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

Table of figures

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[Figure 251]
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[Figure 262]
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[Figure 263]
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[Figure 264]
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[265] 1. figura
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[266] 2. figura.
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[267] 3. figura.
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[268] 4. figura
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[269] 5. figura
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[270] 6. figura
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[Figure 271]
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      <text xml:lang="it" type="free">
        <div xml:id="echoid-div1337" type="section" level="1" n="323">
          <p style="it">
            <s xml:id="echoid-s26410" xml:space="preserve">
              <pb o="402" file="0418" n="418" rhead="GNOMONICES"/>
            diem, hoc eſt, hora S. </s>
            <s xml:id="echoid-s26411" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26412" xml:space="preserve">43. </s>
            <s xml:id="echoid-s26413" xml:space="preserve">poſt mediam noctem: </s>
            <s xml:id="echoid-s26414" xml:space="preserve">Linea autem hui{us} horæ ſecat lineam æquinoctia-
              <lb/>
            lem in G. </s>
            <s xml:id="echoid-s26415" xml:space="preserve">Igitur ducta recta C G, dabit Verticalem grad. </s>
            <s xml:id="echoid-s26416" xml:space="preserve">30 Sic quoque quoniam Sol in Aequatore
              <lb/>
            exiſtens attingit Verticalem grad. </s>
            <s xml:id="echoid-s26417" xml:space="preserve">45. </s>
            <s xml:id="echoid-s26418" xml:space="preserve">hora 2. </s>
            <s xml:id="echoid-s26419" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26420" xml:space="preserve">15. </s>
            <s xml:id="echoid-s26421" xml:space="preserve">ante meridiem, hoc eſt, hora 9. </s>
            <s xml:id="echoid-s26422" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26423" xml:space="preserve">45. </s>
            <s xml:id="echoid-s26424" xml:space="preserve">poſt
              <lb/>
            mediam noctem; </s>
            <s xml:id="echoid-s26425" xml:space="preserve">ſecat autem linea huius horæ æquinoctialem lineam in H, dabit recta ducta C H, Ver
              <lb/>
            ticalem grad. </s>
            <s xml:id="echoid-s26426" xml:space="preserve">45. </s>
            <s xml:id="echoid-s26427" xml:space="preserve">& </s>
            <s xml:id="echoid-s26428" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s26429" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26430" xml:space="preserve">IT Aautem horam, qua Sol Aequatorem percurrens ad propoſitum Verticalem perueniat, inquire
              <lb/>
              <note position="left" xlink:label="note-0418-01" xlink:href="note-0418-01a" xml:space="preserve">Quo pacto ho-
                <lb/>
              ra@nueniatur,
                <lb/>
              qua Sol in Ae-
                <lb/>
              quato re exiſtẽ
                <unsure/>
              s
                <lb/>
              ad quẽ cunque
                <lb/>
              Verticalẽ per-
                <lb/>
              @eniat.</note>
            mus. </s>
            <s xml:id="echoid-s26431" xml:space="preserve">Sit Horizon A B C D; </s>
            <s xml:id="echoid-s26432" xml:space="preserve">Meridianus A C; </s>
            <s xml:id="echoid-s26433" xml:space="preserve">Aequator B E D; </s>
            <s xml:id="echoid-s26434" xml:space="preserve">Verticalis propriè
              <unsure/>
            dictus B F D; </s>
            <s xml:id="echoid-s26435" xml:space="preserve">Ver
              <lb/>
              <figure xlink:label="fig-0418-01" xlink:href="fig-0418-01a" number="276">
                <image file="0418-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0418-01"/>
              </figure>
            ticalis ali{us} quicunque F I H, ſecans Horizontem
              <lb/>
            in quarta orientali, & </s>
            <s xml:id="echoid-s26436" xml:space="preserve">auſtrali A B, & </s>
            <s xml:id="echoid-s26437" xml:space="preserve">Aequatorẽ
              <lb/>
            in I. </s>
            <s xml:id="echoid-s26438" xml:space="preserve">Quærendus igitur eſt arc{us} E I, in Aequatore.
              <lb/>
            </s>
            <s xml:id="echoid-s26439" xml:space="preserve">
              <note position="left" xlink:label="note-0418-02" xlink:href="note-0418-02a" xml:space="preserve">10</note>
            Quoniam in triangulo ſphærico E F I, angulus E, re-
              <lb/>
            ct{us} eſt, erit per propoſ. </s>
            <s xml:id="echoid-s26440" xml:space="preserve">18. </s>
            <s xml:id="echoid-s26441" xml:space="preserve">lib 4. </s>
            <s xml:id="echoid-s26442" xml:space="preserve">Ioan Regiom. </s>
            <s xml:id="echoid-s26443" xml:space="preserve">de
              <lb/>
            triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s26444" xml:space="preserve">14 lib. </s>
            <s xml:id="echoid-s26445" xml:space="preserve">1. </s>
            <s xml:id="echoid-s26446" xml:space="preserve">Gebri, vel per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s26447" xml:space="preserve">42. </s>
            <s xml:id="echoid-s26448" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt
              <lb/>
            ſinus anguli E F I, (qui notus eſt, cum eius arcus
              <lb/>
            A H, ſit complementum distantię Verticalis F H,
              <lb/>
            à Verticali propriè dicto F B,) ad ſinum totum, ita
              <lb/>
            ſin{us} complementi anguli E I F, ad ſinum comple-
              <lb/>
            menti arc{us} E F, altitudinis poli: </s>
            <s xml:id="echoid-s26449" xml:space="preserve">Et conuertendo,
              <lb/>
            vt ſinus totus ad ſinum anguli E F I, hoc eſt, ad ſi-
              <lb/>
              <note position="left" xlink:label="note-0418-03" xlink:href="note-0418-03a" xml:space="preserve">20</note>
            num complementi diſtantiæ Verticalis propoſiti à
              <lb/>
            propriè dicto Verticali, ita ſinus complementi altitu
              <lb/>
            dinis poli ad ſinum complementi anguli E I F. </s>
            <s xml:id="echoid-s26450" xml:space="preserve">Qua-
              <lb/>
            ve angulus E I F, notus erit. </s>
            <s xml:id="echoid-s26451" xml:space="preserve">Quoniam verò rurſus eſt, per propoſ. </s>
            <s xml:id="echoid-s26452" xml:space="preserve">16. </s>
            <s xml:id="echoid-s26453" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s26454" xml:space="preserve">4. </s>
            <s xml:id="echoid-s26455" xml:space="preserve">Ioan Regiom. </s>
            <s xml:id="echoid-s26456" xml:space="preserve">de triangu-
              <lb/>
            lis, vel per propoſ. </s>
            <s xml:id="echoid-s26457" xml:space="preserve">13. </s>
            <s xml:id="echoid-s26458" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s26459" xml:space="preserve">1. </s>
            <s xml:id="echoid-s26460" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s26461" xml:space="preserve">41. </s>
            <s xml:id="echoid-s26462" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus
              <lb/>
            anguli E I F, proximè inuenti ad ſinum arcus E F, altitudinis poli, ita ſinus anguli E F I, complementi
              <lb/>
            distantiæ Verticalis propoſiti à Verticali propriè dicto ad ſinum arcus E I, distantię Solis à meridie:
              <lb/>
            </s>
            <s xml:id="echoid-s26463" xml:space="preserve">Si fiat, vt ſinus tot{us} ad ſinum complementi diſtantiæ Verticalis propoſiti à propriè dicto Verticali, ita
              <lb/>
            ſinus complementi altitudinis poli ad aliud, reperietur ſinus, cui{us} arc{us} complementum ſeruetur. </s>
            <s xml:id="echoid-s26464" xml:space="preserve">Et
              <lb/>
            ſi rurſus fiat, vt ſin{us} hui{us} complementi ſeruati ad ſinum altitudinis poli, ita ſinus complementi diſtan
              <lb/>
            tiæ propoſiti Verticalis à Verticali propriè dicto ad aliud, inuenietur ſinus diſtantiæ Solis à meridie. </s>
            <s xml:id="echoid-s26465" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0418-04" xlink:href="note-0418-04a" xml:space="preserve">30</note>
            Exemplum. </s>
            <s xml:id="echoid-s26466" xml:space="preserve">Ponatur diſtare Verticalis F H, à puncto B, veri ortus verſ{us} auſtrum grad. </s>
            <s xml:id="echoid-s26467" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26468" xml:space="preserve">Si igi-
              <lb/>
              <note position="left" xlink:label="note-0418-05" xlink:href="note-0418-05a" xml:space="preserve">Exemplum
                <unsure/>
              .</note>
            tur fiat, vt 100000. </s>
            <s xml:id="echoid-s26469" xml:space="preserve">ſinus totus ad 86602. </s>
            <s xml:id="echoid-s26470" xml:space="preserve">ſinum complementi diſtantiæ dicti Verticalis à puncto veri
              <lb/>
            ortus, ita 74314. </s>
            <s xml:id="echoid-s26471" xml:space="preserve">ſin{us} complementi altitudinis poli ad aliud, offendem{us} hunc ferè ſinum 64357. </s>
            <s xml:id="echoid-s26472" xml:space="preserve">cui{us}
              <lb/>
            arcus cõplementum continet grad. </s>
            <s xml:id="echoid-s26473" xml:space="preserve">49. </s>
            <s xml:id="echoid-s26474" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26475" xml:space="preserve">56. </s>
            <s xml:id="echoid-s26476" xml:space="preserve">ferè. </s>
            <s xml:id="echoid-s26477" xml:space="preserve">Quòd ſi rurſum fiat, vt 76529. </s>
            <s xml:id="echoid-s26478" xml:space="preserve">ſinus arcus gr. </s>
            <s xml:id="echoid-s26479" xml:space="preserve">49.
              <lb/>
            </s>
            <s xml:id="echoid-s26480" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26481" xml:space="preserve">56. </s>
            <s xml:id="echoid-s26482" xml:space="preserve">proximè inuenti ad 66913. </s>
            <s xml:id="echoid-s26483" xml:space="preserve">ſinum altitudinis poli, ita 86602. </s>
            <s xml:id="echoid-s26484" xml:space="preserve">ſinus complementi diſtantiæ Ver
              <lb/>
            ticalis propoſiti à propriè dicto Verticali ad aliud, inuenietur hic propemodum ſinus 75720. </s>
            <s xml:id="echoid-s26485" xml:space="preserve">cui{us} ar-
              <lb/>
            cus grad. </s>
            <s xml:id="echoid-s26486" xml:space="preserve">49. </s>
            <s xml:id="echoid-s26487" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26488" xml:space="preserve">13. </s>
            <s xml:id="echoid-s26489" xml:space="preserve">dabit diſtantiam Solis tunc à meridie hor. </s>
            <s xml:id="echoid-s26490" xml:space="preserve">3. </s>
            <s xml:id="echoid-s26491" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26492" xml:space="preserve">17. </s>
            <s xml:id="echoid-s26493" xml:space="preserve">Et quoniam hæc diſtantia
              <lb/>
            ante meridiem eſt, quod Verticalis F H, poſit{us} ſit diſtare à vero ortu verſus auſtrum grad. </s>
            <s xml:id="echoid-s26494" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26495" xml:space="preserve">aufere-
              <lb/>
            m{us} eam ex ſemicirculo, hoc eſt, ex 12. </s>
            <s xml:id="echoid-s26496" xml:space="preserve">horis, vt remaneat hora 8. </s>
            <s xml:id="echoid-s26497" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26498" xml:space="preserve">43 poſt mediam noctem. </s>
            <s xml:id="echoid-s26499" xml:space="preserve">Fodẽ
              <lb/>
            pacto, ſi ponatur idem Verticalis diſtare grad. </s>
            <s xml:id="echoid-s26500" xml:space="preserve">45. </s>
            <s xml:id="echoid-s26501" xml:space="preserve">inueniemus horam 2. </s>
            <s xml:id="echoid-s26502" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26503" xml:space="preserve">15. </s>
            <s xml:id="echoid-s26504" xml:space="preserve">ante meridiem, id eſt
              <lb/>
              <note position="left" xlink:label="note-0418-06" xlink:href="note-0418-06a" xml:space="preserve">40</note>
            horam 9. </s>
            <s xml:id="echoid-s26505" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26506" xml:space="preserve">45. </s>
            <s xml:id="echoid-s26507" xml:space="preserve">poſt mediam noctem.</s>
            <s xml:id="echoid-s26508" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26509" xml:space="preserve">IAM verò ſi Verticalis F M, diſtet à vero occaſu D, verſ{us} auſtrum grad. </s>
            <s xml:id="echoid-s26510" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26511" xml:space="preserve">vel 45. </s>
            <s xml:id="echoid-s26512" xml:space="preserve">reperiem{us}
              <lb/>
            tunc eodem artificio horam 3. </s>
            <s xml:id="echoid-s26513" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26514" xml:space="preserve">17. </s>
            <s xml:id="echoid-s26515" xml:space="preserve">poſt meridiem, vel horam 2. </s>
            <s xml:id="echoid-s26516" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26517" xml:space="preserve">15.</s>
            <s xml:id="echoid-s26518" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26519" xml:space="preserve">QVOD ſi propoſitus Verticalis recedat à verò ortu, occaſuve verſ{us} boream, ac proinde Aequa-
              <lb/>
              <note position="left" xlink:label="note-0418-07" xlink:href="note-0418-07a" xml:space="preserve">Quando Verti
                <lb/>
              calis propoſitus
                <lb/>
              deflectit à vero
                <lb/>
              ortu, occaſuve
                <lb/>
              in boream.</note>
            torem ſub Horizonte ſecet, qualis eſt Verticalis F N O, vel F L K, ſecabit quoque idem Verticalis
              <lb/>
            Aequatorem ſupra Horizontem in puncto oppoſito, vt in P, vel I. </s>
            <s xml:id="echoid-s26520" xml:space="preserve">Quare vt prius, diſtantiam Solis E P,
              <lb/>
            poſt meridiem, vel E I, ante meridiem inueſtigabimus. </s>
            <s xml:id="echoid-s26521" xml:space="preserve">Hęc enim ęqualis eſt diſtantię puncti O, poſt me-
              <lb/>
            diam noctem, vel puncti K, ante mediam noctem, & </s>
            <s xml:id="echoid-s26522" xml:space="preserve">c.</s>
            <s xml:id="echoid-s26523" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26524" xml:space="preserve">RVRSVS ſi quando contingat, vt hora à meridie, vel media nocte inuenta, per quam linea Verti
              <lb/>
              <note position="left" xlink:label="note-0418-08" xlink:href="note-0418-08a" xml:space="preserve">Quid agẽ
                <unsure/>
              dum
                <lb/>
              ſit, cum hora,
                <lb/>
              qua Sol in Ae-
                <lb/>
              quatore exiſtẽs,
                <lb/>
              ad propoſitum
                <lb/>
              Verticalem per
                <lb/>
              tienit, lineã æ-
                <lb/>
              quinoctial em
                <lb/>
              @on ſecat.</note>
            calis propoſita ducenda eſt in æquinoctiali linea, non ſecet lineam æquinoctialem, quæremus horam oppo-
              <lb/>
              <note position="left" xlink:label="note-0418-09" xlink:href="note-0418-09a" xml:space="preserve">50</note>
            ſitam in lineaę quinoctiali, & </s>
            <s xml:id="echoid-s26525" xml:space="preserve">per eam ducem{us} lineam Verticalem. </s>
            <s xml:id="echoid-s26526" xml:space="preserve">Hæc namque a Verticali puncto C,
              <lb/>
            verſus æquinoctialem lineam prote
              <unsure/>
            nſa referet ſemicir culum Verticalis propoſiti oppoſitum, at vltra
              <lb/>
            Verticale punctum C, reliquum ſemicirculum, cuius linea deſideratur. </s>
            <s xml:id="echoid-s26527" xml:space="preserve">Vt ſi hac arte ducere velim{us}
              <lb/>
            lineam Verticalem grad. </s>
            <s xml:id="echoid-s26528" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26529" xml:space="preserve">ita vt ei{us} circul{us} Verticalis recedat a vero occaſu verſ{us} auſtrum grad.
              <lb/>
            </s>
            <s xml:id="echoid-s26530" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26531" xml:space="preserve">inueniem{us} Solem in Aequatore exiſtentem peruenturum ad eum Verticalem hora 3. </s>
            <s xml:id="echoid-s26532" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26533" xml:space="preserve">17. </s>
            <s xml:id="echoid-s26534" xml:space="preserve">poſt
              <lb/>
            meridiem: </s>
            <s xml:id="echoid-s26535" xml:space="preserve">Et quia hęc hora post meridiem in noſtro horologio lineam æquinoctialem non poteſt ſecare,
              <lb/>
            inueniemus in linea ęquinoctiali punctum L, horæ 3. </s>
            <s xml:id="echoid-s26536" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26537" xml:space="preserve">17. </s>
            <s xml:id="echoid-s26538" xml:space="preserve">poſt mediam noctem. </s>
            <s xml:id="echoid-s26539" xml:space="preserve">Nam recta C L, da-
              <lb/>
            bit communem ſectionem Verticalis circuli a vero ortu recedentis in boream grad. </s>
            <s xml:id="echoid-s26540" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26541" xml:space="preserve">portio verò eiuſ-
              <lb/>
            dem vltra C, producta communem ſectionẽ Verticalis circuli a vero occaſu in auſtrum recedentis gr. </s>
            <s xml:id="echoid-s26542" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26543" xml:space="preserve">
              <lb/>
            Idem{q́ue} fiat in cæteris.</s>
            <s xml:id="echoid-s26544" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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