Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

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            <s xml:id="echoid-s5501" xml:space="preserve">
              <pb o="97" file="0117" n="117" rhead="LIBER PRIMVS."/>
            tione 4. </s>
            <s xml:id="echoid-s5502" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5503" xml:space="preserve">11. </s>
            <s xml:id="echoid-s5504" xml:space="preserve">Euclidis, erit centrum Solis in puncto H. </s>
            <s xml:id="echoid-s5505" xml:space="preserve">Quare parallelus Solis tunc temporis per pun-
              <lb/>
            ctum H, tranſibit. </s>
            <s xml:id="echoid-s5506" xml:space="preserve">Quoniam verò, ſi in illa poſitione ſemicirculi F H G, per H, ducatur in plano paralle-
              <lb/>
            li Solis linea parallela ipſi I Q, (Poſſe enim per H, in plano paralleli Solis ipſi I Q, duci parallelam,
              <lb/>
            ita perſpicuum fiet. </s>
            <s xml:id="echoid-s5507" xml:space="preserve">Quoniam parallelus Solis, & </s>
            <s xml:id="echoid-s5508" xml:space="preserve">Horizon ad Meridianum recti ſunt, crit communis
              <lb/>
            ſectio illorum ad eundem Meridianum per pendicularis, atque adeo & </s>
            <s xml:id="echoid-s5509" xml:space="preserve">ad rectam B D, in Meridiano exi-
              <lb/>
              <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">19. vndec.</note>
            ſtentem, cum ſit cõmunis ſectio Meridiani & </s>
            <s xml:id="echoid-s5510" xml:space="preserve">Horizontis, perpendicularis erit, per d@fin. </s>
            <s xml:id="echoid-s5511" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5512" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5513" xml:space="preserve">11. </s>
            <s xml:id="echoid-s5514" xml:space="preserve">Eucl.
              <lb/>
            </s>
            <s xml:id="echoid-s5515" xml:space="preserve">ac propterea ipſi I Q, parallela. </s>
            <s xml:id="echoid-s5516" xml:space="preserve">Si igitur in plano paralleli ſolis per H, agatur parallola communi ſectio
              <lb/>
              <note position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">28. primi.</note>
            ni paralleli, & </s>
            <s xml:id="echoid-s5517" xml:space="preserve">Horizontis, erit eadem & </s>
            <s xml:id="echoid-s5518" xml:space="preserve">ipſi I Q, parallela. </s>
            <s xml:id="echoid-s5519" xml:space="preserve">Duci ergo poterit per H, in plano paralle
              <lb/>
              <note position="right" xlink:label="note-0117-03" xlink:href="note-0117-03a" xml:space="preserve">9. undec.</note>
            li ſolis ipſi I Q, linea parallela.) </s>
            <s xml:id="echoid-s5520" xml:space="preserve">linea recta ex O, ducta perpendicula
              <unsure/>
            ris ad Horizontem, atque adeo per
              <lb/>
            definitionem 3. </s>
            <s xml:id="echoid-s5521" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5522" xml:space="preserve">11. </s>
            <s xml:id="echoid-s5523" xml:space="preserve">Euclidis ad rectam B D, & </s>
            <s xml:id="echoid-s5524" xml:space="preserve">ipſi H I, ęqualis, cadit in illam parallelam in paralle-
              <lb/>
              <note position="left" xlink:label="note-0117-04" xlink:href="note-0117-04a" xml:space="preserve">10</note>
            lo ſolis per punctũ H, ductam; </s>
            <s xml:id="echoid-s5525" xml:space="preserve">(Cum enim H I, & </s>
            <s xml:id="echoid-s5526" xml:space="preserve">dicta perpendicularis ex O, ducta, rectæ ſint ad planũ
              <lb/>
            Horizontis, ipſæ erunt inter ſe par allelę. </s>
            <s xml:id="echoid-s5527" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s5528" xml:space="preserve">ęquales ſint ex hypotheſi, erit quoque recta ex H,
              <lb/>
              <note position="right" xlink:label="note-0117-05" xlink:href="note-0117-05a" xml:space="preserve">6. vndec.</note>
            ducta per extremũ punctũ perpendicularis ex O, eductę, ipſi I O, parallela; </s>
            <s xml:id="echoid-s5529" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s5530" xml:space="preserve">adeo dicta perpendicula
              <lb/>
              <note position="right" xlink:label="note-0117-06" xlink:href="note-0117-06a" xml:space="preserve">33. primi.</note>
            ris ex O, ducta cadet in parallelam illam per H, ductã in parallelo Solis: </s>
            <s xml:id="echoid-s5531" xml:space="preserve">alioquin ex eodẽ puncto H, duce-
              <lb/>
            rentur duæ parallelæ ipſi I O, nempe illa, quã per H, diximus debere duci, & </s>
            <s xml:id="echoid-s5532" xml:space="preserve">illa, quæ ex H, per extre-
              <lb/>
            mitatẽ perpendicularis ex O, ductę tranſit, & </s>
            <s xml:id="echoid-s5533" xml:space="preserve">quã ipſi I O, demonſtrauimus eſſe parallelam: </s>
            <s xml:id="echoid-s5534" xml:space="preserve">quod eſt ab-
              <lb/>
            ſurdum. </s>
            <s xml:id="echoid-s5535" xml:space="preserve">Eſſent enim & </s>
            <s xml:id="echoid-s5536" xml:space="preserve">duę illæ ex H, emiſſę inter ſeparallelę, cum tamen in H, coeant.) </s>
            <s xml:id="echoid-s5537" xml:space="preserve">fit, vt cum
              <lb/>
              <note position="right" xlink:label="note-0117-07" xlink:href="note-0117-07a" xml:space="preserve">9. vndec.</note>
            O Q, ſumpta ſit æqualis ipſi H I, & </s>
            <s xml:id="echoid-s5538" xml:space="preserve">perpendicularis ad B D, ſi ſemicirculus B A D, concipiatur mo-
              <lb/>
            @eri circadiametrum B D, donec rectus ſit ad Horizontem, idern
              <unsure/>
            {q́ue} ſit, qui Meridianus, ita vt Q O,
              <lb/>
            perpendicularis ſit ad eundem Horizontem, ex definitione 4. </s>
            <s xml:id="echoid-s5539" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5540" xml:space="preserve">11. </s>
            <s xml:id="echoid-s5541" xml:space="preserve">Euclidis, punctum Q, cadat in illam
              <lb/>
              <note position="left" xlink:label="note-0117-08" xlink:href="note-0117-08a" xml:space="preserve">20</note>
            parallelam per H, ductãin plano paralleli Solis; </s>
            <s xml:id="echoid-s5542" xml:space="preserve">ac idcirco planum paralleli per punctum Q, tranſeat,
              <lb/>
            manente ſemicirculo B A D, in eapoſitione, vt rectus ſit ad Horizontem, inſtar Meridiani. </s>
            <s xml:id="echoid-s5543" xml:space="preserve">Eodem mo-
              <lb/>
            do demonstrabimus idem planum paralleli ſolis per punctum R, tranſire in illa poſitione ſemicirculi
              <lb/>
            B A D. </s>
            <s xml:id="echoid-s5544" xml:space="preserve">Quare recta R Q, communis ſectio erit paralleli Solis, & </s>
            <s xml:id="echoid-s5545" xml:space="preserve">Meridiani A B C D, (Sumimus enim
              <lb/>
            iam hunc cir culum pro Meridiano.) </s>
            <s xml:id="echoid-s5546" xml:space="preserve">ac propterea angulus P R Q, erit angulus altitudinis poli, quod ita
              <lb/>
            maniſeſtum fiet. </s>
            <s xml:id="echoid-s5547" xml:space="preserve">Ducta recta μ ξ, per centrum E, ipſi R Q, parallela, erit μ ξ, communis ſectio Aequa-
              <lb/>
            toris, & </s>
            <s xml:id="echoid-s5548" xml:space="preserve">Meridiani. </s>
            <s xml:id="echoid-s5549" xml:space="preserve">Quare angulus B E μ, erit angulus altitudinis Aequatoris, vel complementi altitis
              <unsure/>
              <lb/>
            dinis poli, ac propterea reliquus angulus ex recto A E μ, erit angulus altitudinis poli. </s>
            <s xml:id="echoid-s5550" xml:space="preserve">Cum igitur hic ſit
              <lb/>
            oppoſito P R Q, æqualis in parallelogrammo E R, erit quoque P R Q, angulus eleuationis poli ſupra
              <lb/>
              <note position="right" xlink:label="note-0117-09" xlink:href="note-0117-09a" xml:space="preserve">34. primi.</note>
            Horizontem. </s>
            <s xml:id="echoid-s5551" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s5552" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p style="it">
            <s xml:id="echoid-s5553" xml:space="preserve">VERVM quoniam facile error aliquis committi poteſt in ducendarecta R Q, quando perpendi-
              <lb/>
            culares P R, O Q, atque adeo puncta R, Q, perexiguam inter ſe diſtantiam habent, vt in dato exemplo
              <lb/>
            contingit, accu@atius rem peragemus, ſi duas obſeruationes vmbrarum Solis elegerim{us}, in quibus dicta
              <lb/>
            puncta R, Q, notabili aliquo ſpatio inter ſe diſtent. </s>
            <s xml:id="echoid-s5554" xml:space="preserve">Immo rectius idem exequemur, ſole exiſtẽte in ſignis
              <lb/>
            Borealibus, ſi vmbram ſl
              <unsure/>
            yli obſeruemus, cum in ipſam A C, communem ſectionem verticalis propriè di
              <lb/>
            cti, & </s>
            <s xml:id="echoid-s5555" xml:space="preserve">circuli A B C D, cadit, vel cum eidem rectæ A C, propinqua fuerit, ſiue ad partes B, ſiue ad par
              <lb/>
            tes D,. </s>
            <s xml:id="echoid-s5556" xml:space="preserve">Ita in præcedenti figur a uides, Sole in ipſo Verticali cir culo existente, vmbraq́, ſtyli in rectam
              <lb/>
            A C, ſiue ante meridiem, ſiue poſt, cadente, rectam E , ſumptam eſſe æqualem perpendiculari Y Z, po ſita tunc Solis altitudine A Y. </s>
            <s xml:id="echoid-s5557" xml:space="preserve">Sic etiam veſpertino tempore, cadente vmbra ſtyli in rectam E ß,
              <lb/>
            & </s>
            <s xml:id="echoid-s5558" xml:space="preserve">Solis altituà
              <unsure/>
            ine existente γ δ
              <unsure/>
            , ſumpta eſt in perpendiculari ε θ, recta θ λ, æqualis perpendicu-
              <lb/>
              <note position="left" xlink:label="note-0117-11" xlink:href="note-0117-11a" xml:space="preserve">40</note>
            lari δ ε, & </s>
            <s xml:id="echoid-s5559" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5560" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5561" xml:space="preserve">QVOD ſi obſeruatio commodè fieri poſſit in Horizonte patenti, & </s>
            <s xml:id="echoid-s5562" xml:space="preserve">expedito, vel in loco aliquo edi
              <lb/>
            to, vbi Sol oriens, vel occidens conſpici queat, eligendus erit eiuſmodi locus. </s>
            <s xml:id="echoid-s5563" xml:space="preserve">Nam ſi Sole oriente, vel occi
              <lb/>
            dente, vmbra ſtyli obſeruetur, & </s>
            <s xml:id="echoid-s5564" xml:space="preserve">ducatur iterum S E, communis ſectio circuli A B C D, & </s>
            <s xml:id="echoid-s5565" xml:space="preserve">verticalis
              <lb/>
            per centrum Solis tunc temporis incedentis, ita vt C S, vel A S, arcus ſit amplitudinis ortiuæ, vel occi
              <lb/>
            duæ; </s>
            <s xml:id="echoid-s5566" xml:space="preserve">Item ducatur ad B D, perpendicularis S T, habebimus in recta B D, punctum T, per quod paralle-
              <lb/>
            lus Solis ducend{us}
              <unsure/>
            eſt, cum recta S T, ſit communis ſectio paralleli Solis, & </s>
            <s xml:id="echoid-s5567" xml:space="preserve">Horizontis. </s>
            <s xml:id="echoid-s5568" xml:space="preserve">I am verò ſi in
              <lb/>
            meridie, vmbra ſtyli cadente in rectam B D, obſeruetur altitudo Solis, ea{q́ue} ſupputetur à B, vſque ad V,
              <lb/>
            tranſibit quoq; </s>
            <s xml:id="echoid-s5569" xml:space="preserve">parallelus tunctemporis per punctum V, in Meridiano. </s>
            <s xml:id="echoid-s5570" xml:space="preserve">Quare recta V T, communis ſe-
              <lb/>
            ctio erit paralleli Solis, & </s>
            <s xml:id="echoid-s5571" xml:space="preserve">Meridiani, vt prius. </s>
            <s xml:id="echoid-s5572" xml:space="preserve">Denique ſi pręter duo puncta Q, R, tertium adhuc inue-
              <lb/>
              <note position="left" xlink:label="note-0117-12" xlink:href="note-0117-12a" xml:space="preserve">50</note>
            niamus, vt α
              <unsure/>
            , vel T, facilius rectam V T, ſine errore per tria puncta ducemus.</s>
            <s xml:id="echoid-s5573" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5574" xml:space="preserve">CAETERVM, quia Sole oriente, vel occidente, vix vmbra styli depręhendi poteſt in plano circuli
              <lb/>
              <note position="right" xlink:label="note-0117-13" xlink:href="note-0117-13a" xml:space="preserve">Amplitudo oc-
                <lb/>
              tiua, occiduaue,
                <lb/>
              qua uia per ſty-
                <lb/>
              lum in muro
                <lb/>
              affixum explo-
                <lb/>
              retur.</note>
            A B C D, vtemur hoc artificio in amplitudine Solis ortiua, occiduave explorãda. </s>
            <s xml:id="echoid-s5575" xml:space="preserve">In tabula aliqua plana,
              <lb/>
            & </s>
            <s xml:id="echoid-s5576" xml:space="preserve">rectangula ducemus rectã A B, infimo lateri C D, parallelã, in ea{q́ue} ſtylum cui{us}vis longitudinis ad an
              <lb/>
            gulos rectos infigemus A E, vel certe, vt ſupra, latus H D, inſtrumenti, quod in principio ſcholij propoſ-
              <lb/>
            23. </s>
            <s xml:id="echoid-s5577" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5578" xml:space="preserve">poſitum eſt, in puncto A, statuemus. </s>
            <s xml:id="echoid-s5579" xml:space="preserve">Deinde Sole oriente, vel occidente latus infimũ tabu-
              <lb/>
            læ C D, meridianæ lineę B D, præcedentis figurę Horizonti æquidiſtantis adaptabimus, it a vt ipſa tabula
              <lb/>
            recta ſit ad planum circuli A B C D, quod facile fiet beneficio perpendiculi ex puncto F, demiſſi. </s>
            <s xml:id="echoid-s5580" xml:space="preserve">Perpen
              <lb/>
            diculo enim adbærente ipſi tabellæ, recta erit tabella ad circulum A B C D. </s>
            <s xml:id="echoid-s5581" xml:space="preserve">Deinde vmbram notabim{us}
              <lb/>
            in recta A B, quæ cad at in punctum B, ita vt radius Solis ſit E B. </s>
            <s xml:id="echoid-s5582" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s5583" xml:space="preserve">ſi in precedenti figura in Ver-
              <lb/>
            ticali linea A C, ſumamus rectam E φ, gnomoni A E, vel lateri H D, dicti inſtrumenti æqualem, &</s>
            <s xml:id="echoid-s5584" xml:space="preserve"/>
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