Vitruvius, De architectura libri decem, 1567

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          <div xml:id="echoid-div769" type="section" level="2" n="142">
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              <s xml:id="echoid-s23472" xml:space="preserve">
                <pb o="309" file="514.01.341" n="341" rhead="ONVS."/>
              mur ſane his temporibus tot quadrantum, radiorum, anulorum, regularum, cylindrorum, torquetorum, hemicy-
                <lb/>
              clioru, planiſpbæriorum, & </s>
              <s xml:id="echoid-s23473" xml:space="preserve">cæterorum instrumentorum multitudine, quæ olim a ueteribus accurate inuenta & </s>
              <s xml:id="echoid-s23474" xml:space="preserve">
                <lb/>
              deſcripta ſunt. </s>
              <s xml:id="echoid-s23475" xml:space="preserve">Habendæ nibilominus gratiæ ſunt ijs, qui faciliorem uſum, & </s>
              <s xml:id="echoid-s23476" xml:space="preserve">commodiorem tractationem in-
                <lb/>
              uenerunt, uel quæ obſcura erant, & </s>
              <s xml:id="echoid-s23477" xml:space="preserve">in tenebris deliteſcebant, ſtudio, & </s>
              <s xml:id="echoid-s23478" xml:space="preserve">diligentia ad communem utilitatem
                <lb/>
              protulere, & </s>
              <s xml:id="echoid-s23479" xml:space="preserve">præclara ueterum inuenta ab iniurijs ſæculorum uindicarunt. </s>
              <s xml:id="echoid-s23480" xml:space="preserve">Sed ad rem. </s>
              <s xml:id="echoid-s23481" xml:space="preserve">Inſistam ego quoque
                <lb/>
              in ijs, quæ a Ptolomæo, & </s>
              <s xml:id="echoid-s23482" xml:space="preserve">Commandino iacta ſunt fundamenta, & </s>
              <s xml:id="echoid-s23483" xml:space="preserve">analemmatis uſum, quantum potero fa -
                <lb/>
              sile explicabo, Matbematic as illis demonſtrationes relinquens. </s>
              <s xml:id="echoid-s23484" xml:space="preserve">Nulli dubium eſt, Solem temporibus atque
                <lb/>
              boris alijs, alias altitudines, & </s>
              <s xml:id="echoid-s23485" xml:space="preserve">ſitus alios occupare. </s>
              <s xml:id="echoid-s23486" xml:space="preserve">Cernimus enim æstate orientem, & </s>
              <s xml:id="echoid-s23487" xml:space="preserve">cadentem Solem,
                <lb/>
              duarum & </s>
              <s xml:id="echoid-s23488" xml:space="preserve">amplius borarum ſpatio ab oriente, & </s>
              <s xml:id="echoid-s23489" xml:space="preserve">occidente ſeptentrionem uerſus conſurgere. </s>
              <s xml:id="echoid-s23490" xml:space="preserve">cernimus quo-
                <lb/>
                <note position="left" xlink:label="note-514.01.341-01" xlink:href="note-514.01.341-01a" xml:space="preserve">10</note>
              que Solem interdum inter orientem', & </s>
              <s xml:id="echoid-s23491" xml:space="preserve">meridiem, & </s>
              <s xml:id="echoid-s23492" xml:space="preserve">in meridie, ac demum ad occidentem a meridie incli-
                <lb/>
              nari, & </s>
              <s xml:id="echoid-s23493" xml:space="preserve">ijs temporibus modo altiores, modo depreſſiores cœli partes tenere, quæ omnia noſſe accurate opor-
                <lb/>
              tet, ſieius effectus in mundo ſcire uelimus, unde analemmatum deſcriptiones comparanantur: </s>
              <s xml:id="echoid-s23494" xml:space="preserve">noſſe autem ex-
                <lb/>
              quiſite illa non poterimus, niſi lineas multas, & </s>
              <s xml:id="echoid-s23495" xml:space="preserve">circulos angulosq́; </s>
              <s xml:id="echoid-s23496" xml:space="preserve">fingamus, quibus quaſi cancellis pictorũ
                <lb/>
              certos Solis ſitus inueniamus. </s>
              <s xml:id="echoid-s23497" xml:space="preserve">Quoniam uero ut libet in diuerſis planis, hoc eſt finitori, uerticali, & </s>
              <s xml:id="echoid-s23498" xml:space="preserve">meridia-
                <lb/>
              no ( de quibus ſuperius dixi) æquidistantibus conficere boraria poſſumus, ideo ſcire neceſſe est; </s>
              <s xml:id="echoid-s23499" xml:space="preserve">qui circuli,
                <lb/>
              quæ lineæ, qui anguli, quibus planis inſeruiant, ut illis poſitis tanquam terminis, Solis radios, quorum effectus
                <lb/>
              in mundo conſpicitur per gnomonem, & </s>
              <s xml:id="echoid-s23500" xml:space="preserve">umbras uenari poſſimus. </s>
              <s xml:id="echoid-s23501" xml:space="preserve">Formauimus antea tria plana finitorem,
                <lb/>
              uerticale, & </s>
              <s xml:id="echoid-s23502" xml:space="preserve">meridianum; </s>
              <s xml:id="echoid-s23503" xml:space="preserve">diametros quoque illvrum poſuimus, & </s>
              <s xml:id="echoid-s23504" xml:space="preserve">quid unumquodque muneris habeat, ex-
                <lb/>
              poſuimus; </s>
              <s xml:id="echoid-s23505" xml:space="preserve">nunc dicimus finxiſſe nos ill.</s>
              <s xml:id="echoid-s23506" xml:space="preserve">i imrnota, & </s>
              <s xml:id="echoid-s23507" xml:space="preserve">permanentia, & </s>
              <s xml:id="echoid-s23508" xml:space="preserve">ad ea quoque tria mobilia addenda eſſe,
                <lb/>
                <note position="left" xlink:label="note-514.01.341-02" xlink:href="note-514.01.341-02a" xml:space="preserve">20</note>
              ita ut finitor immotus ſit, & </s>
              <s xml:id="echoid-s23509" xml:space="preserve">finitor mobilis, itemq; </s>
              <s xml:id="echoid-s23510" xml:space="preserve">uerticalis firmus, & </s>
              <s xml:id="echoid-s23511" xml:space="preserve">uerticalis motus: </s>
              <s xml:id="echoid-s23512" xml:space="preserve">eadem ratio de me-
                <lb/>
              ridiano. </s>
              <s xml:id="echoid-s23513" xml:space="preserve">& </s>
              <s xml:id="echoid-s23514" xml:space="preserve">moueatur quodlibet mobile ſupra diametrum ſui immoti. </s>
              <s xml:id="echoid-s23515" xml:space="preserve">Iam notum eſt, quæ ſint diametri il-
                <lb/>
              lorum planorum, nam finitoris a labro orientis ad occidens terminatur. </s>
              <s xml:id="echoid-s23516" xml:space="preserve">uerticalis a ſummo uertice ad imas
                <lb/>
              ſub terræ partes. </s>
              <s xml:id="echoid-s23517" xml:space="preserve">meridiani linea meridiana diameter eſt, atque omnes ſe in centro mundi ad rectos angulos
                <lb/>
              ſecant. </s>
              <s xml:id="echoid-s23518" xml:space="preserve">Si ergo finit or moueri fingatur, & </s>
              <s xml:id="echoid-s23519" xml:space="preserve">circum ſuum diametrum, tanquam circa axem conuolui, certe pars
                <lb/>
              una ſupra finitorem immobilem extolletur, & </s>
              <s xml:id="echoid-s23520" xml:space="preserve">altera deprimetur. </s>
              <s xml:id="echoid-s23521" xml:space="preserve">Si uero uerticalis moue atur, pars altera
                <lb/>
              progredietur, altera regredietur firma diametro uerticalis permanente. </s>
              <s xml:id="echoid-s23522" xml:space="preserve">Si demum meridianus mouebitur,
                <lb/>
              pars altera ad finitorem proclinabit, altera ad finitorem conſurget. </s>
              <s xml:id="echoid-s23523" xml:space="preserve">His poſitis esto Sol ad notum gradibus
                <lb/>
              quadraginta a finitore altus, moueatur finitor, & </s>
              <s xml:id="echoid-s23524" xml:space="preserve">tantum extollatur ut centrum Solis medium ſecet, mouea-
                <lb/>
              tur item uerticalis, & </s>
              <s xml:id="echoid-s23525" xml:space="preserve">progrediatur ad notum uſque quo Solem eo loci contingat, quo finitor mobilis So-
                <lb/>
                <note position="left" xlink:label="note-514.01.341-03" xlink:href="note-514.01.341-03a" xml:space="preserve">30</note>
              lem ſecabat. </s>
              <s xml:id="echoid-s23526" xml:space="preserve">moueatur denique meridianus, & </s>
              <s xml:id="echoid-s23527" xml:space="preserve">tantum deprimatur, ut Solem quoque medium ſecet, ſanè tria
                <lb/>
              illa mobilia plana relictis immobilibus, ſe ſe mutuo ibi ſecabunt, ubi ſingula Solem ſecant, idest ubi Sol cum
                <lb/>
              fuerit, radios ſuos emittit in mundum. </s>
              <s xml:id="echoid-s23528" xml:space="preserve">Nunc uideamus eorum planorum effectus, & </s>
              <s xml:id="echoid-s23529" xml:space="preserve">quo fine eos antiqui fin-
                <lb/>
              xerunt. </s>
              <s xml:id="echoid-s23530" xml:space="preserve">ac primum in quibus conueniant explicemus. </s>
              <s xml:id="echoid-s23531" xml:space="preserve">Conueniunt ſanè in eo, quod cum ab immobili quodq;
                <lb/>
              </s>
              <s xml:id="echoid-s23532" xml:space="preserve">ſuo diſcedit, & </s>
              <s xml:id="echoid-s23533" xml:space="preserve">cum Sole mouetur, duos conficiunt angulos, alterum ex rectis lineis, alterum ex planis eo-
                <lb/>
              rum circulorum, idest mobilis, & </s>
              <s xml:id="echoid-s23534" xml:space="preserve">immobilis. </s>
              <s xml:id="echoid-s23535" xml:space="preserve">Quoniam uero angulos ex circinatione circuli metimur, ideo
                <lb/>
              alia circinationis pars ſubtendet angulos a lineis rectis, alia ab illis planis confectos. </s>
              <s xml:id="echoid-s23536" xml:space="preserve">vterque uero angulus
                <lb/>
              neceſſarius est, ut uerus Solis ſitus habeatur. </s>
              <s xml:id="echoid-s23537" xml:space="preserve">ideſt Solis altitudo, & </s>
              <s xml:id="echoid-s23538" xml:space="preserve">pars unde Sol ſuos radios demittit in
                <lb/>
              mundum. </s>
              <s xml:id="echoid-s23539" xml:space="preserve">Nunc ſeparatim unumquodque ſumamus. </s>
              <s xml:id="echoid-s23540" xml:space="preserve">Eſto Sol, ut prius, ad notum, moueatur uerticale
                <lb/>
              mobile ad Solem progrediens, & </s>
              <s xml:id="echoid-s23541" xml:space="preserve">Solem ſecet, ut ante: </s>
              <s xml:id="echoid-s23542" xml:space="preserve">dico duos ex hoc motu angulos effici, alterumq́; </s>
              <s xml:id="echoid-s23543" xml:space="preserve">rectis
                <lb/>
                <note position="left" xlink:label="note-514.01.341-04" xlink:href="note-514.01.341-04a" xml:space="preserve">40</note>
              lineis conſtare, alterum planis illis, ideſt uerticalis fixi, & </s>
              <s xml:id="echoid-s23544" xml:space="preserve">uerticalis mobilis. </s>
              <s xml:id="echoid-s23545" xml:space="preserve">Angulus rectis lineis constans,
                <lb/>
              fit Solis radio, & </s>
              <s xml:id="echoid-s23546" xml:space="preserve">diametro uerticalis, ideſt gnomonis, & </s>
              <s xml:id="echoid-s23547" xml:space="preserve">ambitus ſeu circinatio hunc angulum ſubtendens,
                <lb/>
              eſt pars ſiue arcus ille uerticalis mobilis, quod uertice nostro, & </s>
              <s xml:id="echoid-s23548" xml:space="preserve">puncto, in quo eſt Sol, continetur. </s>
              <s xml:id="echoid-s23549" xml:space="preserve">cum igi-
                <lb/>
              tur uertex a finitore tetrantem distet, ſequitur reliquum arcus uerticali, quod eſt a Sole ad finitorem, Solis
                <lb/>
              altitudinem ſupra finitorem oſtendere. </s>
              <s xml:id="echoid-s23550" xml:space="preserve">ideo ſi uerticalis arcus a uertice ad Solem erit partium quinquagin-
                <lb/>
              ta, Sola finitore tolletur gradus quadraginta, hoc eſt reliquum tetrantis a uertice ad finitorem. </s>
              <s xml:id="echoid-s23551" xml:space="preserve">huius ergo
                <lb/>
              anguli cognitio ad Solis altitudinem cognoſcendam ſpectat, unde umbrarum longitudo deprehenditur. </s>
              <s xml:id="echoid-s23552" xml:space="preserve">Sed
                <lb/>
              angulus a uertic ali mobili, & </s>
              <s xml:id="echoid-s23553" xml:space="preserve">firmo factus comprehenditur eo finitoris ambitu, qui inter cipitur inter punctum
                <lb/>
              orientis, & </s>
              <s xml:id="echoid-s23554" xml:space="preserve">punctum, quo uerticalis mobilis finitorem ſecat. </s>
              <s xml:id="echoid-s23555" xml:space="preserve">atque ambitus hic uel arcus, latitudo Solis, uel
                <lb/>
              arcus horizontalis nominatur. </s>
              <s xml:id="echoid-s23556" xml:space="preserve">huius anguli cognitio id nobis præſtat, ut parum ſciamus in quam radius Solis
                <lb/>
                <note position="left" xlink:label="note-514.01.341-05" xlink:href="note-514.01.341-05a" xml:space="preserve">50</note>
              uergat, unde partem in quam umbra protenditur agnoſcamus, ſemper enim umbra in oppoſitam radio par-
                <lb/>
              tem proijcitur. </s>
              <s xml:id="echoid-s23557" xml:space="preserve">nam ſi ab euro radius emittitur, umbra in caurum tendit. </s>
              <s xml:id="echoid-s23558" xml:space="preserve">ſi ab aquilone Sol, umbra in
                <lb/>
              africum uergit. </s>
              <s xml:id="echoid-s23559" xml:space="preserve">Ecce uſum horum angulorum, & </s>
              <s xml:id="echoid-s23560" xml:space="preserve">munus uerticalis mobilis. </s>
              <s xml:id="echoid-s23561" xml:space="preserve">nam ſi in plano finitori paral-
                <lb/>
              lelo uolueris horologium deſcribere, duos hos angulos neceſſarios cognoſces, quos uerticalis mobilis facit .
                <lb/>
              </s>
              <s xml:id="echoid-s23562" xml:space="preserve">Sed ad reliquos mutatur meridianus mobilis ad Solem in noto poſitum, cum eo peruenerit, ut Solem ſecet,
                <lb/>
              duos & </s>
              <s xml:id="echoid-s23563" xml:space="preserve">ipſe angulos reddet, alterum ex rectis lineis, alterum faciet ipſe cum meridiano immobili. </s>
              <s xml:id="echoid-s23564" xml:space="preserve">rectæ lineæ
                <lb/>
              quæ angulum conſtituunt erunt Solis radius, & </s>
              <s xml:id="echoid-s23565" xml:space="preserve">diametros meridiani; </s>
              <s xml:id="echoid-s23566" xml:space="preserve">ambitus hunc angulum ſubtendens, in-
                <lb/>
              tercipitur interpunctum extremum diametri meridiani, & </s>
              <s xml:id="echoid-s23567" xml:space="preserve">punctum in quo est Sol. </s>
              <s xml:id="echoid-s23568" xml:space="preserve">& </s>
              <s xml:id="echoid-s23569" xml:space="preserve">hinc Solis altitudo ter
                <lb/>
              minatur ſupra uerticalem circulum. </s>
              <s xml:id="echoid-s23570" xml:space="preserve">Angulus autem ex meridiano mobili, & </s>
              <s xml:id="echoid-s23571" xml:space="preserve">meridiano firmo factus, com-
                <lb/>
              prebenditur ambitu decl inationis meridiani mobilis a meridiano immo bili in circulo uerticali. </s>
              <s xml:id="echoid-s23572" xml:space="preserve">Huius anguli
                <lb/>
                <note position="left" xlink:label="note-514.01.341-06" xlink:href="note-514.01.341-06a" xml:space="preserve">60</note>
              cognitio eò ſpectat, ut partem & </s>
              <s xml:id="echoid-s23573" xml:space="preserve">ſitum Solis agnoſcamus, ut umbræ partem eliciamus in plano </s>
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