xml:space="preserve">quod ex partitione effeceris duci-
                <lb/>
              to in ſextum, & </s>
              <s xml:id="echoid-s8263" xml:space="preserve">progenitum partire per ſecundum, habebis quæſitum numerum quintum. </s>
              <s xml:id="echoid-s8264" xml:space="preserve">Exempli gratia i-
                <lb/>
                <note position="left" xlink:label="note-514.01.119-01" xlink:href="note-514.01.119-01a" xml:space="preserve">10</note>
              gnoretur numerus. </s>
              <s xml:id="echoid-s8265" xml:space="preserve">6. </s>
              <s xml:id="echoid-s8266" xml:space="preserve">qui quintus es
                <unsure/>
              t in ordine . </s>
              <s xml:id="echoid-s8267" xml:space="preserve">ducito. </s>
              <s xml:id="echoid-s8268" xml:space="preserve">1. </s>
              <s xml:id="echoid-s8269" xml:space="preserve">in 4. </s>
              <s xml:id="echoid-s8270" xml:space="preserve">reddet 4. </s>
              <s xml:id="echoid-s8271" xml:space="preserve">qui partitus per 3. </s>
              <s xml:id="echoid-s8272" xml:space="preserve">red-
                <lb/>
              det unum & </s>
              <s xml:id="echoid-s8273" xml:space="preserve">tertiam. </s>
              <s xml:id="echoid-s8274" xml:space="preserve">hunc multiplicato per. </s>
              <s xml:id="echoid-s8275" xml:space="preserve">9. </s>
              <s xml:id="echoid-s8276" xml:space="preserve">produces duodecim, qui numerus ſi per. </s>
              <s xml:id="echoid-s8277" xml:space="preserve">2. </s>
              <s xml:id="echoid-s8278" xml:space="preserve">partiatur igno
                <lb/>
              ratum numerum manifes
                <unsure/>
              tabit, hoc eſt. </s>
              <s xml:id="echoid-s8279" xml:space="preserve">6. </s>
              <s xml:id="echoid-s8280" xml:space="preserve">ſed ſi quartus quærendus ſit, duc ſecundum in tertium, & </s>
              <s xml:id="echoid-s8281" xml:space="preserve">produ-
                <lb/>
              ctum partire per primum, & </s>
              <s xml:id="echoid-s8282" xml:space="preserve">quotum numerum inde prouenientem , per quintum ducito , & </s>
              <s xml:id="echoid-s8283" xml:space="preserve">productum per
                <lb/>
              ſextum partire, hoc modo, ignoretur 4. </s>
              <s xml:id="echoid-s8284" xml:space="preserve">ducito duo in tria reddentur. </s>
              <s xml:id="echoid-s8285" xml:space="preserve">6. </s>
              <s xml:id="echoid-s8286" xml:space="preserve">partire ſex per unum reddent
                <lb/>
              6. </s>
              <s xml:id="echoid-s8287" xml:space="preserve">Hæcper. </s>
              <s xml:id="echoid-s8288" xml:space="preserve">6. </s>
              <s xml:id="echoid-s8289" xml:space="preserve">numeri quintirurſum multiplicabis, reddentur. </s>
              <s xml:id="echoid-s8290" xml:space="preserve">36. </s>
              <s xml:id="echoid-s8291" xml:space="preserve">quæ partita per nouem dabunt. </s>
              <s xml:id="echoid-s8292" xml:space="preserve">4.
                <lb/>
              </s>
              <s xml:id="echoid-s8293" xml:space="preserve">qui optatus, & </s>
              <s xml:id="echoid-s8294" xml:space="preserve">ignoratus numerus quærebatur. </s>
              <s xml:id="echoid-s8295" xml:space="preserve">At ſi tertius ignoretur, duc primum in quartum, conſur-
                <lb/>
              gentem partire per ſecundum, prouenientem ex partitione illa ducito in ſextum, & </s>
              <s xml:id="echoid-s8296" xml:space="preserve">procreatum inde terminum
                <lb/>
              partire per quintum hoc modo. </s>
              <s xml:id="echoid-s8297" xml:space="preserve">Ignoretur numerus. </s>
              <s xml:id="echoid-s8298" xml:space="preserve">3. </s>
              <s xml:id="echoid-s8299" xml:space="preserve">duc unum in 4. </s>
              <s xml:id="echoid-s8300" xml:space="preserve">reddes. </s>
              <s xml:id="echoid-s8301" xml:space="preserve">4. </s>
              <s xml:id="echoid-s8302" xml:space="preserve">quæ diuiſa per. </s>
              <s xml:id="echoid-s8303" xml:space="preserve">2. </s>
              <s xml:id="echoid-s8304" xml:space="preserve">
                <lb/>
              dabunt. </s>
              <s xml:id="echoid-s8305" xml:space="preserve">2. </s>
              <s xml:id="echoid-s8306" xml:space="preserve">hæc multiplica per 9. </s>
              <s xml:id="echoid-s8307" xml:space="preserve">habebis. </s>
              <s xml:id="echoid-s8308" xml:space="preserve">18. </s>
              <s xml:id="echoid-s8309" xml:space="preserve">quæ partita per ſex, dabunt tria, qui numerus quæreba-
                <lb/>
                <note position="left" xlink:label="note-514.01.119-02" xlink:href="note-514.01.119-02a" xml:space="preserve">20</note>
              tur. </s>
              <s xml:id="echoid-s8310" xml:space="preserve">Quinto ſi ſec undum quæſieris, duc primum in quartum, productum partire per tertium, quotum proue-
                <lb/>
              nientem ducito in ſextum, productum demum partire per quintum, hoc modo . </s>
              <s xml:id="echoid-s8311" xml:space="preserve">Duc unum in 4. </s>
              <s xml:id="echoid-s8312" xml:space="preserve">reddentur
                <lb/>
              4. </s>
              <s xml:id="echoid-s8313" xml:space="preserve">quæ diuiſa per 3. </s>
              <s xml:id="echoid-s8314" xml:space="preserve">reddent unam & </s>
              <s xml:id="echoid-s8315" xml:space="preserve">tertiam. </s>
              <s xml:id="echoid-s8316" xml:space="preserve">quæ ducta per nouem efficient duodecim, hæc diuiſa per ſex
                <lb/>
              dabunt binarium repertum numerum. </s>
              <s xml:id="echoid-s8317" xml:space="preserve">Demum ſi primum numerum quæris, ducito ſecundum in tertium, pro-
                <lb/>
              uenientem partire per quartum, quotus ex ipſa diuiſione ducito per quintum, productumque diuidito per ſex-
                <lb/>
              tum, relinquetur primus hoc modo, quæratur unitas, quæ prima erat in ordine, ducito. </s>
              <s xml:id="echoid-s8318" xml:space="preserve">2. </s>
              <s xml:id="echoid-s8319" xml:space="preserve">in 3. </s>
              <s xml:id="echoid-s8320" xml:space="preserve">efficies
                <lb/>
              6. </s>
              <s xml:id="echoid-s8321" xml:space="preserve">quæ diuiſa per quatuor, dabunt unum & </s>
              <s xml:id="echoid-s8322" xml:space="preserve">dimidium, quæmultiplicata per 6. </s>
              <s xml:id="echoid-s8323" xml:space="preserve">producunt 9. </s>
              <s xml:id="echoid-s8324" xml:space="preserve">quæ per quæ
                <lb/>
              hoc est ſe xtum partita restituunt unitatem, quæ antea ignorabatur . </s>
              <s xml:id="echoid-s8325" xml:space="preserve">Hæc ſunt quæ de proportionibus, ac de
                <lb/>
              earum comparationibus afferre uolui, quæ ſi diligenter examinabuntur, nullum erit quæſitum, nullum abdi-
                <lb/>
              tum, & </s>
              <s xml:id="echoid-s8326" xml:space="preserve">ignoratum quod non prodibit in lucem , ſiue in ciuilibus negotijs, ſiue in ſpeculatricibus ſcientijs uer-
                <lb/>
                <note position="left" xlink:label="note-514.01.119-03" xlink:href="note-514.01.119-03a" xml:space="preserve">30</note>
              ſari uelimus. </s>
              <s xml:id="echoid-s8327" xml:space="preserve">Quod recte norunt, qui harũ rerum ſtudio delectantur. </s>
              <s xml:id="echoid-s8328" xml:space="preserve">ſed tempus est, ut ad Vitruuiũ accedamus.</s>
              <s xml:id="echoid-s8329" xml:space="preserve"/>
            </p>
            <p>
              <s xml:id="echoid-s8330" xml:space="preserve">
                <emph style="sc">Aedivm</emph>
              compoſitio conſtat ex ſymmetria, cuius rationem diligentiſsime Architecti tenere de
                <lb/>
              bent. </s>
              <s xml:id="echoid-s8331" xml:space="preserve">Ea autem paritur a proportione, quæ Græcè analogia dicitur. </s>
              <s xml:id="echoid-s8332" xml:space="preserve">Proportio eſt ratæ partis mem-
                <lb/>
              brorum in omni opere, totiusq́; </s>
              <s xml:id="echoid-s8333" xml:space="preserve">commodulatio , ex qua ratio efficitur ſymmetriarum.</s>
              <s xml:id="echoid-s8334" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s8335" xml:space="preserve">De ſacris Deorum ædibus tertio, & </s>
              <s xml:id="echoid-s8336" xml:space="preserve">quarto libro agitur. </s>
              <s xml:id="echoid-s8337" xml:space="preserve">Totum hoc negocium his rebus abſoluitur. </s>
              <s xml:id="echoid-s8338" xml:space="preserve">Primo
                <lb/>
              neceßitas oſtenditur Architecto cognoſcendarum menſurarum, mox unde menſuræ deſumptæ ſunt, declaratur,
                <lb/>
              & </s>
              <s xml:id="echoid-s8339" xml:space="preserve">quia statim a principio de compoſitione ſacrarum ædium agere exorditur, ideo in hac tractatione diſcuti-
                <lb/>
              tur quicquid primo ſub aſpectum cadit, ita enim ratio poſtulat, ut a confuſis inc pientes ad diſtincta peruenia-
                <lb/>
              mus. </s>
              <s xml:id="echoid-s8340" xml:space="preserve">Cadunt autem ſub aſpectum, & </s>
              <s xml:id="echoid-s8341" xml:space="preserve">e longinquo figuræ, formæq́; </s>
              <s xml:id="echoid-s8342" xml:space="preserve">frontium, & </s>
              <s xml:id="echoid-s8343" xml:space="preserve">laterum templorum, quæ
                <lb/>
                <note position="left" xlink:label="note-514.01.119-04" xlink:href="note-514.01.119-04a" xml:space="preserve">40</note>
              quinario numero colliguntur, mox diſtinctiori cognitione intercolumnia comprehenduntur , ſpatiaq́; </s>
              <s xml:id="echoid-s8344" xml:space="preserve">eorum cer
                <lb/>
              ta deſignantur, & </s>
              <s xml:id="echoid-s8345" xml:space="preserve">ut res ſuis conſtert numeris. </s>
              <s xml:id="echoid-s8346" xml:space="preserve">De fundatione agitur, deq́; </s>
              <s xml:id="echoid-s8347" xml:space="preserve">baſium, columnarum , capitulo-
                <lb/>
              rumq́; </s>
              <s xml:id="echoid-s8348" xml:space="preserve">formatione tractatur, inde de ijs, quæ columnis , & </s>
              <s xml:id="echoid-s8349" xml:space="preserve">capitulis ſuperponuntur, cuiuſmodi ſunt trabes,
                <lb/>
              Zophori, coronæ, & </s>
              <s xml:id="echoid-s8350" xml:space="preserve">huiuſmodi, quibus & </s>
              <s xml:id="echoid-s8351" xml:space="preserve">tecta adijciuntur, quorum ratio diligentiſſime examinatur, ita ut
                <lb/>
              a fundamentis ad ſummum tectum omnia exquiſite ponderentur. </s>
              <s xml:id="echoid-s8352" xml:space="preserve">Ornamenta inſuper, & </s>
              <s xml:id="echoid-s8353" xml:space="preserve">opportunitates om-
                <lb/>
              nes exponuntur, unde gradus, podia, ſtylobata, diminutiones, ſtriæ, proiecturæ, adiectionesq́; </s>
              <s xml:id="echoid-s8354" xml:space="preserve">perquiruntur ,
                <lb/>
              ac demum per portarum genera templa ingreditur, quorum altitudines, longitudines , latitudinesq́; </s>
              <s xml:id="echoid-s8355" xml:space="preserve">exequi-
                <lb/>
              tur, cellas, pronaum, & </s>
              <s xml:id="echoid-s8356" xml:space="preserve">pos
                <unsure/>
              ticum, altareq́; </s>
              <s xml:id="echoid-s8357" xml:space="preserve">facit, ac Deorum ſimulacra, quorum cauſa ædes conſtruuntur, im-
                <lb/>
              ponit. </s>
              <s xml:id="echoid-s8358" xml:space="preserve">Primo igitur capite neceſſitatem, & </s>
              <s xml:id="echoid-s8359" xml:space="preserve">inuentionem menſurarum proponit: </s>
              <s xml:id="echoid-s8360" xml:space="preserve">Aitq́; </s>
              <s xml:id="echoid-s8361" xml:space="preserve">neceſſe eſſe, ut qui
                <lb/>
              ſacras ædes conſtruere cupit, agnoſcat uim, reſponſumq́; </s>
              <s xml:id="echoid-s8362" xml:space="preserve">menſurarum, cuius ratio in promptu est, nam licet
                <lb/>
                <note position="left" xlink:label="note-514.01.119-05" xlink:href="note-514.01.119-05a" xml:space="preserve">50</note>
              ædificatio omnis ratione menſuranda ſit, tamen cum conſideramus quanto humanitate diuinitas præstat, debe-
                <lb/>
              mus omni conatu pulchritudinem affectare in obſeruatione rerum diuinarum. </s>
              <s xml:id="echoid-s8363" xml:space="preserve">& </s>
              <s xml:id="echoid-s8364" xml:space="preserve">quomam diuinum in terris
                <lb/>
              humana mens capit, ideo mentem maxime exercere debemus , ut Deos honoremus. </s>
              <s xml:id="echoid-s8365" xml:space="preserve">Dij enim ſunt, qui uere
                <unsure/>
                <lb/>
              Deum colunt , ſed multo magis Deum Deorum honorare debemus, quare in ſacratiſſimo illius templo conſtruẽ-
                <lb/>
              do omnem laborem, induſtriam, diligentiam, ingeniumque ponemus, & </s>
              <s xml:id="echoid-s8366" xml:space="preserve">a falſo Dæmonum cultu ad ueros ritus
                <lb/>
              opes noſtras conuertemus. </s>
              <s xml:id="echoid-s8367" xml:space="preserve">Optimum humanæ mentis ratio iudicatur, hæc excellentiſſime in proportionibus
                <lb/>
              oſtenditur, quare cum Vitr. </s>
              <s xml:id="echoid-s8368" xml:space="preserve">dixerit. </s>
              <s xml:id="echoid-s8369" xml:space="preserve">ſymmetriæ, & </s>
              <s xml:id="echoid-s8370" xml:space="preserve">commenſus rationem diligentißime Architectos tenere de
                <lb/>
              bere , ueram, honeſtam, debitamq́; </s>
              <s xml:id="echoid-s8371" xml:space="preserve">diuinitate rem protulit, & </s>
              <s xml:id="echoid-s8372" xml:space="preserve">ſi quid mortale es
                <unsure/>
              t , quod ſatis immortalitatem
                <lb/>
              uener aripoteſt , dicerem ego precioſas quasque res proportionibus ſubijciendas eſſe in ædium constructione,
                <lb/>
              ut & </s>
              <s xml:id="echoid-s8373" xml:space="preserve">forma, & </s>
              <s xml:id="echoid-s8374" xml:space="preserve">materia cæleſtem, ac diuinam rem honeſtent. </s>
              <s xml:id="echoid-s8375" xml:space="preserve">Neceſſaria igit ur eſt ſymmetriæ cognitio, quæ
                <lb/>
              unde ortum ſumat. </s>
              <s xml:id="echoid-s8376" xml:space="preserve">docet Vitr.</s>
              <s xml:id="echoid-s8377" xml:space="preserve"/>
            </p>
            <note position="left" xml:space="preserve">60</note>
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