Vitruvius, De architectura libri decem, 1567

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        <div xml:id="echoid-div1" type="section" level="1" n="1">
          <div xml:id="echoid-div718" type="section" level="2" n="135">
            <p style="it">
              <s xml:id="echoid-s20720" xml:space="preserve">
                <pb o="275" file="514.01.307" n="307" rhead="NONVS."/>
              Quoniamlinea A D, diameter eſt ſemicirculi A B D, & </s>
              <s xml:id="echoid-s20721" xml:space="preserve">diameter etiaim est ſemicirculi erecti ſupra
                <lb/>
              A B D, ideo dum mouetur ſemicirculus erectus à D, uerſus B, & </s>
              <s xml:id="echoid-s20722" xml:space="preserve">à B. </s>
              <s xml:id="echoid-s20723" xml:space="preserve">uerſus A. </s>
              <s xml:id="echoid-s20724" xml:space="preserve">immobili perma-
                <lb/>
              nente ſigno A, tanquam cardini, ſecumſeret ſuam diamertron, & </s>
              <s xml:id="echoid-s20725" xml:space="preserve">ita ex duabus diametris, quæ prius in unam
                <lb/>
              lineam conueniebant, altera non diſcedet a loco ſuo, nimirum A D. </s>
              <s xml:id="echoid-s20726" xml:space="preserve">ſemicirculi plani, altera loci permuta-
                <lb/>
              tione à D uerſus E, & </s>
              <s xml:id="echoid-s20727" xml:space="preserve">àB. </s>
              <s xml:id="echoid-s20728" xml:space="preserve">uerſus A, unà cum ſemicirculo erecto diuerſas partes hemic ylindrij ſeca-
                <lb/>
              bit, donec fiet A C. </s>
              <s xml:id="echoid-s20729" xml:space="preserve">extra ſuperficiem hemicylindrij, & </s>
              <s xml:id="echoid-s20730" xml:space="preserve">recte cadet ſuper ſignum A. </s>
              <s xml:id="echoid-s20731" xml:space="preserve">quod est extremum
                <lb/>
              diametri A D. </s>
              <s xml:id="echoid-s20732" xml:space="preserve">cum in integra illa uerſatione ſigno D, deſcripſerit circuli tetrantem. </s>
              <s xml:id="echoid-s20733" xml:space="preserve">& </s>
              <s xml:id="echoid-s20734" xml:space="preserve">quoniam diame-
                <lb/>
              tros A D, translata à D uerſus B. </s>
              <s xml:id="echoid-s20735" xml:space="preserve">& </s>
              <s xml:id="echoid-s20736" xml:space="preserve">à B. </s>
              <s xml:id="echoid-s20737" xml:space="preserve">uerſus A. </s>
              <s xml:id="echoid-s20738" xml:space="preserve">ubicunque ſiſtitur ſecat lineam ſemicirculi
                <lb/>
              A B D, ſecetigitur eam in ſignis E F G H I K L M N O P Q R S T. </s>
              <s xml:id="echoid-s20739" xml:space="preserve">& </s>
              <s xml:id="echoid-s20740" xml:space="preserve">ab A. </s>
              <s xml:id="echoid-s20741" xml:space="preserve">ad ſingula
                <lb/>
                <note position="left" xlink:label="note-514.01.307-01" xlink:href="note-514.01.307-01a" xml:space="preserve">10</note>
              ea ſigna, ducantur ſaltem imaginatione rectæ A F. </s>
              <s xml:id="echoid-s20742" xml:space="preserve">A G. </s>
              <s xml:id="echoid-s20743" xml:space="preserve">A H. </s>
              <s xml:id="echoid-s20744" xml:space="preserve">A I. </s>
              <s xml:id="echoid-s20745" xml:space="preserve">A K. </s>
              <s xml:id="echoid-s20746" xml:space="preserve">A L, A M. </s>
              <s xml:id="echoid-s20747" xml:space="preserve">A N.
                <lb/>
              </s>
              <s xml:id="echoid-s20748" xml:space="preserve">A O. </s>
              <s xml:id="echoid-s20749" xml:space="preserve">A P. </s>
              <s xml:id="echoid-s20750" xml:space="preserve">A Q. </s>
              <s xml:id="echoid-s20751" xml:space="preserve">A R. </s>
              <s xml:id="echoid-s20752" xml:space="preserve">A S. </s>
              <s xml:id="echoid-s20753" xml:space="preserve">A T. </s>
              <s xml:id="echoid-s20754" xml:space="preserve">& </s>
              <s xml:id="echoid-s20755" xml:space="preserve">producantur ad tetrantis circumſerentiam in ſigna. </s>
              <s xml:id="echoid-s20756" xml:space="preserve">
                <lb/>
              e. </s>
              <s xml:id="echoid-s20757" xml:space="preserve">f. </s>
              <s xml:id="echoid-s20758" xml:space="preserve">g. </s>
              <s xml:id="echoid-s20759" xml:space="preserve">h. </s>
              <s xml:id="echoid-s20760" xml:space="preserve">i. </s>
              <s xml:id="echoid-s20761" xml:space="preserve">k. </s>
              <s xml:id="echoid-s20762" xml:space="preserve">φ. </s>
              <s xml:id="echoid-s20763" xml:space="preserve">m. </s>
              <s xml:id="echoid-s20764" xml:space="preserve">n. </s>
              <s xml:id="echoid-s20765" xml:space="preserve">o. </s>
              <s xml:id="echoid-s20766" xml:space="preserve">p. </s>
              <s xml:id="echoid-s20767" xml:space="preserve">q. </s>
              <s xml:id="echoid-s20768" xml:space="preserve">r. </s>
              <s xml:id="echoid-s20769" xml:space="preserve">s. </s>
              <s xml:id="echoid-s20770" xml:space="preserve">t. </s>
              <s xml:id="echoid-s20771" xml:space="preserve">& </s>
              <s xml:id="echoid-s20772" xml:space="preserve">Singulæ ex his lineæ referent diametrum ſemicirculi
                <lb/>
              translatam circa cylindri ſuperficiem. </s>
              <s xml:id="echoid-s20773" xml:space="preserve">Diuidatur media diametros A D, in X, & </s>
              <s xml:id="echoid-s20774" xml:space="preserve">centro A, inter-
                <lb/>
              uallo A X, tetrans circuli deſcribatur x y, linea circinationis tetrantis x y ſingulas diametros me-
                <lb/>
              dias ſecabit, & </s>
              <s xml:id="echoid-s20775" xml:space="preserve">occaſionem dabit terminandi ſingulas illas lineas, quæ a ſigno D. </s>
              <s xml:id="echoid-s20776" xml:space="preserve">omnium communi termi-
                <lb/>
              no proficiſcentes ſe ſe conſequentes alio eorum extremo ad circinationis lineam, quæ ſupra diametrum de-
                <lb/>
              ſcriberetur, peruenirent. </s>
              <s xml:id="echoid-s20777" xml:space="preserve">ſupra diametrum dico, quam quæ libet earum ſecat in circinatione A B D. </s>
              <s xml:id="echoid-s20778" xml:space="preserve">ima-
                <lb/>
              ginemur itaque ſemicirculos ſupra ſingulas diametros a e. </s>
              <s xml:id="echoid-s20779" xml:space="preserve">a f. </s>
              <s xml:id="echoid-s20780" xml:space="preserve">a g. </s>
              <s xml:id="echoid-s20781" xml:space="preserve">a h. </s>
              <s xml:id="echoid-s20782" xml:space="preserve">& </s>
              <s xml:id="echoid-s20783" xml:space="preserve">reliquas quæ ab A. </s>
              <s xml:id="echoid-s20784" xml:space="preserve">pro-
                <lb/>
              gredientes ad circinationis tetrantis B C. </s>
              <s xml:id="echoid-s20785" xml:space="preserve">perueniunt. </s>
              <s xml:id="echoid-s20786" xml:space="preserve">& </s>
              <s xml:id="echoid-s20787" xml:space="preserve">a ſigno D, per ſingula puncta, in quibus Linea
                <lb/>
                <note position="left" xlink:label="note-514.01.307-02" xlink:href="note-514.01.307-02a" xml:space="preserve">20</note>
              circinationis A B D, ſecat ſingulas diametros mobiles, & </s>
              <s xml:id="echoid-s20788" xml:space="preserve">in quibus mutuo ab ipſis ſecatur,& </s>
              <s xml:id="echoid-s20789" xml:space="preserve">erigantur
                <lb/>
              lineæ, quæ ad circinationes ſemicirculorum,quos imaginati ſumus, perueniant adſigna α. </s>
              <s xml:id="echoid-s20790" xml:space="preserve">β. </s>
              <s xml:id="echoid-s20791" xml:space="preserve">γ. </s>
              <s xml:id="echoid-s20792" xml:space="preserve">δ. </s>
              <s xml:id="echoid-s20793" xml:space="preserve">ε. </s>
              <s xml:id="echoid-s20794" xml:space="preserve">η.
                <lb/>
              </s>
              <s xml:id="echoid-s20795" xml:space="preserve">{σθ} ι κ. </s>
              <s xml:id="echoid-s20796" xml:space="preserve">λ μ. </s>
              <s xml:id="echoid-s20797" xml:space="preserve">ν. </s>
              <s xml:id="echoid-s20798" xml:space="preserve">ξ. </s>
              <s xml:id="echoid-s20799" xml:space="preserve">ο. </s>
              <s xml:id="echoid-s20800" xml:space="preserve">π. </s>
              <s xml:id="echoid-s20801" xml:space="preserve">Aio ſingulas lineas E α. </s>
              <s xml:id="echoid-s20802" xml:space="preserve">F β. </s>
              <s xml:id="echoid-s20803" xml:space="preserve">G γ. </s>
              <s xml:id="echoid-s20804" xml:space="preserve">H δ I. </s>
              <s xml:id="echoid-s20805" xml:space="preserve">ε. </s>
              <s xml:id="echoid-s20806" xml:space="preserve">K ζ. </s>
              <s xml:id="echoid-s20807" xml:space="preserve">L η. </s>
              <s xml:id="echoid-s20808" xml:space="preserve">M ξ N ι. </s>
              <s xml:id="echoid-s20809" xml:space="preserve">
                <lb/>
              O κ. </s>
              <s xml:id="echoid-s20810" xml:space="preserve">P λ. </s>
              <s xml:id="echoid-s20811" xml:space="preserve">q. </s>
              <s xml:id="echoid-s20812" xml:space="preserve">μ. </s>
              <s xml:id="echoid-s20813" xml:space="preserve">R ν. </s>
              <s xml:id="echoid-s20814" xml:space="preserve">S ξ T ο. </s>
              <s xml:id="echoid-s20815" xml:space="preserve">V π. </s>
              <s xml:id="echoid-s20816" xml:space="preserve">eſſe medias comparabiles inter eas diametri partes, quas in illa
                <lb/>
              ſecant in aliquo dictorum ſignorum. </s>
              <s xml:id="echoid-s20817" xml:space="preserve">Deſcribatur ſupra diametrum A φ ſemicirculus A η φ. </s>
              <s xml:id="echoid-s20818" xml:space="preserve">aio lineam
                <lb/>
              n L. </s>
              <s xml:id="echoid-s20819" xml:space="preserve">eſſe mediã inter partes diametri A L. </s>
              <s xml:id="echoid-s20820" xml:space="preserve">& </s>
              <s xml:id="echoid-s20821" xml:space="preserve">L φ. </s>
              <s xml:id="echoid-s20822" xml:space="preserve">quam diametron ipſa ſecat in ſigno L. </s>
              <s xml:id="echoid-s20823" xml:space="preserve">& </s>
              <s xml:id="echoid-s20824" xml:space="preserve">quoniam an-
                <lb/>
              guli A. </s>
              <s xml:id="echoid-s20825" xml:space="preserve">L D. </s>
              <s xml:id="echoid-s20826" xml:space="preserve">η λ φ.</s>
              <s xml:id="echoid-s20827" xml:space="preserve">oppoſiti ſunt,ideo æ quales ſunt, ex decima quinta primi elementorum. </s>
              <s xml:id="echoid-s20828" xml:space="preserve">Sed angulus A L
                <lb/>
              D, quia eſt in ſemicirculo,rectus eſt ex trigeſima prima tertij: </s>
              <s xml:id="echoid-s20829" xml:space="preserve">Angulus ergo η L φ rectus erit. </s>
              <s xml:id="echoid-s20830" xml:space="preserve">Ex ſigno L. </s>
              <s xml:id="echoid-s20831" xml:space="preserve">
                <lb/>
              erecta est diametro A φ ad angulos rectos linearcta L.</s>
              <s xml:id="echoid-s20832" xml:space="preserve">x. </s>
              <s xml:id="echoid-s20833" xml:space="preserve">quæ peruenit ad circinationem circumferen-
                <lb/>
              tia A η ο ergo recta η L erit media proportione reſpondens inter lineas A L. </s>
              <s xml:id="echoid-s20834" xml:space="preserve">& </s>
              <s xml:id="echoid-s20835" xml:space="preserve">L φ extertia de-
                <lb/>
              cima ſexti. </s>
              <s xml:id="echoid-s20836" xml:space="preserve">Aio præ terea lineam n L, ſupra planum ſemicirculi A B D. </s>
              <s xml:id="echoid-s20837" xml:space="preserve">in ſigno L. </s>
              <s xml:id="echoid-s20838" xml:space="preserve">ad rectos angulos
                <lb/>
                <note position="left" xlink:label="note-514.01.307-03" xlink:href="note-514.01.307-03a" xml:space="preserve">30</note>
              stare. </s>
              <s xml:id="echoid-s20839" xml:space="preserve">Quoniam ſemicirculus A η φ rectus eſt ad planum ſemicirculi A B D
                <lb/>
              D. </s>
              <s xml:id="echoid-s20840" xml:space="preserve">& </s>
              <s xml:id="echoid-s20841" xml:space="preserve">ab uno circinationis ſi- gno A η φ ſcilicet η.</s>
              <s xml:id="echoid-s20842" xml:space="preserve">ducta eſt recta η L, quæ peruenit ad planum ſemicirculi A B D. </s>
              <s xml:id="echoid-s20843" xml:space="preserve">ergo x L re-
                <lb/>
              cte ſtabit ad planum ſemicirculi A B D. </s>
              <s xml:id="echoid-s20844" xml:space="preserve">Sed n L quoniam comparabiles estinter A L. </s>
              <s xml:id="echoid-s20845" xml:space="preserve">& </s>
              <s xml:id="echoid-s20846" xml:space="preserve">L. </s>
              <s xml:id="echoid-s20847" xml:space="preserve">φ. </s>
              <s xml:id="echoid-s20848" xml:space="preserve">ad
                <lb/>
              rectos angulos cadit in L, commume rectarum A
                <unsure/>
              & </s>
              <s xml:id="echoid-s20849" xml:space="preserve">D L ſegmentum; </s>
              <s xml:id="echoid-s20850" xml:space="preserve">ideo n L a rctos stabit an-
                <lb/>
              gulos ſupra ſemicirculi A B D. </s>
              <s xml:id="echoid-s20851" xml:space="preserve">planum, in ſigno L. </s>
              <s xml:id="echoid-s20852" xml:space="preserve">& </s>
              <s xml:id="echoid-s20853" xml:space="preserve">quoniam ad id planum ſemicriculi, A B D, re-
                <lb/>
              ctum & </s>
              <s xml:id="echoid-s20854" xml:space="preserve">hemcylindrium, ita quod eius baſis diametros, diametro ſemicir culi quadrat, & </s>
              <s xml:id="echoid-s20855" xml:space="preserve">circinationis linea
                <lb/>
              unius conuenit lineæ circinationis alterius. </s>
              <s xml:id="echoid-s20856" xml:space="preserve">n L. </s>
              <s xml:id="echoid-s20857" xml:space="preserve">pariter rectè cadet ſupra lmeam circinationis baſis bemicy
                <lb/>
              lindrij in ſigno L. </s>
              <s xml:id="echoid-s20858" xml:space="preserve">& </s>
              <s xml:id="echoid-s20859" xml:space="preserve">bac ratione recta η L in ſi perficie hemicylindrij reperietur.</s>
              <s xml:id="echoid-s20860" xml:space="preserve">atque etiam in plano ſe-
                <lb/>
              micirculi. </s>
              <s xml:id="echoid-s20861" xml:space="preserve">A η φ. </s>
              <s xml:id="echoid-s20862" xml:space="preserve">ita ut pariter in utroque plano ſtare contingct. </s>
              <s xml:id="echoid-s20863" xml:space="preserve">Semicirculus ergo A η φ. </s>
              <s xml:id="echoid-s20864" xml:space="preserve">tanget he-
                <lb/>
              micylindrium in ſigno H. </s>
              <s xml:id="echoid-s20865" xml:space="preserve">Similiratione ac uia demonſtrabitur ſingulas rectarum linearum. </s>
              <s xml:id="echoid-s20866" xml:space="preserve">E α. </s>
              <s xml:id="echoid-s20867" xml:space="preserve">F β.
                <lb/>
              </s>
              <s xml:id="echoid-s20868" xml:space="preserve">
                <note position="left" xlink:label="note-514.01.307-04" xlink:href="note-514.01.307-04a" xml:space="preserve">40</note>
              G γ & </s>
              <s xml:id="echoid-s20869" xml:space="preserve">reliquas eſſe medias comparabiles inter diametri partes, & </s>
              <s xml:id="echoid-s20870" xml:space="preserve">rectas cadere conſequenter u-
                <lb/>
              nam poſt aliam ſuper lineam baſis hemicylindrij. </s>
              <s xml:id="echoid-s20871" xml:space="preserve">& </s>
              <s xml:id="echoid-s20872" xml:space="preserve">quod quæ libet erit in utroque plano, quam pri-
                <lb/>
              mum peruenerit ad hemicylindrij ſuperſiciem, ad ſuam quæ q; </s>
              <s xml:id="echoid-s20873" xml:space="preserve">altitudinem in ſignis ſcilicet.
                <lb/>
              </s>
              <s xml:id="echoid-s20874" xml:space="preserve">θ. </s>
              <s xml:id="echoid-s20875" xml:space="preserve">ι. </s>
              <s xml:id="echoid-s20876" xml:space="preserve">κ. </s>
              <s xml:id="echoid-s20877" xml:space="preserve">λ. </s>
              <s xml:id="echoid-s20878" xml:space="preserve">μ. </s>
              <s xml:id="echoid-s20879" xml:space="preserve">ν. </s>
              <s xml:id="echoid-s20880" xml:space="preserve">ξ. </s>
              <s xml:id="echoid-s20881" xml:space="preserve">ο. </s>
              <s xml:id="echoid-s20882" xml:space="preserve">π. </s>
              <s xml:id="echoid-s20883" xml:space="preserve">in quibus ſignis ſemicirculus mobilis tranſlatus, ( ut dictum eſt) neceſſario he-
                <lb/>
              micylindrij ſuperficiem tanget, & </s>
              <s xml:id="echoid-s20884" xml:space="preserve">quæſitam lineam illi circumſcribet. </s>
              <s xml:id="echoid-s20885" xml:space="preserve">V nde ſi ducatur linea, quæ per ſingula
                <lb/>
              illa ſigna tranſeat, & </s>
              <s xml:id="echoid-s20886" xml:space="preserve">eam hemicylindrij partem ſecet, quæ illi ſubiacet, abſque ullo impedimento circumagi
                <lb/>
              poterit dictus ſemucirculus circa ſuperficiem hemicylindrij, & </s>
              <s xml:id="echoid-s20887" xml:space="preserve">ſemper ſua circinatione per ſingula ſigna tan-
                <lb/>
              get lineam nuper deſcriptam in hemicylindri ſuperficie. </s>
              <s xml:id="echoid-s20888" xml:space="preserve">A ſingulis autem ſignis E. </s>
              <s xml:id="echoid-s20889" xml:space="preserve">F. </s>
              <s xml:id="echoid-s20890" xml:space="preserve">G. </s>
              <s xml:id="echoid-s20891" xml:space="preserve">H. </s>
              <s xml:id="echoid-s20892" xml:space="preserve">I. </s>
              <s xml:id="echoid-s20893" xml:space="preserve">K. </s>
              <s xml:id="echoid-s20894" xml:space="preserve">L. </s>
              <s xml:id="echoid-s20895" xml:space="preserve">
                <lb/>
              M. </s>
              <s xml:id="echoid-s20896" xml:space="preserve">N. </s>
              <s xml:id="echoid-s20897" xml:space="preserve">O. </s>
              <s xml:id="echoid-s20898" xml:space="preserve">P. </s>
              <s xml:id="echoid-s20899" xml:space="preserve">Q. </s>
              <s xml:id="echoid-s20900" xml:space="preserve">R. </s>
              <s xml:id="echoid-s20901" xml:space="preserve">S. </s>
              <s xml:id="echoid-s20902" xml:space="preserve">T. </s>
              <s xml:id="echoid-s20903" xml:space="preserve">inſuper planum A B D, ſecundum ſuperficiem hemicylindrij erigantur
                <lb/>
              ſub ſequentis rectæ lineæ æ quales ſingulæ ſingulis ijs, quæ ab eodem ſigno ductæ ſunt, in plana eorum circulo-
                <lb/>
                <note position="left" xlink:label="note-514.01.307-05" xlink:href="note-514.01.307-05a" xml:space="preserve">50</note>
              rum, quos imaginat ione ſinximus, & </s>
              <s xml:id="echoid-s20904" xml:space="preserve">quȩ oſtenſæ ſunt mediæ comparabiles inter ſuarum diametrorum par-
                <lb/>
              tes.</s>
              <s xml:id="echoid-s20905" xml:space="preserve">Poſt hæc deſcribātur lineæ, quæ per omnia extrema earum ſigna tranſeant, quæ ſuperius terminum habent
                <lb/>
              circa hemicylindrij ſuperſiciem,& </s>
              <s xml:id="echoid-s20906" xml:space="preserve">ita perfectum erit, quod quærebatur. </s>
              <s xml:id="echoid-s20907" xml:space="preserve">poterimus quoque ſupra diametrum
                <lb/>
              A B. </s>
              <s xml:id="echoid-s20908" xml:space="preserve">æquare parallelogrammum A D σ ν quod referet hemicylindrium, & </s>
              <s xml:id="echoid-s20909" xml:space="preserve">a ſingulis prædictis iam ſi-
                <lb/>
              gnis circinationis A B D. </s>
              <s xml:id="echoid-s20910" xml:space="preserve">parallelas ducere lateribus A σ D ν quæ ſuper latus σ ν cadant, at-
                <lb/>
              que incipiendo a ſignis E F G H. </s>
              <s xml:id="echoid-s20911" xml:space="preserve">& </s>
              <s xml:id="echoid-s20912" xml:space="preserve">reliquis deſcendendo ad baſim σ ν excipere lineas ſingulis præ-
                <lb/>
              dictarum medias comparabiles, & </s>
              <s xml:id="echoid-s20913" xml:space="preserve">inde lineam deſcribere, quæ per ſingula extrema ſigna tranſeat, quæ ſigna
                <lb/>
              termini ſunt dictarum linearum ad baſim σ ν. </s>
              <s xml:id="echoid-s20914" xml:space="preserve">& </s>
              <s xml:id="echoid-s20915" xml:space="preserve">habebitur hoc modo lineatio cylindricæ linæ a nobis quæ-
                <lb/>
              ſitæ, quemadmodum in diagrammate cerni potest.</s>
              <s xml:id="echoid-s20916" xml:space="preserve"/>
            </p>
            <note position="left" xml:space="preserve">60</note>
          </div>
        </div>
      </text>
    </echo>
Impressum