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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        <div xml:id="echoid-div390" type="section" level="1" n="134">
          <pb o="115" file="0135" n="135" rhead="LIBER PRIMVS."/>
          <p>
            <s xml:id="echoid-s6859" xml:space="preserve">QVONIAM plerique parallelis, vel arcubus ſignorum Zodiaci in horologijs (quos in quo-
              <lb/>
            libet horologio deſcribere docebimus in ſequentibus duobus libris) aſcribere ſolent quantitates
              <lb/>
            dierum, & </s>
            <s xml:id="echoid-s6860" xml:space="preserve">crepuſculorum longitudines, non omnino ab re erit, breuiter hoc loco (licet alicui
              <lb/>
            videri poſsit quodammodo eſſe pręter inſtitutum, cum ad alium locum hęc res pertineat) demon
              <lb/>
            ſtrare, quo pacto & </s>
            <s xml:id="echoid-s6861" xml:space="preserve">quantitates dierum, & </s>
            <s xml:id="echoid-s6862" xml:space="preserve">crepuſculorum longitudines ad quamcunque latitudi-
              <lb/>
            nem loci, cognita declinatione Solis, ſupputentur, vt & </s>
            <s xml:id="echoid-s6863" xml:space="preserve">nos in horologio quocunque, ſi viſum
              <lb/>
            ſuerit, parallelis ſignorum Zodiaci eas apponere poſſimus. </s>
            <s xml:id="echoid-s6864" xml:space="preserve">Pro quantitatibus igitur dierum in-
              <lb/>
            quirendis indagabimus arcus ſemidiurnos. </s>
            <s xml:id="echoid-s6865" xml:space="preserve">Hi namque duplicati totos arcus diurnos conſiciunt.
              <lb/>
            </s>
            <s xml:id="echoid-s6866" xml:space="preserve">Præ omnibus autem vijs (multis enim modis diei magnitudo reperiri poteſt) hanc in primis dele-
              <lb/>
            gimus, quę parum ab ea differre videtur, qua in pręcedenti propoſ. </s>
            <s xml:id="echoid-s6867" xml:space="preserve">vſi ſumus in declinatione pa-
              <lb/>
              <note position="left" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">10</note>
            ralleli, cuius arcus diurnus datus ſit, ſupputanda. </s>
            <s xml:id="echoid-s6868" xml:space="preserve">Hic enim è contrario ex data declinatione pa-
              <lb/>
            ralleli eius diurnus arcus proponitur perueſtigandus. </s>
            <s xml:id="echoid-s6869" xml:space="preserve">Sed prius amplitudo ortiua, occiduaue ex-
              <lb/>
            ploranda erit. </s>
            <s xml:id="echoid-s6870" xml:space="preserve">Ex hac enim ſtatim arcus ſemidiurnus colligetur.</s>
            <s xml:id="echoid-s6871" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6872" xml:space="preserve">REPETATVR ergo poſtrema ſigurat
              <unsure/>
            præcedentis propoſ. </s>
            <s xml:id="echoid-s6873" xml:space="preserve">in qua Horizon eſt A B C D;
              <lb/>
            </s>
            <s xml:id="echoid-s6874" xml:space="preserve">
              <note position="right" xlink:label="note-0135-02" xlink:href="note-0135-02a" xml:space="preserve">A mplitudo or-
                <lb/>
              tiua, occiduaue,
                <lb/>
              qua ratione in-
                <lb/>
              @eſtigetur.</note>
            Meridianus A C; </s>
            <s xml:id="echoid-s6875" xml:space="preserve">Aequator B D, Meridianum ſe-
              <lb/>
              <figure xlink:label="fig-0135-01" xlink:href="fig-0135-01a" number="97">
                <image file="0135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0135-01"/>
              </figure>
            cans in E; </s>
            <s xml:id="echoid-s6876" xml:space="preserve">parallelus ſiue borealis, ſiue auſtralis
              <lb/>
            F G, ſecans Meridianum in k, vt ſit arcus ſemidiur-
              <lb/>
            nus inquirendus F K, vel G K. </s>
            <s xml:id="echoid-s6877" xml:space="preserve">Meridianus enim
              <lb/>
            A C, tranſiens per polos Horizontis, & </s>
            <s xml:id="echoid-s6878" xml:space="preserve">paralleli
              <lb/>
            FG, ſecat ſegmentũ FG, per propoſ. </s>
            <s xml:id="echoid-s6879" xml:space="preserve">9. </s>
            <s xml:id="echoid-s6880" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6881" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6882" xml:space="preserve">Theod.
              <lb/>
            </s>
            <s xml:id="echoid-s6883" xml:space="preserve">
              <note position="left" xlink:label="note-0135-03" xlink:href="note-0135-03a" xml:space="preserve">20</note>
            bifariam. </s>
            <s xml:id="echoid-s6884" xml:space="preserve">Suſcipiatur polus arcticus H, per quem,
              <lb/>
            & </s>
            <s xml:id="echoid-s6885" xml:space="preserve">per punctum F, ducatur, per propoſ. </s>
            <s xml:id="echoid-s6886" xml:space="preserve">20. </s>
            <s xml:id="echoid-s6887" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6888" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s6889" xml:space="preserve">Theodoſii, circulus maximus declinationem pa-
              <lb/>
            ralleli ab Aequatore metiens H F, ſecans Aequato-
              <lb/>
            rem in 1. </s>
            <s xml:id="echoid-s6890" xml:space="preserve">Erit arcus Aequatoris I E, per propoſ. </s>
            <s xml:id="echoid-s6891" xml:space="preserve">10. </s>
            <s xml:id="echoid-s6892" xml:space="preserve">
              <lb/>
            lib. </s>
            <s xml:id="echoid-s6893" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6894" xml:space="preserve">Theodoſii, ſimilis arcui diurno I E; </s>
            <s xml:id="echoid-s6895" xml:space="preserve">atque
              <lb/>
            adeo in uento arcu I E, cognitus erit & </s>
            <s xml:id="echoid-s6896" xml:space="preserve">arcus ſemi-
              <lb/>
            diurnus F k, qui quæritur; </s>
            <s xml:id="echoid-s6897" xml:space="preserve">cũ tot gradus, horæve
              <lb/>
            in arcu I E, contineantur, quot in F k, propter ho-
              <lb/>
            rum arcuũ ſimilitudinẽ. </s>
            <s xml:id="echoid-s6898" xml:space="preserve">Arcum autem I E, ita in-
              <lb/>
              <note position="left" xlink:label="note-0135-04" xlink:href="note-0135-04a" xml:space="preserve">30</note>
            ueniemus. </s>
            <s xml:id="echoid-s6899" xml:space="preserve">Quoniã in triãgulo ſphærico rectangu
              <lb/>
            lo C F H, (Eſt enim angulus C, rectus, cum Meridianus A C, per polũ Horizõtis ductus rectus ſit,
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s6900" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6901" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6902" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6903" xml:space="preserve">Theodoſii, ad Horizontẽ) nullus arcuũ quadrãs eſt, vt in præcedenti propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s6904" xml:space="preserve">oſtenſum eſt, erit per propoſ. </s>
            <s xml:id="echoid-s6905" xml:space="preserve">19. </s>
            <s xml:id="echoid-s6906" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6907" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6908" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s6909" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s6910" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s6911" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6912" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6913" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6914" xml:space="preserve">Gebri,
              <lb/>
            vel certè per propoſ. </s>
            <s xml:id="echoid-s6915" xml:space="preserve">43. </s>
            <s xml:id="echoid-s6916" xml:space="preserve">noſtrorũ triangulorũ ſphæricorũ, vt ſinus cõplementi arcus H F, hoc eſt,
              <lb/>
            vt ſinus arcus declinationis I F, (Tam enim iu parallelo auſtrali, quàm boreali, arcus declinationis
              <lb/>
            I F, cõplementum eſt arcus H F, cũ H I, per coroll propoſ. </s>
            <s xml:id="echoid-s6917" xml:space="preserve">16. </s>
            <s xml:id="echoid-s6918" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6919" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6920" xml:space="preserve">Theod quadrans ſit) ad ſinũ
              <lb/>
            cõplementi arcus altitudinis poli C H, ita ſinus cõplementi arcus C F, id eſt, ita ſinus arcus B F,
              <lb/>
            (qui eſt cõplementũ arcus C F, cum C B, quadrans ſit; </s>
            <s xml:id="echoid-s6921" xml:space="preserve">metiturq́; </s>
            <s xml:id="echoid-s6922" xml:space="preserve">amplitudinẽ ortiuã, occiduam ve
              <lb/>
            paralleli F G) ad ſinum totum. </s>
            <s xml:id="echoid-s6923" xml:space="preserve">Quocirca & </s>
            <s xml:id="echoid-s6924" xml:space="preserve">conuertendo erit, vt ſinus complementi altitudinis
              <lb/>
              <note position="left" xlink:label="note-0135-05" xlink:href="note-0135-05a" xml:space="preserve">40</note>
            poli ad ſinum declinationis paralleli propoſiti, ita ſinus totus ad ſinum arcus B F, latitudinis or-
              <lb/>
            tiuæ, vel occiduæ. </s>
            <s xml:id="echoid-s6925" xml:space="preserve">Quod etiam hoc modo, & </s>
            <s xml:id="echoid-s6926" xml:space="preserve">fortaſſis commodius, demonſtrabitur. </s>
            <s xml:id="echoid-s6927" xml:space="preserve">Quia in trian
              <lb/>
            gulo ſphærico B I F, angulus I, rectus eſt, cum circulus maximus H I, per polos mundi, ſeu Aequa
              <lb/>
            toris B D, ductus rectus ſit, per propoſ. </s>
            <s xml:id="echoid-s6928" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6929" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6930" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6931" xml:space="preserve">Theodoſii, ad Aequatorem; </s>
            <s xml:id="echoid-s6932" xml:space="preserve">& </s>
            <s xml:id="echoid-s6933" xml:space="preserve">angulus B, incli-
              <lb/>
            nationem Aequatoris ad Horizontem, vel, quod idem eſt, altitudinem Aequatoris ſupra Horizon
              <lb/>
            tem metitur, id eſt, arcum Meridiani A E, cum B, polus ſit Meridiani A C; </s>
            <s xml:id="echoid-s6934" xml:space="preserve">erunt duo anguli I,
              <lb/>
            & </s>
            <s xml:id="echoid-s6935" xml:space="preserve">B, trianguli B I F, noti. </s>
            <s xml:id="echoid-s6936" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s6937" xml:space="preserve">arcus I F, declinationis cognitus. </s>
            <s xml:id="echoid-s6938" xml:space="preserve">Cum ergo, per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s6939" xml:space="preserve">16. </s>
            <s xml:id="echoid-s6940" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6941" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6942" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s6943" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s6944" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s6945" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6946" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6947" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6948" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s6949" xml:space="preserve">41. </s>
            <s xml:id="echoid-s6950" xml:space="preserve">noſtrorum
              <lb/>
            triangulorum ſphæricorum, ſit vt ſinus anguli B, altitudinis Aequatoris, vel complementi altitu-
              <lb/>
            dinis poli, ad ſinum arcus I F, declinationis paralleli propoſiti, ita ſinus anguli recti I, hoc eſt, ita
              <lb/>
              <note position="left" xlink:label="note-0135-06" xlink:href="note-0135-06a" xml:space="preserve">50</note>
            ſinus totus ad ſinum arcus B F, latitudinis ortiuę, vel occiduæ. </s>
            <s xml:id="echoid-s6951" xml:space="preserve">Igitur ex tribus cognitis & </s>
            <s xml:id="echoid-s6952" xml:space="preserve">quar-
              <lb/>
            tum, nempe arcus latitudinis ortiuę, cognoſcetur. </s>
            <s xml:id="echoid-s6953" xml:space="preserve">Itaque ſi ſiat, vt ſinus complementi altitudinis
              <lb/>
            poli ad ſinum declinationis paralleli propoſiti, ita ſinus totus ad aliud, reperietur ſinus latitudinis
              <lb/>
            ortiuæ, ſiue occidue, ex quo ipſa latitudo ortiua, occiduave cognita erit.</s>
            <s xml:id="echoid-s6954" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6955" xml:space="preserve">RVRSVS quia in triangulo eodem rectangulo B I F, angulus I, rectus eſt, vt proximè di-
              <lb/>
              <note position="right" xlink:label="note-0135-07" xlink:href="note-0135-07a" xml:space="preserve">Arcus ſemidiu@
                <lb/>
              nus, quo modo
                <lb/>
              ex latitudine or
                <lb/>
              tiua, occiduaue
                <lb/>
              ſit exquitend@@</note>
            ctum eſt, & </s>
            <s xml:id="echoid-s6956" xml:space="preserve">nullus arcuum quadrãs eſt, cum omnes ſint partes quadrantum; </s>
            <s xml:id="echoid-s6957" xml:space="preserve">(Nam I F, in triangu-
              <lb/>
            lo boreali pars eſt quadrantis H I, in auſtrali verò pars illius quadrantis, qui ex I, per F, vſque ad
              <lb/>
            polum antarcticum ducitur. </s>
            <s xml:id="echoid-s6958" xml:space="preserve">Item I B, in auſtrali triangulo pars eſt quadrantis B E, in boreali au-
              <lb/>
            tem portio illius quadrantis, qui ex B, per I, vſque ad Meridianum infra Horizontem extenditur.
              <lb/>
            </s>
            <s xml:id="echoid-s6959" xml:space="preserve">B F, tandem pars eſt quadrantis B C, vel B A) erit per propoſ. </s>
            <s xml:id="echoid-s6960" xml:space="preserve">19. </s>
            <s xml:id="echoid-s6961" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6962" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6963" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s6964" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s6965" xml:space="preserve">de triangu-
              <lb/>
            lis, vel per propoſ. </s>
            <s xml:id="echoid-s6966" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6967" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6968" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6969" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s6970" xml:space="preserve">43. </s>
            <s xml:id="echoid-s6971" xml:space="preserve">noſtrorum triangulorum ſphæricorum, </s>
          </p>
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