Vitruvius, De architectura libri decem, 1567

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          <div xml:id="echoid-div718" type="section" level="2" n="135">
            <p style="it">
              <s xml:id="echoid-s20529" xml:space="preserve">
                <pb o="274" file="514.01.306" n="306" rhead="LIBER"/>
              erit minor, ergo b g. </s>
              <s xml:id="echoid-s20530" xml:space="preserve">iuſto maior ſumpta fuerit. </s>
              <s xml:id="echoid-s20531" xml:space="preserve">propterea b g, paulo minor ſumenda erit, & </s>
              <s xml:id="echoid-s20532" xml:space="preserve">eadem de-
                <lb/>
              ſcriptio erit reſumenda, & </s>
              <s xml:id="echoid-s20533" xml:space="preserve">eò uſque tentando experiri oportebit, donec o q. </s>
              <s xml:id="echoid-s20534" xml:space="preserve">æqualis fiat lmeæ m c. </s>
              <s xml:id="echoid-s20535" xml:space="preserve">Esto
                <lb/>
              ergo m c æqualis o q. </s>
              <s xml:id="echoid-s20536" xml:space="preserve">& </s>
              <s xml:id="echoid-s20537" xml:space="preserve">m q. </s>
              <s xml:id="echoid-s20538" xml:space="preserve">æquidistantes erunt ex poſitione,&</s>
              <s xml:id="echoid-s20539" xml:space="preserve">ex trigeſima primi elementorum.
                <lb/>
              </s>
              <s xml:id="echoid-s20540" xml:space="preserve">Demum a b. </s>
              <s xml:id="echoid-s20541" xml:space="preserve">g i. </s>
              <s xml:id="echoid-s20542" xml:space="preserve">m o. </s>
              <s xml:id="echoid-s20543" xml:space="preserve">c d. </s>
              <s xml:id="echoid-s20544" xml:space="preserve">erunt primæ æquidistantes, ſed a g. </s>
              <s xml:id="echoid-s20545" xml:space="preserve">m i. </s>
              <s xml:id="echoid-s20546" xml:space="preserve">c o. </s>
              <s xml:id="echoid-s20547" xml:space="preserve">pos̃teriores: </s>
              <s xml:id="echoid-s20548" xml:space="preserve">aio lineis
                <lb/>
              a b. </s>
              <s xml:id="echoid-s20549" xml:space="preserve">& </s>
              <s xml:id="echoid-s20550" xml:space="preserve">c d. </s>
              <s xml:id="echoid-s20551" xml:space="preserve">medias eſſe comparabiles g i. </s>
              <s xml:id="echoid-s20552" xml:space="preserve">& </s>
              <s xml:id="echoid-s20553" xml:space="preserve">m o. </s>
              <s xml:id="echoid-s20554" xml:space="preserve">Eſto igitur a d, & </s>
              <s xml:id="echoid-s20555" xml:space="preserve">b c. </s>
              <s xml:id="echoid-s20556" xml:space="preserve">productæ ad r, & </s>
              <s xml:id="echoid-s20557" xml:space="preserve">
                <lb/>
              quoniam propter triangulorum ſimilitudinem,ut eſt a r. </s>
              <s xml:id="echoid-s20558" xml:space="preserve">ad r i. </s>
              <s xml:id="echoid-s20559" xml:space="preserve">in primis æquidiſtantibus, ita b r. </s>
              <s xml:id="echoid-s20560" xml:space="preserve">ad
                <lb/>
              r g. </s>
              <s xml:id="echoid-s20561" xml:space="preserve">& </s>
              <s xml:id="echoid-s20562" xml:space="preserve">ut in ſecundis a r ad r i. </s>
              <s xml:id="echoid-s20563" xml:space="preserve">ita g r. </s>
              <s xml:id="echoid-s20564" xml:space="preserve">ad r m. </s>
              <s xml:id="echoid-s20565" xml:space="preserve">& </s>
              <s xml:id="echoid-s20566" xml:space="preserve">ut in primis g r. </s>
              <s xml:id="echoid-s20567" xml:space="preserve">ad r m. </s>
              <s xml:id="echoid-s20568" xml:space="preserve">ita i r. </s>
              <s xml:id="echoid-s20569" xml:space="preserve">ad r
                <lb/>
              o, & </s>
              <s xml:id="echoid-s20570" xml:space="preserve">in ſecundis,ut i r. </s>
              <s xml:id="echoid-s20571" xml:space="preserve">ad r o. </s>
              <s xml:id="echoid-s20572" xml:space="preserve">ita m r. </s>
              <s xml:id="echoid-s20573" xml:space="preserve">ad r c. </s>
              <s xml:id="echoid-s20574" xml:space="preserve">Sunt ergo continenter comparabiles b r. </s>
              <s xml:id="echoid-s20575" xml:space="preserve">r g. </s>
              <s xml:id="echoid-s20576" xml:space="preserve">
                <lb/>
              m r. </s>
              <s xml:id="echoid-s20577" xml:space="preserve">r o. </s>
              <s xml:id="echoid-s20578" xml:space="preserve">Sed ſub eadem proportione per quartam ſexti elementorum etiam eſt,ut ſicut a b. </s>
              <s xml:id="echoid-s20579" xml:space="preserve">ad g i. </s>
              <s xml:id="echoid-s20580" xml:space="preserve">
                <lb/>
              ita g i. </s>
              <s xml:id="echoid-s20581" xml:space="preserve">ad m o. </s>
              <s xml:id="echoid-s20582" xml:space="preserve">& </s>
              <s xml:id="echoid-s20583" xml:space="preserve">m o. </s>
              <s xml:id="echoid-s20584" xml:space="preserve">ad c d. </s>
              <s xml:id="echoid-s20585" xml:space="preserve">Inter ergo duas datas rectas a b. </s>
              <s xml:id="echoid-s20586" xml:space="preserve">& </s>
              <s xml:id="echoid-s20587" xml:space="preserve">c d. </s>
              <s xml:id="echoid-s20588" xml:space="preserve">inuentæ ſunt duæ
                <lb/>
                <note position="left" xlink:label="note-514.01.306-01" xlink:href="note-514.01.306-01a" xml:space="preserve">10</note>
              mediæ continenter comparabiles,ut propoſitum fuit. </s>
              <s xml:id="echoid-s20589" xml:space="preserve">Atque his ſimilibus rationibus quot libuerit medias in-
                <lb/>
              uenire poterimus. </s>
              <s xml:id="echoid-s20590" xml:space="preserve">Vt igitur duas etiam medias inter duas rectas inueniamus, b f. </s>
              <s xml:id="echoid-s20591" xml:space="preserve">erit tertia pars lineæ
                <lb/>
              b c. </s>
              <s xml:id="echoid-s20592" xml:space="preserve">quoniam b g, excedit tertiam partem lineæ b c. </s>
              <s xml:id="echoid-s20593" xml:space="preserve">aliquantum,& </s>
              <s xml:id="echoid-s20594" xml:space="preserve">nunquam minor eſt, neque æqua-
                <lb/>
              lis lineæ b f. </s>
              <s xml:id="echoid-s20595" xml:space="preserve">vt uero tres medias inueniamus b f. </s>
              <s xml:id="echoid-s20596" xml:space="preserve">erit quarta pars b c. </s>
              <s xml:id="echoid-s20597" xml:space="preserve">& </s>
              <s xml:id="echoid-s20598" xml:space="preserve">b g, aliqnanto maior ip-
                <lb/>
              ſa b f. </s>
              <s xml:id="echoid-s20599" xml:space="preserve">uelut quinta pars ipſius b c. </s>
              <s xml:id="echoid-s20600" xml:space="preserve">atque hoc modo ipſx b c erit diuiſa una parte amplior, quà m ſunt
                <lb/>
              mediæ lineæ, quas quærimus inuenire, & </s>
              <s xml:id="echoid-s20601" xml:space="preserve">ſemper una ex illis erit b f, & </s>
              <s xml:id="echoid-s20602" xml:space="preserve">b g. </s>
              <s xml:id="echoid-s20603" xml:space="preserve">aliquanto maior, quàm
                <lb/>
              b f. </s>
              <s xml:id="echoid-s20604" xml:space="preserve">& </s>
              <s xml:id="echoid-s20605" xml:space="preserve">propterea b f æ que ſumitur ac b c, ut facilius longitudo b c. </s>
              <s xml:id="echoid-s20606" xml:space="preserve">coniectari poſſit. </s>
              <s xml:id="echoid-s20607" xml:space="preserve">Accedamus
                <lb/>
              denique ad Architæ Tarentini inuentionem difficilem ſanè ac ſubtilem, adeo ut inſtrumento nullo exerceri
                <lb/>
              poſſe hactenus creditum ſit, cæterum. </s>
              <s xml:id="echoid-s20608" xml:space="preserve">Antonius Maria Paccius uir doctus, & </s>
              <s xml:id="echoid-s20609" xml:space="preserve">probus instrumentum eius rei,
                <lb/>
              & </s>
              <s xml:id="echoid-s20610" xml:space="preserve">uſum ad me miſit, quale in ſubiectis deſcriptionibus oſtendam, ut amico gratias habeam. </s>
              <s xml:id="echoid-s20611" xml:space="preserve">Primum au-
                <lb/>
                <note position="left" xlink:label="note-514.01.306-02" xlink:href="note-514.01.306-02a" xml:space="preserve">20</note>
              tem demonstrationem ſecundum aliorum ſenſism apponam, deinde præ dictum inſtrumentum deſcribam. </s>
              <s xml:id="echoid-s20612" xml:space="preserve">Pro-
                <lb/>
              ponantur duærectæ, quæ ſint a d, quidem maior, c, uero minor,inter eas duas medias comparabiles in-
                <lb/>
              uenire oportet. </s>
              <s xml:id="echoid-s20613" xml:space="preserve">Sumatur ergo maior, ſcilicet a d. </s>
              <s xml:id="echoid-s20614" xml:space="preserve">circum quam ducatur linea circmationis ita, ut ipſa a
                <lb/>
              d. </s>
              <s xml:id="echoid-s20615" xml:space="preserve">fiat eius diameter, ac circinationis linea ſit a b d f. </s>
              <s xml:id="echoid-s20616" xml:space="preserve">in eaq́; </s>
              <s xml:id="echoid-s20617" xml:space="preserve">circinatione ex prima tertij elementorum
                <lb/>
              line a æ qualis ipſi c. </s>
              <s xml:id="echoid-s20618" xml:space="preserve">aptetur, & </s>
              <s xml:id="echoid-s20619" xml:space="preserve">ſit illa a b. </s>
              <s xml:id="echoid-s20620" xml:space="preserve">quæ ultra circinationem producatur, uſq; </s>
              <s xml:id="echoid-s20621" xml:space="preserve">ad ſignum p. </s>
              <s xml:id="echoid-s20622" xml:space="preserve">quod
                <lb/>
              erit extremum lineæ contingentis circinationem in ſigno d. </s>
              <s xml:id="echoid-s20623" xml:space="preserve">cuius alterum extremum ſit ubi ſignum o. </s>
              <s xml:id="echoid-s20624" xml:space="preserve">ita ut
                <lb/>
              integra linea ſit p d o. </s>
              <s xml:id="echoid-s20625" xml:space="preserve">cui æ quidiſtans protrahatur,quæ ſecet lineam a d. </s>
              <s xml:id="echoid-s20626" xml:space="preserve">in ſigno e. </s>
              <s xml:id="echoid-s20627" xml:space="preserve">Intelligatur po-
                <lb/>
              Stea hemicylindrium rectum ſupra dimidium circulum a b d, & </s>
              <s xml:id="echoid-s20628" xml:space="preserve">deinceps imaginemur in parallelogramo
                <lb/>
              hemicylindri ſuper a d. </s>
              <s xml:id="echoid-s20629" xml:space="preserve">deſcriptus ſemicirculus, qui tanquam parallelogramum hemicylindri. </s>
              <s xml:id="echoid-s20630" xml:space="preserve">ad rectos
                <lb/>
              angulos eſt ipſius a b d f circuli deſcripti in plano. </s>
              <s xml:id="echoid-s20631" xml:space="preserve">Is ſemicirculus ductus a ſigno d. </s>
              <s xml:id="echoid-s20632" xml:space="preserve">inſignum b. </s>
              <s xml:id="echoid-s20633" xml:space="preserve">im-
                <lb/>
              mobilis permanet in ſigno a. </s>
              <s xml:id="echoid-s20634" xml:space="preserve">quod terminus eſt diametri a d. </s>
              <s xml:id="echoid-s20635" xml:space="preserve">abſcindet in eius. </s>
              <s xml:id="echoid-s20636" xml:space="preserve">circunductu eam ſuperficiem
                <lb/>
                <note position="left" xlink:label="note-514.01.306-03" xlink:href="note-514.01.306-03a" xml:space="preserve">30</note>
              hemicylindri, & </s>
              <s xml:id="echoid-s20637" xml:space="preserve">in ea quandam lineam deſcribet. </s>
              <s xml:id="echoid-s20638" xml:space="preserve">præ terhæc ſiprima a d. </s>
              <s xml:id="echoid-s20639" xml:space="preserve">linea trigonum a b d, circun-
                <lb/>
              ductum contrariam fecerit femicirculo motionem, conicam ſuperſiciem lineæ rectæ a p, deſcribet, quæſi
                <lb/>
              circunducatur iungetur in aliquo ſigno eius linea, quæ prius deſcripta fuit ex ductu ſemicirculi in ſuperficie
                <lb/>
              hemicylindrij. </s>
              <s xml:id="echoid-s20640" xml:space="preserve">pari forma & </s>
              <s xml:id="echoid-s20641" xml:space="preserve">b. </s>
              <s xml:id="echoid-s20642" xml:space="preserve">deſcribet ſemicirculum in ſuperficie coni. </s>
              <s xml:id="echoid-s20643" xml:space="preserve">ipſe tandem ſemicirculus a d e.
                <lb/>
              </s>
              <s xml:id="echoid-s20644" xml:space="preserve">poſt motum ſuum collocetur in loco, ubi lineæ cadentes concurrunt, & </s>
              <s xml:id="echoid-s20645" xml:space="preserve">trigonum, quod contra mouetur habeat
                <lb/>
              hanc poſitionem d l a, & </s>
              <s xml:id="echoid-s20646" xml:space="preserve">ſignum in quo incidunt, ſit k. </s>
              <s xml:id="echoid-s20647" xml:space="preserve">deſcribatur etiam per b. </s>
              <s xml:id="echoid-s20648" xml:space="preserve">ſemicirculus b m f. </s>
              <s xml:id="echoid-s20649" xml:space="preserve">
                <lb/>
              & </s>
              <s xml:id="echoid-s20650" xml:space="preserve">commune ſegmentum eius, & </s>
              <s xml:id="echoid-s20651" xml:space="preserve">circuli b d f a. </s>
              <s xml:id="echoid-s20652" xml:space="preserve">ſit b f. </s>
              <s xml:id="echoid-s20653" xml:space="preserve">inde aſigno k. </s>
              <s xml:id="echoid-s20654" xml:space="preserve">adſuperficiem ſemcirculi b
                <lb/>
              d a. </s>
              <s xml:id="echoid-s20655" xml:space="preserve">cadat perpendicularis, certum eſt quod in circuli ſuperficiem cadet, quoniam in ſuperficie circuli eiuſ-
                <lb/>
              dem erectum fuit hemicylindrium. </s>
              <s xml:id="echoid-s20656" xml:space="preserve">Cadat igitur, & </s>
              <s xml:id="echoid-s20657" xml:space="preserve">ſit k i. </s>
              <s xml:id="echoid-s20658" xml:space="preserve">& </s>
              <s xml:id="echoid-s20659" xml:space="preserve">linea, quæ a ſigno i. </s>
              <s xml:id="echoid-s20660" xml:space="preserve">ad a. </s>
              <s xml:id="echoid-s20661" xml:space="preserve">ſignum duci-
                <lb/>
                <note position="left" xlink:label="note-514.01.306-04" xlink:href="note-514.01.306-04a" xml:space="preserve">40</note>
              tur, in ſigno h, iungatur cum linea b f. </s>
              <s xml:id="echoid-s20662" xml:space="preserve">Sed quoniam uterque ſemicirculus ideſt d k a b. </s>
              <s xml:id="echoid-s20663" xml:space="preserve">& </s>
              <s xml:id="echoid-s20664" xml:space="preserve">b m f,
                <lb/>
              erectus est in ſubiecto plano circuli a b d f. </s>
              <s xml:id="echoid-s20665" xml:space="preserve">Ideo commune eorum ſegmentum in h. </s>
              <s xml:id="echoid-s20666" xml:space="preserve">est ad angulosre-
                <lb/>
              ctos in plano circuli a b d f. </s>
              <s xml:id="echoid-s20667" xml:space="preserve">unde etiam ſupra b f. </s>
              <s xml:id="echoid-s20668" xml:space="preserve">erecta eſtipſa m h. </s>
              <s xml:id="echoid-s20669" xml:space="preserve">Igitur quod eſt ſub b h f.
                <lb/>
              </s>
              <s xml:id="echoid-s20670" xml:space="preserve">ideſt ſub a h i. </s>
              <s xml:id="echoid-s20671" xml:space="preserve">æ quale eſt illi, quod ab h m oritur. </s>
              <s xml:id="echoid-s20672" xml:space="preserve">Ergo angulus a m i rectuseſt ob conuerſionem co-
                <lb/>
              rollarij octauæ propoſitionis libri ſexti, & </s>
              <s xml:id="echoid-s20673" xml:space="preserve">trigonum a m i. </s>
              <s xml:id="echoid-s20674" xml:space="preserve">Simile eſt utriſque trigonis m a h. </s>
              <s xml:id="echoid-s20675" xml:space="preserve">& </s>
              <s xml:id="echoid-s20676" xml:space="preserve">a k
                <lb/>
              d. </s>
              <s xml:id="echoid-s20677" xml:space="preserve">& </s>
              <s xml:id="echoid-s20678" xml:space="preserve">quoniam angulus d k a. </s>
              <s xml:id="echoid-s20679" xml:space="preserve">per trigeſimam primam tertij elementorum rectus eſt, nam in ſemicirculo
                <lb/>
              poni ſubiectum fuit, & </s>
              <s xml:id="echoid-s20680" xml:space="preserve">quemadmodum innotuit angulus a m i. </s>
              <s xml:id="echoid-s20681" xml:space="preserve">rectus eſt, ideo per uigeſimam nonam pri-
                <lb/>
              mi d k. </s>
              <s xml:id="echoid-s20682" xml:space="preserve">m i. </s>
              <s xml:id="echoid-s20683" xml:space="preserve">ſunt æquidiſtantes, & </s>
              <s xml:id="echoid-s20684" xml:space="preserve">per eandem propoſitionem k i. </s>
              <s xml:id="echoid-s20685" xml:space="preserve">m k.</s>
              <s xml:id="echoid-s20686" xml:space="preserve">ſunt æ quidistantes, quoniam
                <lb/>
              & </s>
              <s xml:id="echoid-s20687" xml:space="preserve">per ea, quæ ſubiecimus, & </s>
              <s xml:id="echoid-s20688" xml:space="preserve">per ea, quæ demonstrauimus, k i, & </s>
              <s xml:id="echoid-s20689" xml:space="preserve">m k, ad perpendiculum cadunt in pla-
                <lb/>
              num circuli a b d f. </s>
              <s xml:id="echoid-s20690" xml:space="preserve">ratione igitur comparabile eſt,ut ſit d a. </s>
              <s xml:id="echoid-s20691" xml:space="preserve">ad a k, ita k a. </s>
              <s xml:id="echoid-s20692" xml:space="preserve">ad a i. </s>
              <s xml:id="echoid-s20693" xml:space="preserve">& </s>
              <s xml:id="echoid-s20694" xml:space="preserve">ita i a. </s>
              <s xml:id="echoid-s20695" xml:space="preserve">
                <lb/>
              ad a m. </s>
              <s xml:id="echoid-s20696" xml:space="preserve">quoniam trigoni d a k, h a i, i m a. </s>
              <s xml:id="echoid-s20697" xml:space="preserve">ſimiles ſunt, ex quarta ſexti elementorum, ergo con-
                <lb/>
                <note position="left" xlink:label="note-514.01.306-05" xlink:href="note-514.01.306-05a" xml:space="preserve">50</note>
              ſequitur quatuor rectas lineas d a. </s>
              <s xml:id="echoid-s20698" xml:space="preserve">a k. </s>
              <s xml:id="echoid-s20699" xml:space="preserve">a i. </s>
              <s xml:id="echoid-s20700" xml:space="preserve">a m. </s>
              <s xml:id="echoid-s20701" xml:space="preserve">mutua ratione inter ſe eſſe comparatas. </s>
              <s xml:id="echoid-s20702" xml:space="preserve">Est uero
                <lb/>
              a m æ qualis ipſi c. </s>
              <s xml:id="echoid-s20703" xml:space="preserve">ex communi ſententia, quæ uni,& </s>
              <s xml:id="echoid-s20704" xml:space="preserve">eidem ſunt æqua, inter ſe etiam æqua eſſe. </s>
              <s xml:id="echoid-s20705" xml:space="preserve">quoniam
                <lb/>
              a m, ipſi a b. </s>
              <s xml:id="echoid-s20706" xml:space="preserve">æ qualis eſt. </s>
              <s xml:id="echoid-s20707" xml:space="preserve">Duabus igitur propoſitis rectis lineis duas medias comparatas inuenimus ſci-
                <lb/>
              licet a k. </s>
              <s xml:id="echoid-s20708" xml:space="preserve">& </s>
              <s xml:id="echoid-s20709" xml:space="preserve">a i. </s>
              <s xml:id="echoid-s20710" xml:space="preserve">ut patet ex diagrammate V. </s>
              <s xml:id="echoid-s20711" xml:space="preserve">inferius poſito. </s>
              <s xml:id="echoid-s20712" xml:space="preserve">Nunc uero ad demonstratiunem & </s>
              <s xml:id="echoid-s20713" xml:space="preserve">or-
                <lb/>
              ganum Paccij ueniamus. </s>
              <s xml:id="echoid-s20714" xml:space="preserve">Ita ergo inquit ille. </s>
              <s xml:id="echoid-s20715" xml:space="preserve">Sit A B D ſemicirculus in plano imaginemur hemicylin-
                <lb/>
              drum erectum ſuper A B D, ſemicirculum, & </s>
              <s xml:id="echoid-s20716" xml:space="preserve">ſupra diametrum A D, alium ſemicir culum erectum ſta-
                <lb/>
              tuamus in hemicylindri parallelogrammo, ſemicirculus is circumactus,uerbi gratia a D, uerſus E. </s>
              <s xml:id="echoid-s20717" xml:space="preserve">ma-
                <lb/>
              nente in A, ſigno extremo diametri A D. </s>
              <s xml:id="echoid-s20718" xml:space="preserve">firmo, in circumactione ſecabit ſuperſiciem cylindri,& </s>
              <s xml:id="echoid-s20719" xml:space="preserve">linea
                <lb/>
              ſuæ circumactionis circa eius ſuperficiem deſcribet quandam lineam, cuius lineationem inuenire oportet.
                <lb/>
              </s>
              <s xml:id="echoid-s20720" xml:space="preserve">
                <note position="left" xlink:label="note-514.01.306-06" xlink:href="note-514.01.306-06a" xml:space="preserve">60</note>
              </s>
            </p>
          </div>
        </div>
      </text>
    </echo>
Impressum