Vitruvius, De architectura libri decem, 1567

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          <div xml:id="echoid-div769" type="section" level="2" n="142">
            <p>
              <s xml:id="echoid-s24210" xml:space="preserve">
                <pb o="319" file="514.01.351" n="351" rhead="NONVS."/>
              transferatur in meridianum 10. </s>
              <s xml:id="echoid-s24211" xml:space="preserve">& </s>
              <s xml:id="echoid-s24212" xml:space="preserve">2. </s>
              <s xml:id="echoid-s24213" xml:space="preserve">& </s>
              <s xml:id="echoid-s24214" xml:space="preserve">circunferentia inter 10. </s>
              <s xml:id="echoid-s24215" xml:space="preserve">& </s>
              <s xml:id="echoid-s24216" xml:space="preserve">2, & </s>
              <s xml:id="echoid-s24217" xml:space="preserve">ſignum 0. </s>
              <s xml:id="echoid-s24218" xml:space="preserve">erit arcus al-
                <lb/>
              titudinis Solis ſupra meridianum hora decima, & </s>
              <s xml:id="echoid-s24219" xml:space="preserve">ſecunda. </s>
              <s xml:id="echoid-s24220" xml:space="preserve">Hac autem ratione, & </s>
              <s xml:id="echoid-s24221" xml:space="preserve">uia ſumentur reliquæ
                <lb/>
              ectemoriæ circunferentiæ, tam tropici Capricorni infra, quàm tropici Cancri ſupra, ut in diagrammate A.
                <lb/>
              </s>
              <s xml:id="echoid-s24222" xml:space="preserve">uidere potes. </s>
              <s xml:id="echoid-s24223" xml:space="preserve">Vtigitur prædictas circunferentias horologio accommodemus, & </s>
              <s xml:id="echoid-s24224" xml:space="preserve">linearum multitudinem fu-
                <lb/>
              giamus, fiet diagramma B. </s>
              <s xml:id="echoid-s24225" xml:space="preserve">Esto igitur circulus o p q n. </s>
              <s xml:id="echoid-s24226" xml:space="preserve">pro meridiano, binis diametris in quatuor
                <lb/>
              tetrantes diſſectus: </s>
              <s xml:id="echoid-s24227" xml:space="preserve">in diametro autem p q. </s>
              <s xml:id="echoid-s24228" xml:space="preserve">ſumatur gnomonis longitudo ab e. </s>
              <s xml:id="echoid-s24229" xml:space="preserve">ad t. </s>
              <s xml:id="echoid-s24230" xml:space="preserve">tam ſupra e. </s>
              <s xml:id="echoid-s24231" xml:space="preserve">quã
                <lb/>
              infra, perq́; </s>
              <s xml:id="echoid-s24232" xml:space="preserve">ſigna t. </s>
              <s xml:id="echoid-s24233" xml:space="preserve">ducantur lineæ æquidistantes diametro o n. </s>
              <s xml:id="echoid-s24234" xml:space="preserve">quæ ſint r t s. </s>
              <s xml:id="echoid-s24235" xml:space="preserve">bælineæ planitiam, in
                <lb/>
              qua umbræ protenduntur, oſtendunt. </s>
              <s xml:id="echoid-s24236" xml:space="preserve">Vtigitur umbrarum longitudines in planitiæ lineas traducas, ſumito a
                <lb/>
              diagrammate A. </s>
              <s xml:id="echoid-s24237" xml:space="preserve">circunferentias ectemorias, & </s>
              <s xml:id="echoid-s24238" xml:space="preserve">transferas in diagramma B. </s>
              <s xml:id="echoid-s24239" xml:space="preserve">Eas quidem quæ ſunt Cancri
                <lb/>
                <note position="left" xlink:label="note-514.01.351-01" xlink:href="note-514.01.351-01a" xml:space="preserve">10</note>
              in quartam n p. </s>
              <s xml:id="echoid-s24240" xml:space="preserve">ab n. </s>
              <s xml:id="echoid-s24241" xml:space="preserve">quæ uero Capricorni in quartam n g. </s>
              <s xml:id="echoid-s24242" xml:space="preserve">ab n. </s>
              <s xml:id="echoid-s24243" xml:space="preserve">& </s>
              <s xml:id="echoid-s24244" xml:space="preserve">reſpondentes horarum nume-
                <lb/>
              ros appones a. </s>
              <s xml:id="echoid-s24245" xml:space="preserve">quibus lineas per e. </s>
              <s xml:id="echoid-s24246" xml:space="preserve">centrum ad oppoſitas planum r t s. </s>
              <s xml:id="echoid-s24247" xml:space="preserve">traduces. </s>
              <s xml:id="echoid-s24248" xml:space="preserve">ubi lineæ Cancri in
                <lb/>
              r s t. </s>
              <s xml:id="echoid-s24249" xml:space="preserve">quæ est infra o e n. </s>
              <s xml:id="echoid-s24250" xml:space="preserve">Capricorm uero in linea r s t. </s>
              <s xml:id="echoid-s24251" xml:space="preserve">quæ ſuperius eſt, deſignabuntur. </s>
              <s xml:id="echoid-s24252" xml:space="preserve">Cum uero
                <lb/>
              horologium ad ortum ſpectans deſcribere uolueris, diagramma facies C. </s>
              <s xml:id="echoid-s24253" xml:space="preserve">ubi circulus a b c d. </s>
              <s xml:id="echoid-s24254" xml:space="preserve">in cen-
                <lb/>
              tro e. </s>
              <s xml:id="echoid-s24255" xml:space="preserve">diameter a c. </s>
              <s xml:id="echoid-s24256" xml:space="preserve">erit ſectio communis ipſimeridiano, & </s>
              <s xml:id="echoid-s24257" xml:space="preserve">finitori. </s>
              <s xml:id="echoid-s24258" xml:space="preserve">b d. </s>
              <s xml:id="echoid-s24259" xml:space="preserve">uero communis ſectio meri-
                <lb/>
              diani, & </s>
              <s xml:id="echoid-s24260" xml:space="preserve">uerticalis. </s>
              <s xml:id="echoid-s24261" xml:space="preserve">ita ut a. </s>
              <s xml:id="echoid-s24262" xml:space="preserve">ad meridiem, c, ad ſeptentrionem ſtatuas. </s>
              <s xml:id="echoid-s24263" xml:space="preserve">ducatur item alia diametros mediæ
                <lb/>
              inter a d. </s>
              <s xml:id="echoid-s24264" xml:space="preserve">quæ ſit f g. </s>
              <s xml:id="echoid-s24265" xml:space="preserve">communis ſectio æquinoctialis, & </s>
              <s xml:id="echoid-s24266" xml:space="preserve">meridiani, quæ diametros tantũ ſuper a extollatur
                <lb/>
              quantum in analemmate tollitur æquinoctialis ſupra finitorem, in hoc diagrammate, quod C. </s>
              <s xml:id="echoid-s24267" xml:space="preserve">litera indicat
                <lb/>
              ponendæ ſunt meridianæ circunferentiæ, ac illæ primum, quæ ſunt Cancri c o. </s>
              <s xml:id="echoid-s24268" xml:space="preserve">c i. </s>
              <s xml:id="echoid-s24269" xml:space="preserve">c l. </s>
              <s xml:id="echoid-s24270" xml:space="preserve">c u. </s>
              <s xml:id="echoid-s24271" xml:space="preserve">c r. </s>
              <s xml:id="echoid-s24272" xml:space="preserve">a pun-
                <lb/>
              cto c. </s>
              <s xml:id="echoid-s24273" xml:space="preserve">uerſus d. </s>
              <s xml:id="echoid-s24274" xml:space="preserve">& </s>
              <s xml:id="echoid-s24275" xml:space="preserve">notandi ſunt reſpondentium horarum numeri. </s>
              <s xml:id="echoid-s24276" xml:space="preserve">quae omnia literis, numeris, ſeu cha-
                <lb/>
                <note position="left" xlink:label="note-514.01.351-02" xlink:href="note-514.01.351-02a" xml:space="preserve">20</note>
              racteribus delebilibus notabis. </s>
              <s xml:id="echoid-s24277" xml:space="preserve">expeditis his diuiſionibus in diagrammate C. </s>
              <s xml:id="echoid-s24278" xml:space="preserve">lineas duces a punctis o.
                <lb/>
              </s>
              <s xml:id="echoid-s24279" xml:space="preserve">i. </s>
              <s xml:id="echoid-s24280" xml:space="preserve">l. </s>
              <s xml:id="echoid-s24281" xml:space="preserve">u. </s>
              <s xml:id="echoid-s24282" xml:space="preserve">r. </s>
              <s xml:id="echoid-s24283" xml:space="preserve">per centrum e. </s>
              <s xml:id="echoid-s24284" xml:space="preserve">ad oppoſitas partes circinationis, tam eas, quæad Cancrum, quàm eas, quæ
                <lb/>
              ad Capricornum pertinent, inde a diagrammate B. </s>
              <s xml:id="echoid-s24285" xml:space="preserve">deduces in diagramma C. </s>
              <s xml:id="echoid-s24286" xml:space="preserve">longitudines umbræ, ſuper li-
                <lb/>
              neas reſpondentes horis iam ductis a circunferentia ectemoria. </s>
              <s xml:id="echoid-s24287" xml:space="preserve">deinde connectes horas Cancri, cum horis Ca-
                <lb/>
              pricorni, & </s>
              <s xml:id="echoid-s24288" xml:space="preserve">habebis horologium ad ortum. </s>
              <s xml:id="echoid-s24289" xml:space="preserve">Eadem ratione horologium facies ad occaſum ſpectantem, tranſ-
                <lb/>
              ferendo lineas omnes in quartum a b. </s>
              <s xml:id="echoid-s24290" xml:space="preserve">& </s>
              <s xml:id="echoid-s24291" xml:space="preserve">notando poſt meridianas horas, quemadmodum eſt in diagramma-
                <lb/>
              te D. </s>
              <s xml:id="echoid-s24292" xml:space="preserve">At in diagrammate E. </s>
              <s xml:id="echoid-s24293" xml:space="preserve">horæ ſunt a meridie, ante meridianæ. </s>
              <s xml:id="echoid-s24294" xml:space="preserve">in F. </s>
              <s xml:id="echoid-s24295" xml:space="preserve">Vero pomeridianæ. </s>
              <s xml:id="echoid-s24296" xml:space="preserve">ſicut in H. </s>
              <s xml:id="echoid-s24297" xml:space="preserve">
                <lb/>
              horæ ab occaſu antemeridianæ, & </s>
              <s xml:id="echoid-s24298" xml:space="preserve">in G. </s>
              <s xml:id="echoid-s24299" xml:space="preserve">pomeridianæ. </s>
              <s xml:id="echoid-s24300" xml:space="preserve">Iam uerticalia, plana, & </s>
              <s xml:id="echoid-s24301" xml:space="preserve">meridiana explicata
                <lb/>
              ſunt, anguliq́; </s>
              <s xml:id="echoid-s24302" xml:space="preserve">expoſiti, & </s>
              <s xml:id="echoid-s24303" xml:space="preserve">circunferentiæ omnes, unde latitudines, & </s>
              <s xml:id="echoid-s24304" xml:space="preserve">longitudines umbrarum excipiebantur,
                <lb/>
              Modo rationem oſtendemus, qua horologia in plano æquinoctialis conficere poſſimus, rem quidem non minus
                <lb/>
              facilem, quàm iucundam. </s>
              <s xml:id="echoid-s24305" xml:space="preserve">Esto meridianus a b c d. </s>
              <s xml:id="echoid-s24306" xml:space="preserve">cuius diameter a c. </s>
              <s xml:id="echoid-s24307" xml:space="preserve">æquinoctiali detur. </s>
              <s xml:id="echoid-s24308" xml:space="preserve">in eo
                <lb/>
                <note position="left" xlink:label="note-514.01.351-03" xlink:href="note-514.01.351-03a" xml:space="preserve">30</note>
              ſint, quemadmodum in analemmate diametri circulorum ſignorum f h. </s>
              <s xml:id="echoid-s24309" xml:space="preserve">Cancri, & </s>
              <s xml:id="echoid-s24310" xml:space="preserve">Capricorni h m. </s>
              <s xml:id="echoid-s24311" xml:space="preserve">Ge-
                <lb/>
              minorum, & </s>
              <s xml:id="echoid-s24312" xml:space="preserve">Sagittarij. </s>
              <s xml:id="echoid-s24313" xml:space="preserve">g l. </s>
              <s xml:id="echoid-s24314" xml:space="preserve">Tauri, & </s>
              <s xml:id="echoid-s24315" xml:space="preserve">Virginis. </s>
              <s xml:id="echoid-s24316" xml:space="preserve">Sumatur in linea e b. </s>
              <s xml:id="echoid-s24317" xml:space="preserve">gnomonis longitudo e z. </s>
              <s xml:id="echoid-s24318" xml:space="preserve">& </s>
              <s xml:id="echoid-s24319" xml:space="preserve">
                <lb/>
              per z. </s>
              <s xml:id="echoid-s24320" xml:space="preserve">linea planitiæ l o. </s>
              <s xml:id="echoid-s24321" xml:space="preserve">ducatur in quam per e. </s>
              <s xml:id="echoid-s24322" xml:space="preserve">centrum a ſignis f g h. </s>
              <s xml:id="echoid-s24323" xml:space="preserve">ducantur lineæ g e t. </s>
              <s xml:id="echoid-s24324" xml:space="preserve">h
                <lb/>
              e s. </s>
              <s xml:id="echoid-s24325" xml:space="preserve">f e r. </s>
              <s xml:id="echoid-s24326" xml:space="preserve">ita ut z r. </s>
              <s xml:id="echoid-s24327" xml:space="preserve">ſit longitudo umbrætropicorum. </s>
              <s xml:id="echoid-s24328" xml:space="preserve">z s, Geminorum, & </s>
              <s xml:id="echoid-s24329" xml:space="preserve">Sagittarij. </s>
              <s xml:id="echoid-s24330" xml:space="preserve">z t, Tauri,
                <lb/>
              & </s>
              <s xml:id="echoid-s24331" xml:space="preserve">Virginis. </s>
              <s xml:id="echoid-s24332" xml:space="preserve">ut uides in diagrãmate A. </s>
              <s xml:id="echoid-s24333" xml:space="preserve">ex quo ſumes interuallum z t. </s>
              <s xml:id="echoid-s24334" xml:space="preserve">& </s>
              <s xml:id="echoid-s24335" xml:space="preserve">circulum duces a b c d. </s>
              <s xml:id="echoid-s24336" xml:space="preserve">in
                <lb/>
              centro e. </s>
              <s xml:id="echoid-s24337" xml:space="preserve">in quo circulum alium facies æquidiſtantem, iuxta interuallum z s. </s>
              <s xml:id="echoid-s24338" xml:space="preserve">ab eodem diagrammate A.
                <lb/>
              </s>
              <s xml:id="echoid-s24339" xml:space="preserve">Erit autem f g h i. </s>
              <s xml:id="echoid-s24340" xml:space="preserve">demum, ex interuallo z r. </s>
              <s xml:id="echoid-s24341" xml:space="preserve">alium ſacies k l m n. </s>
              <s xml:id="echoid-s24342" xml:space="preserve">hi circuli referunt in plano æ-
                <lb/>
              quinoctiali parallelos ſignorum a diagrammate A. </s>
              <s xml:id="echoid-s24343" xml:space="preserve">ſiumptas ab umbrarum longitudinibus in planitiæ linea
                <lb/>
              l z o. </s>
              <s xml:id="echoid-s24344" xml:space="preserve">diuidatur deinceps minor circulus k l m n. </s>
              <s xml:id="echoid-s24345" xml:space="preserve">in duis partes inæquales iuxta ſectionem Cancri, quæ
                <lb/>
              eſt ſupra finitorem, ita quod k l m. </s>
              <s xml:id="echoid-s24346" xml:space="preserve">ſit maior, quæ Cancri k n m. </s>
              <s xml:id="echoid-s24347" xml:space="preserve">m: </s>
              <s xml:id="echoid-s24348" xml:space="preserve">nor, quæ ſit Capricorni, & </s>
              <s xml:id="echoid-s24349" xml:space="preserve">produ-
                <lb/>
                <note position="left" xlink:label="note-514.01.351-04" xlink:href="note-514.01.351-04a" xml:space="preserve">40</note>
              cta linea k m. </s>
              <s xml:id="echoid-s24350" xml:space="preserve">ad extremam circinationem ad ſigna a c. </s>
              <s xml:id="echoid-s24351" xml:space="preserve">diuidentur reliqui circuli iuxtas proprias ſe-
                <lb/>
              ctiones per lineam a f k m h c. </s>
              <s xml:id="echoid-s24352" xml:space="preserve">communes illius plani, & </s>
              <s xml:id="echoid-s24353" xml:space="preserve">finitoris. </s>
              <s xml:id="echoid-s24354" xml:space="preserve">Quare ſi uelis horas antiquorum
                <lb/>
              deſcribere, diuides utramque portionem in duodenas partes incipiens a ſectione illius plani, & </s>
              <s xml:id="echoid-s24355" xml:space="preserve">finitoris. </s>
              <s xml:id="echoid-s24356" xml:space="preserve">in mi-
                <lb/>
              nori quidem circulo ab m. </s>
              <s xml:id="echoid-s24357" xml:space="preserve">in maiori uero ab e. </s>
              <s xml:id="echoid-s24358" xml:space="preserve">& </s>
              <s xml:id="echoid-s24359" xml:space="preserve">ita ſingula tria ſigna continenti linea coniunges, ut in dia-
                <lb/>
              grammate B. </s>
              <s xml:id="echoid-s24360" xml:space="preserve">Quod ſi horas ab occaſu uelis, diuiſionem incipias ab m. </s>
              <s xml:id="echoid-s24361" xml:space="preserve">minoris & </s>
              <s xml:id="echoid-s24362" xml:space="preserve">à c. </s>
              <s xml:id="echoid-s24363" xml:space="preserve">maioris circuli
                <lb/>
              tam ſupra quam infra finitoris lineam ut in diagrammate D. </s>
              <s xml:id="echoid-s24364" xml:space="preserve">horas autem ab ortuinuerſum hoc dabit horo-
                <lb/>
              logium. </s>
              <s xml:id="echoid-s24365" xml:space="preserve">ut in digrammate E. </s>
              <s xml:id="echoid-s24366" xml:space="preserve">A meridie uero a meridiano b. </s>
              <s xml:id="echoid-s24367" xml:space="preserve">diuiſio incipienda eſt. </s>
              <s xml:id="echoid-s24368" xml:space="preserve">ut in diagrammatæ C.
                <lb/>
              </s>
              <s xml:id="echoid-s24369" xml:space="preserve">Quoniam uero nimis diſtat ab æquinoctiali initium Tauri, & </s>
              <s xml:id="echoid-s24370" xml:space="preserve">Virginis, aut a Libra Scorpius, & </s>
              <s xml:id="echoid-s24371" xml:space="preserve">Piſces: </s>
              <s xml:id="echoid-s24372" xml:space="preserve">ideo
                <lb/>
              ſi proprius umbram earum parallelorum in diagrammate A. </s>
              <s xml:id="echoid-s24373" xml:space="preserve">ſumpſeris, ut in ſigno q. </s>
              <s xml:id="echoid-s24374" xml:space="preserve">& </s>
              <s xml:id="echoid-s24375" xml:space="preserve">à q. </s>
              <s xml:id="echoid-s24376" xml:space="preserve">traijcies
                <lb/>
              lineam per e. </s>
              <s xml:id="echoid-s24377" xml:space="preserve">ad planitiam l z o. </s>
              <s xml:id="echoid-s24378" xml:space="preserve">habebis maiorem circulum, in quo tres alios incluſos & </s>
              <s xml:id="echoid-s24379" xml:space="preserve">horarijs lineis
                <lb/>
                <note position="left" xlink:label="note-514.01.351-05" xlink:href="note-514.01.351-05a" xml:space="preserve">50</note>
              iam distinctos, & </s>
              <s xml:id="echoid-s24380" xml:space="preserve">parallelos conſtitues. </s>
              <s xml:id="echoid-s24381" xml:space="preserve">In his iam dictis horologijs duas habebis ſuperficies, altera ad uer-
                <lb/>
              ticem, & </s>
              <s xml:id="echoid-s24382" xml:space="preserve">polum ſuperiorem, altera ad inferiorem ſpectabit. </s>
              <s xml:id="echoid-s24383" xml:space="preserve">prior erit in portione a b c. </s>
              <s xml:id="echoid-s24384" xml:space="preserve">in qua horæ erunt
                <lb/>
              ſignorum ſeptentrionalium. </s>
              <s xml:id="echoid-s24385" xml:space="preserve">Poſterior erit in portione a d c. </s>
              <s xml:id="echoid-s24386" xml:space="preserve">in qua horæ erunt ſignorum meridianorum: </s>
              <s xml:id="echoid-s24387" xml:space="preserve">in
                <lb/>
              utraque tamen ponetur gnomon in e. </s>
              <s xml:id="echoid-s24388" xml:space="preserve">ad angulos rectos. </s>
              <s xml:id="echoid-s24389" xml:space="preserve">Quoniam uero non ſolum fiunt horologia in planis
                <lb/>
              illis immobilibus, qualia bactenus declarata ſunt, ſed etiam in planis mobilibus deſcribuntur, quæ inclinata
                <lb/>
              uocantur, quia ad aliquod ex immobilibus plams non ſunt ad angulos rectos, ideo hoc loco uelim, ut ex his,
                <lb/>
              quæ dicta ſunt, ingenioſi, ac studioſi gnomonices uiam, & </s>
              <s xml:id="echoid-s24390" xml:space="preserve">modum inueniant horum horologiorum conficien-
                <lb/>
              dorum. </s>
              <s xml:id="echoid-s24391" xml:space="preserve">ut autem prorſus non declinent a ſcopo, exemplum afferam, tanquam initium huiuſce ſpeculationis.
                <lb/>
              </s>
              <s xml:id="echoid-s24392" xml:space="preserve">Horologium igitur in plano uerticalis mobilis ratione finitoris immobilis illi eſt ad angulos rectos, ſed ratione
                <lb/>
              meridiani immobilis, atque etiam uerticalis immobilis non est illis ad angulos rectos. </s>
              <s xml:id="echoid-s24393" xml:space="preserve">Similiter quoque horo-
                <lb/>
                <note position="left" xlink:label="note-514.01.351-06" xlink:href="note-514.01.351-06a" xml:space="preserve">60</note>
              </s>
            </p>
          </div>
        </div>
      </text>
    </echo>
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