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-div375" type="section" level="1" n="132">
          <p>
            <s xml:id="echoid-s6538" xml:space="preserve">
              <pb o="108" file="0128" n="128" rhead="GNOMONICES"/>
            ſtralis F G, ſecans Meridianum in K, vt ſit arcus ſemidiurnus datus F k. </s>
            <s xml:id="echoid-s6539" xml:space="preserve">Per puncta
              <emph style="sc">H</emph>
            , & </s>
            <s xml:id="echoid-s6540" xml:space="preserve">F, quorũ
              <lb/>
              <emph style="sc">H</emph>
            , ſit polus arcticus, ducatur per propoſ. </s>
            <s xml:id="echoid-s6541" xml:space="preserve">20. </s>
            <s xml:id="echoid-s6542" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6543" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6544" xml:space="preserve">Theodoſii, circulus maximus
              <emph style="sc">H</emph>
            F, ſecans Ae-
              <lb/>
            quatorem in I. </s>
            <s xml:id="echoid-s6545" xml:space="preserve">Erit arcus Aequatoris I E, ſimilis arcui ſemidiurno dato F K, ex propoſ. </s>
            <s xml:id="echoid-s6546" xml:space="preserve">10. </s>
            <s xml:id="echoid-s6547" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6548" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s6549" xml:space="preserve">Theodoſij, ac propterea notus, totidem videlicet graduum, quot arcus F K, cõplectitur. </s>
            <s xml:id="echoid-s6550" xml:space="preserve">Et quoniã
              <lb/>
            I E, arcus eſt anguli I
              <emph style="sc">H</emph>
            E, quòd arcus
              <emph style="sc">H</emph>
            E,
              <emph style="sc">H</emph>
            I, ex coroll. </s>
            <s xml:id="echoid-s6551" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s6552" xml:space="preserve">16. </s>
            <s xml:id="echoid-s6553" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6554" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6555" xml:space="preserve">Theodoſij quadrantes
              <lb/>
            ſint; </s>
            <s xml:id="echoid-s6556" xml:space="preserve">erit angulus I
              <emph style="sc">H</emph>
            E, totidem graduum, quot arcus ſemidiurnus datus continet. </s>
            <s xml:id="echoid-s6557" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s6558" xml:space="preserve">
              <lb/>
            reliquus duorum rectorum (qui grad. </s>
            <s xml:id="echoid-s6559" xml:space="preserve">180. </s>
            <s xml:id="echoid-s6560" xml:space="preserve">continent) I
              <emph style="sc">H</emph>
            C, notus erit. </s>
            <s xml:id="echoid-s6561" xml:space="preserve">Quoniam igitur in
              <lb/>
            triangulo ſphærico C F
              <emph style="sc">H</emph>
            , angulus C, rectus eſt; </s>
            <s xml:id="echoid-s6562" xml:space="preserve">(Meridianus enim A C, per polum Hori-
              <lb/>
            zontis ductus ad Horizontem rectus eſt, per propoſ. </s>
            <s xml:id="echoid-s6563" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6564" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6565" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6566" xml:space="preserve">Theodoſii) & </s>
            <s xml:id="echoid-s6567" xml:space="preserve">nullus arcuum
              <lb/>
            quadrans eſt; </s>
            <s xml:id="echoid-s6568" xml:space="preserve">(propterea quòd C
              <emph style="sc">H</emph>
            , arcus altitudinis poli minor ſemper eſt quadrante; </s>
            <s xml:id="echoid-s6569" xml:space="preserve">& </s>
            <s xml:id="echoid-s6570" xml:space="preserve">C B,
              <lb/>
              <note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">10</note>
            arcus Horizontis inter Meridianum, & </s>
            <s xml:id="echoid-s6571" xml:space="preserve">Aequatorem quadrans, ac proinde, ſi parallelus eſt Septen
              <lb/>
            trionalis, arcus C F, minor quadrãte, vel ſi parallelus eſt auſtralis, quadrante maior; </s>
            <s xml:id="echoid-s6572" xml:space="preserve">ſimiliter arcus
              <lb/>
            H I, inter polum, & </s>
            <s xml:id="echoid-s6573" xml:space="preserve">Aequatorem quadrans, & </s>
            <s xml:id="echoid-s6574" xml:space="preserve">idcirco H F, in parallelo boreali quadrante minor,
              <lb/>
              <figure xlink:label="fig-0128-01" xlink:href="fig-0128-01a" number="94">
                <image file="0128-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0128-01"/>
              </figure>
            in auſtrali verò maior quadrante) erit per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s6575" xml:space="preserve">18. </s>
            <s xml:id="echoid-s6576" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6577" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6578" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s6579" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s6580" xml:space="preserve">de triangulis, vel per pro
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s6581" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6582" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6583" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6584" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s6585" xml:space="preserve">42. </s>
            <s xml:id="echoid-s6586" xml:space="preserve">noſtrorum
              <lb/>
            triangulorum ſphęricorum, vt ſinus anguli C H F,
              <lb/>
            noti ad ſinum totum, ita ſinus complementi an-
              <lb/>
            guli C F H, ad ſinum complementi arcus C H: </s>
            <s xml:id="echoid-s6587" xml:space="preserve">
              <lb/>
            Et conuertendo, vt ſinus totus ad ſinum anguli
              <lb/>
              <note position="left" xlink:label="note-0128-02" xlink:href="note-0128-02a" xml:space="preserve">20</note>
            C H F, noti, ita ſinus complementi arcus C H, al-
              <lb/>
            titudinis poli, ad ſinum cõplementi anguli C F H.
              <lb/>
            </s>
            <s xml:id="echoid-s6588" xml:space="preserve">Cum ergo priora tria ſint cognita, cognoſcetur & </s>
            <s xml:id="echoid-s6589" xml:space="preserve">
              <lb/>
            quartum, nempe ſinus complementi anguli CFH,
              <lb/>
            ex regula proportionum; </s>
            <s xml:id="echoid-s6590" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s6591" xml:space="preserve">comple-
              <lb/>
            mentum anguli ex tabula ſinuum, & </s>
            <s xml:id="echoid-s6592" xml:space="preserve">angulus ipſe
              <lb/>
            C F H, & </s>
            <s xml:id="echoid-s6593" xml:space="preserve">ei oppoſitus (ſi parallelus eſt borealis)
              <lb/>
            I F B, notus erit. </s>
            <s xml:id="echoid-s6594" xml:space="preserve">Rurſus cum in triangulo ſphæri-
              <lb/>
            co B F I, angulus B F I, notus ſit, & </s>
            <s xml:id="echoid-s6595" xml:space="preserve">angulus F B I,
              <lb/>
            altitudini Aequatoris ſupra Horizontem æqualis,
              <lb/>
              <note position="left" xlink:label="note-0128-03" xlink:href="note-0128-03a" xml:space="preserve">30</note>
            hoc eſt, complemento altitudinis poli; </s>
            <s xml:id="echoid-s6596" xml:space="preserve">ſitq́; </s>
            <s xml:id="echoid-s6597" xml:space="preserve">per propoſ. </s>
            <s xml:id="echoid-s6598" xml:space="preserve">16. </s>
            <s xml:id="echoid-s6599" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6600" xml:space="preserve">4. </s>
            <s xml:id="echoid-s6601" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s6602" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s6603" xml:space="preserve">de triangulis,
              <lb/>
            vel per propoſ. </s>
            <s xml:id="echoid-s6604" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6605" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6606" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6607" xml:space="preserve">Gebri, vel certè per propoſ. </s>
            <s xml:id="echoid-s6608" xml:space="preserve">41. </s>
            <s xml:id="echoid-s6609" xml:space="preserve">noſtrorum triangulorum ſphæricorum,
              <lb/>
            vt ſinus arcus I B, noti (eſt enim I B, differen tia inter arcum ſemidiurnum I E, datum, & </s>
            <s xml:id="echoid-s6610" xml:space="preserve">quadran
              <lb/>
            tem B E) ad ſinum anguli B F I, noti, ita ſinus arcus I F, ad ſinum anguli I B F, altitudinis Aequa-
              <lb/>
            toris: </s>
            <s xml:id="echoid-s6611" xml:space="preserve">Et conuertendo, vt ſinus anguli B F I, noti ad ſinum arcus I B, noti, ita ſinus anguli I B F,
              <lb/>
            noti ad ſinum arcus I F; </s>
            <s xml:id="echoid-s6612" xml:space="preserve">fiet ex tribus prioribus notis etiam quartum notum, ex regula proportio-
              <lb/>
            num, nimirum ſinus arcus I F, declinationis paralleli propoſiti; </s>
            <s xml:id="echoid-s6613" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s6614" xml:space="preserve">ipſe arcus decli-
              <lb/>
            nationis I F, notus fiet.</s>
            <s xml:id="echoid-s6615" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6616" xml:space="preserve">ITAQVE ſi fiat, vt ſinus totus ad ſinum arcus, quo arcus ſemidiurnus datus à ſemicirculo
              <lb/>
            differt, hoc eſt, ad ſinum anguli C H F, (qui cum E H I, angulo arcus ſemidiurni duos rectos an-
              <lb/>
              <note position="left" xlink:label="note-0128-04" xlink:href="note-0128-04a" xml:space="preserve">40</note>
            gulos conficit) ita ſinus complementi arcus C H, altitudinis poli ad aliud, inuenietur ſinus com-
              <lb/>
            plementi anguli C F H, vel I F B; </s>
            <s xml:id="echoid-s6617" xml:space="preserve">ac idcirco complementum ipſius anguli notum erit, & </s>
            <s xml:id="echoid-s6618" xml:space="preserve">ex hoc an
              <lb/>
            gulus ipſe I F B. </s>
            <s xml:id="echoid-s6619" xml:space="preserve">Quòd ſi rurſus fiat, vt ſinus anguli I F B, iam noti, ad ſinum arcus I B, quo arcus
              <lb/>
            ſemidiurnus à quadrante differt, ita ſinus altitudinis Aequatoris, vel complementi altitudinis po
              <lb/>
            li, nempe anguli I B F, ad aliud, notus efficietur ſinus arcus I F, declinationis paralleli F G, quæſi-
              <lb/>
            tæ; </s>
            <s xml:id="echoid-s6620" xml:space="preserve">ac proinde ex tabula ſinuum, & </s>
            <s xml:id="echoid-s6621" xml:space="preserve">ipſa declinatio nota euadet.</s>
            <s xml:id="echoid-s6622" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6623" xml:space="preserve">EXEMPLVM. </s>
            <s xml:id="echoid-s6624" xml:space="preserve">Sit rurſus datus arcus diurnus horarum 14. </s>
            <s xml:id="echoid-s6625" xml:space="preserve">vel 10. </s>
            <s xml:id="echoid-s6626" xml:space="preserve">ac proinde ſemidiurnus
              <lb/>
              <note position="left" xlink:label="note-0128-05" xlink:href="note-0128-05a" xml:space="preserve">Exemplum.</note>
            I E, horarum 7. </s>
            <s xml:id="echoid-s6627" xml:space="preserve">vel 5. </s>
            <s xml:id="echoid-s6628" xml:space="preserve">hoc eſt, grad. </s>
            <s xml:id="echoid-s6629" xml:space="preserve">105. </s>
            <s xml:id="echoid-s6630" xml:space="preserve">vel 75. </s>
            <s xml:id="echoid-s6631" xml:space="preserve">Vnde arcus I B, continebit vnam horam, hoc eſt,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s6632" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6633" xml:space="preserve">Si igitur fiat, vt 100000. </s>
            <s xml:id="echoid-s6634" xml:space="preserve">ſinus totus, ad 96592. </s>
            <s xml:id="echoid-s6635" xml:space="preserve">ſinum anguli C H F, (cum enim arcus
              <lb/>
            I E, comprehendat horas 7. </s>
            <s xml:id="echoid-s6636" xml:space="preserve">ſiue grad. </s>
            <s xml:id="echoid-s6637" xml:space="preserve">105. </s>
            <s xml:id="echoid-s6638" xml:space="preserve">loquimur enim de parallelo boreali, comprehendet re-
              <lb/>
              <note position="left" xlink:label="note-0128-06" xlink:href="note-0128-06a" xml:space="preserve">50</note>
            liquus arcus ſemicirculi horas quinque, hoc eſt, grad. </s>
            <s xml:id="echoid-s6639" xml:space="preserve">75. </s>
            <s xml:id="echoid-s6640" xml:space="preserve">quibus predictus ſinus 96592. </s>
            <s xml:id="echoid-s6641" xml:space="preserve">debetur.
              <lb/>
            </s>
            <s xml:id="echoid-s6642" xml:space="preserve">Quòd ſi de parallelo auſtrali ſit ſermo, erit arcus I E, horarum 5. </s>
            <s xml:id="echoid-s6643" xml:space="preserve">ſiue grad. </s>
            <s xml:id="echoid-s6644" xml:space="preserve">75. </s>
            <s xml:id="echoid-s6645" xml:space="preserve">& </s>
            <s xml:id="echoid-s6646" xml:space="preserve">reliquus ex ſemi-
              <lb/>
            circulo horatum 7. </s>
            <s xml:id="echoid-s6647" xml:space="preserve">hoc eſt, grad. </s>
            <s xml:id="echoid-s6648" xml:space="preserve">105. </s>
            <s xml:id="echoid-s6649" xml:space="preserve">quibus idem ſinus reſpondet) ita 74314. </s>
            <s xml:id="echoid-s6650" xml:space="preserve">ſinus complemen-
              <lb/>
            ti arcus C H, altitudinis poli, ad aliud, inuenietur ſinus complementi anguli C F H, vel I F B,
              <lb/>
            71781. </s>
            <s xml:id="echoid-s6651" xml:space="preserve">cui reſpondet arcus grad. </s>
            <s xml:id="echoid-s6652" xml:space="preserve">45. </s>
            <s xml:id="echoid-s6653" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6654" xml:space="preserve">52. </s>
            <s xml:id="echoid-s6655" xml:space="preserve">Huius complementum grad. </s>
            <s xml:id="echoid-s6656" xml:space="preserve">44. </s>
            <s xml:id="echoid-s6657" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6658" xml:space="preserve">8. </s>
            <s xml:id="echoid-s6659" xml:space="preserve">erit quan-
              <lb/>
            titas anguli I F B. </s>
            <s xml:id="echoid-s6660" xml:space="preserve">Si ergo rurſus fiat, vt 69633. </s>
            <s xml:id="echoid-s6661" xml:space="preserve">ſinus anguli I F B, ad 25881, ſinum arcus I B, grad. </s>
            <s xml:id="echoid-s6662" xml:space="preserve">
              <lb/>
            15. </s>
            <s xml:id="echoid-s6663" xml:space="preserve">ita 74314. </s>
            <s xml:id="echoid-s6664" xml:space="preserve">ſinus anguli IBF, vel altitudinis Aequatoris, ad aliud, reperietur ſinus arcus decli-
              <lb/>
            nationis I F, 27621. </s>
            <s xml:id="echoid-s6665" xml:space="preserve">ferè. </s>
            <s xml:id="echoid-s6666" xml:space="preserve">Quare arcus ipſe declinationis I F, continebit grad. </s>
            <s xml:id="echoid-s6667" xml:space="preserve">16. </s>
            <s xml:id="echoid-s6668" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6669" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6670" xml:space="preserve">ferè, ſicu-
              <lb/>
            ti prius. </s>
            <s xml:id="echoid-s6671" xml:space="preserve">Eodem pacto deprehendemus parallelum, cuius arcus diurnus contineat horas 15. </s>
            <s xml:id="echoid-s6672" xml:space="preserve">vel
              <lb/>
            9. </s>
            <s xml:id="echoid-s6673" xml:space="preserve">declinationẽ habere grad. </s>
            <s xml:id="echoid-s6674" xml:space="preserve">23. </s>
            <s xml:id="echoid-s6675" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6676" xml:space="preserve">2. </s>
            <s xml:id="echoid-s6677" xml:space="preserve">ferè, & </s>
            <s xml:id="echoid-s6678" xml:space="preserve">ſic de cęteris. </s>
            <s xml:id="echoid-s6679" xml:space="preserve">Quocirca dato arcu diurno, & </s>
            <s xml:id="echoid-s6680" xml:space="preserve">lati
              <lb/>
            tudine loci, declinationẽ paralleli illius arcus ab Aequatore inquiſiuimus. </s>
            <s xml:id="echoid-s6681" xml:space="preserve">Quod faciendũ erat.</s>
            <s xml:id="echoid-s6682" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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