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 contents

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[161.] I. Sole exiſtente in principio ♈.
[162.] II. Sole exiſtente in principio ♎.
[163.] III. Sole exiſtente in principio ♋.
[164.] IIII. Sole exiſtente in principio ♑.
[165.] Arcus ſemidiurni in initijs ſignorum, ad latitudinem grad. 42.
[166.] VI. Mediationes cœli, & anguli terræ, eorumq́; declinationes, orientibus 12. ſignorum Zodiaci initiis, ad latitudinem grad. 42.
[167.] VII. Puncta Eclipticæ in circulo horę 6. conſtituta, eorumq́ue declinationes, orientibus 12. ſignorum Zodiaci principijs, ad latitudinem grad. 42.
[168.] VIII. Puncta Eclipticæ in circulo horę 11. exiſtentia, eorumq́; declinationes, cum principia 12. ſignorum Zodiaci oriuntur, ad latitudinem grad. 42.
[169.] SCHOLIVM.
[170.] SEQVVNTVR TABELLÆ.
[171.] PROBLEMA. 10. PROPOSITIO 10.
[172.] SCHOLIVM.
[173.] PROBLEMA. 11. PROPOSITIO 11.
[174.] SCHOLIVM.
[175.] PROBLEMA 12. PROPOSITIO 12.
[176.] SCHOLIVM.
[177.] DE HOROLOGIIS VERTICALIBVS. PROBLEMA 13. PROPOSITIO 13.
[178.] SCHOLIVM.
[179.] PROBLEMA 14. PROPOSITIO 14.
[180.] SCHOLIVM.
[181.] PROBLEMA 15. PROPOSITIO 15.
[182.] PROBLEMA. 16. PROPOSITIO 16.
[183.] SCHOLIVM.
[184.] PROBLEMA 17. PROPOSITIO 17.
[185.] PROBLEMA 18. PROPOSITIO 18.
[186.] SCHOLIVM.
[187.] PROBLEMA 19. PROPOSITIO 19.
[188.] PROBLEMA 20. PROPOSITIO 20.
[189.] SCHOLIVM.
[190.] PROBLEMA 21. PROPOSITIO 21.
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        <div xml:id="echoid-div733" type="section" level="1" n="179">
          <p>
            <s xml:id="echoid-s14825" xml:space="preserve">
              <pb o="217" file="0237" n="237" rhead="LIBER SECVNDVS."/>
            cet & </s>
            <s xml:id="echoid-s14826" xml:space="preserve">arcus auſtrales horologii auſtralis mutantur in boreali horologio in arcus boreales, & </s>
            <s xml:id="echoid-s14827" xml:space="preserve">con-
              <lb/>
            tra, vt ſupra dictum eſt.</s>
            <s xml:id="echoid-s14828" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14829" xml:space="preserve">DEMONSTRATIO autem huius rei non differt ab ea, quam in horologio horizontali
              <lb/>
            adduximus propoſ. </s>
            <s xml:id="echoid-s14830" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14831" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s14832" xml:space="preserve">Eſtenim & </s>
            <s xml:id="echoid-s14833" xml:space="preserve">Verticalis circulus Horizon quidam, & </s>
            <s xml:id="echoid-s14834" xml:space="preserve">angulus
              <lb/>
            D H I, æqualis altitudini poli ſupra ipſum, vt conſtat. </s>
            <s xml:id="echoid-s14835" xml:space="preserve">Quare eadem erit demonſtratio in vtro-
              <lb/>
            que horologio.</s>
            <s xml:id="echoid-s14836" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14837" xml:space="preserve">CÆTERVM in horologio Auſtrali arcus ſignorum auſtralium continentur inter centrũ
              <lb/>
              <note position="right" xlink:label="note-0237-01" xlink:href="note-0237-01a" xml:space="preserve">Qni arcus ad
                <lb/>
              ſigna auſtralia,
                <lb/>
              & qui ad borea
                <lb/>
              lia pertineant.</note>
            horologii, & </s>
            <s xml:id="echoid-s14838" xml:space="preserve">lineam æquinoctialem, borealium vero vltra lineam æquinoctialem: </s>
            <s xml:id="echoid-s14839" xml:space="preserve">In boreali au-
              <lb/>
            tem horologio contrario modo ſe res habet; </s>
            <s xml:id="echoid-s14840" xml:space="preserve">vt ex Analemmate huius propoſ. </s>
            <s xml:id="echoid-s14841" xml:space="preserve">colligitur. </s>
            <s xml:id="echoid-s14842" xml:space="preserve">Idem
              <lb/>
            etiam hinc apparere poteſt, quòd Sol in auſtralibus ſignis exiſtens breuiores vmbras facit in horo-
              <lb/>
              <note position="left" xlink:label="note-0237-02" xlink:href="note-0237-02a" xml:space="preserve">10</note>
            gio auſtrali circa meridiem, quàm cum in borealibus ſignis moratur: </s>
            <s xml:id="echoid-s14843" xml:space="preserve">quia in his maiores meridia
              <lb/>
            nas altitudines habet, quàm in illis. </s>
            <s xml:id="echoid-s14844" xml:space="preserve">Vnde cum breuiores vmbræ meridianæ fiant inter centrum
              <lb/>
            horologii auſtralis, & </s>
            <s xml:id="echoid-s14845" xml:space="preserve">lineam æquinoctialem, longiores autem vltra eandem lineam æquinoctia-
              <lb/>
            lem; </s>
            <s xml:id="echoid-s14846" xml:space="preserve">perſpicuum eſt, ſigna auſtralia eſſe inter centrum & </s>
            <s xml:id="echoid-s14847" xml:space="preserve">æquinoctialem lineam, borealia vero
              <lb/>
            vltra lineam æquinoctialem, &</s>
            <s xml:id="echoid-s14848" xml:space="preserve">c.</s>
            <s xml:id="echoid-s14849" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14850" xml:space="preserve">QVORVM autem ſignorum arcus ſint hyperbolæ, vel parabolæ, aut Ellipſes, percipiemus
              <lb/>
            exiis, quæ propoſ. </s>
            <s xml:id="echoid-s14851" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14852" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14853" xml:space="preserve">ſcripſimus.</s>
            <s xml:id="echoid-s14854" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quomodo ex
            <lb/>
          uno arcu oppo-
            <lb/>
          ſicus arcus de-
            <lb/>
          ſcribatur, &c.</note>
          <p>
            <s xml:id="echoid-s14855" xml:space="preserve">HIC etiam commodius, & </s>
            <s xml:id="echoid-s14856" xml:space="preserve">accuratius deſcribemus hyperbolas ſignorum borealium infra li-
              <lb/>
            neam æquinoctialem, beneficio hyperbolarum ſignorum auſtralium ſupra lineam æquinoctialem
              <lb/>
            deſcriptarum; </s>
            <s xml:id="echoid-s14857" xml:space="preserve">ſi per doctrinam, quam propoſ. </s>
            <s xml:id="echoid-s14858" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14859" xml:space="preserve">huius libri tradidimus, prius inueniantur dia-
              <lb/>
              <note position="left" xlink:label="note-0237-04" xlink:href="note-0237-04a" xml:space="preserve">20</note>
            metri tranſuerſæ ſectionum oppoſitarum, earumq́; </s>
            <s xml:id="echoid-s14860" xml:space="preserve">centra, &</s>
            <s xml:id="echoid-s14861" xml:space="preserve">c.</s>
            <s xml:id="echoid-s14862" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14863" xml:space="preserve">POSSVMVS quoque vti duobus illis modis, quos ad finem eiuſdem propoſ. </s>
            <s xml:id="echoid-s14864" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14865" xml:space="preserve">huius libri
              <lb/>
            ſcripſimus. </s>
            <s xml:id="echoid-s14866" xml:space="preserve">Qua de re conſule ea, quæ ibi tradidimus. </s>
            <s xml:id="echoid-s14867" xml:space="preserve">Parallelos igitur, ſiue arcus ſignorum Zo-
              <lb/>
            diaci in Verticali horologio prædicto deſcripſimus. </s>
            <s xml:id="echoid-s14868" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s14869" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div749" type="section" level="1" n="180">
          <head xml:id="echoid-head183" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s14870" xml:space="preserve">HOC modo eaſdem lineas horarias præcedentis figuræ ex H, egredientes deſcribit Andreas Schone
              <lb/>
              <note position="right" xlink:label="note-0237-05" xlink:href="note-0237-05a" xml:space="preserve">Praxis pulcher-
                <lb/>
              rima pro lineis
                <lb/>
              horariis in figu
                <lb/>
              ra radioiũ Zo-
                <lb/>
              diaei ducendis,
                <lb/>
              ſine interuallis
                <lb/>
              horariis horo-
                <lb/>
              logii.</note>
            rus. </s>
            <s xml:id="echoid-s14871" xml:space="preserve">Ducta recta H I B, quæ conſtituat angulum A H B, æqualem complemẽto altitudinis poli ſupra Ho
              <lb/>
            rizontem, vel ipſi altitudini poli ſupra Verticalem circulũ, vt & </s>
            <s xml:id="echoid-s14872" xml:space="preserve">nos fecimus, ſumit in ea punctũ quod-
              <lb/>
              <note position="left" xlink:label="note-0237-06" xlink:href="note-0237-06a" xml:space="preserve">30</note>
            cunque φ, per quod ipſi D H, parallelam agit φ V, quæ rectã ductam ex H, ipſi D C, parallelã ſecet in
              <lb/>
            V, puncto, è quo, vt centro, interuallo {q́ue} V φ, circulum deſcribit. </s>
            <s xml:id="echoid-s14873" xml:space="preserve">Hoc diuiſo in partes 24. </s>
            <s xml:id="echoid-s14874" xml:space="preserve">æquales, eadẽ
              <lb/>
            facit, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s14875" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14876" xml:space="preserve">huius libri de borizontali horologio docuimus.</s>
            <s xml:id="echoid-s14877" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14878" xml:space="preserve">EX figura autem radiorum conſtructa, vt docet Andreas Schonerus, deſcribi poterit horologiũ Ver
              <lb/>
              <note position="right" xlink:label="note-0237-07" xlink:href="note-0237-07a" xml:space="preserve">Deſcriptio ho-
                <lb/>
              rologii
                <unsure/>
              Vertica
                <lb/>
              lis ex figura ra-
                <lb/>
              diorũ Andreæ
                <lb/>
              Schoneri.</note>
            ticale ad datam ſtyli magnitudinem, vt de horizontali diximus in ſcholio propoſ. </s>
            <s xml:id="echoid-s14879" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14880" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14881" xml:space="preserve">dummodo
              <lb/>
            angulus ρ D H, æqualis fiat altitudini poli, non autem eius complemento, vt in horizont ali horologio.</s>
            <s xml:id="echoid-s14882" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14883" xml:space="preserve">STYLVS iuxta poſteriorem modum deſcribendi parallelos ſignorum, qui per figur am radiorum Zo
              <lb/>
              <note position="right" xlink:label="note-0237-08" xlink:href="note-0237-08a" xml:space="preserve">Qua ratione ex
                <lb/>
              figura radiorũ
                <lb/>
              longitudo ſtyli,
                <lb/>
              eiusq́; locus in
                <lb/>
              horologio inue
                <lb/>
              niatur.</note>
            diaci abſoluitur, habetur, ſi ex D, ad H I, perpendicularis ducatur D ρ, vel certe recta D ρ, faciens angu
              <lb/>
            lum ρ D I, æqualem angulo complemento altitudinis poli ſupra Horizontem. </s>
            <s xml:id="echoid-s14884" xml:space="preserve">Longitudo enim ſtyli eſt ip-
              <lb/>
            ſa recta D ρ: </s>
            <s xml:id="echoid-s14885" xml:space="preserve">Locus vero eius eſt punctum ρ, diſtans ab H, centro horologij interuallo H ρ, in linea me
              <lb/>
              <note position="left" xlink:label="note-0237-09" xlink:href="note-0237-09a" xml:space="preserve">40</note>
            ridiana, vel ab æquinoctiali linea F K, ſpatio I ρ, in eadem linea meridiana, verſus centrum H.</s>
            <s xml:id="echoid-s14886" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14887" xml:space="preserve">DESCRIPTIS autem lineis horarijs in proxime antecedenti figura ex puncto H, ſi ſecundum
              <lb/>
              <note position="right" xlink:label="note-0237-10" xlink:href="note-0237-10a" xml:space="preserve">Quomodo per
                <lb/>
              figuram radio-
                <lb/>
              rum Zodiaci
                <lb/>
              maius aut mi-
                <lb/>
              nus horologiũ
                <lb/>
              deſcubendum
                <lb/>
              ſit.</note>
            poſteriorem hunc modum ex dicta figura radiorum zodiaci deſumptum, maius, aut minus horologium cõ
              <lb/>
            ſtruendum ſit, deſcribenda erit figura radiorum Zodiaci magis, vel minus diſtans à puncto H, &</s>
            <s xml:id="echoid-s14888" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14889" xml:space="preserve">vt de
              <lb/>
            horologio Horizontali dictum eſt in ſcholio propoſ. </s>
            <s xml:id="echoid-s14890" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14891" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s14892" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14893" xml:space="preserve">QVOD ſimagnitudo ſiyli data ſit, inueniemus hac ratione diſtantiam figuræ radiorum Zodiaci à
              <lb/>
              <note position="right" xlink:label="note-0237-11" xlink:href="note-0237-11a" xml:space="preserve">Quomodo ex
                <lb/>
              data ſtyli longi
                <lb/>
              tudine inuenia
                <lb/>
              tur diſtantia ra
                <lb/>
              diorum Zodia-
                <lb/>
              ci à puncto H,
                <lb/>
              in figura radio-
                <lb/>
              rum.</note>
            puncto H, in axe H D. </s>
            <s xml:id="echoid-s14894" xml:space="preserve">In portione Analemmatis propoſ. </s>
            <s xml:id="echoid-s14895" xml:space="preserve">præcedentis abſcindatur ex B D C, protracta
              <lb/>
            recta D M, æqualis gnomoni dato, & </s>
            <s xml:id="echoid-s14896" xml:space="preserve">per M, ipſi A D, diametro Verticalis parallela agatur N O, ſecans
              <lb/>
            axem D E, in N, & </s>
            <s xml:id="echoid-s14897" xml:space="preserve">Aequatoris diametrum F D, in O. </s>
            <s xml:id="echoid-s14898" xml:space="preserve">Punctum enim D, figurę radiorum huius pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s14899" xml:space="preserve">in quo conueniunt omnes radij zodiaci, diſtare debet ab H, interuallo D N, vt de horologio horizõ-
              <lb/>
              <note position="left" xlink:label="note-0237-12" xlink:href="note-0237-12a" xml:space="preserve">50</note>
            tali diximus in ſcholio propoſ. </s>
            <s xml:id="echoid-s14900" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14901" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s14902" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14903" xml:space="preserve">HIC etiam in horologio illo, quod in ſcholio præcedentis propoſ. </s>
            <s xml:id="echoid-s14904" xml:space="preserve">docuimus conficere, etiam ſi centrũ
              <lb/>
              <note position="right" xlink:label="note-0237-13" xlink:href="note-0237-13a" xml:space="preserve">Qua ratione at
                <lb/>
              cus ſignorũ in
                <lb/>
              horologio Ver-
                <lb/>
              ticali, vbi cen-
                <lb/>
              trum non habe
                <lb/>
              tur, deſcriban-
                <lb/>
              tur.</note>
            eius non habeatur, deſcribemus arcus ſignorum, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s14905" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14906" xml:space="preserve">huius libri tradidimus.</s>
            <s xml:id="echoid-s14907" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14908" xml:space="preserve">QV AMVIS autem rectè demonſtratum ſit hac propoſ. </s>
            <s xml:id="echoid-s14909" xml:space="preserve">portionem ſuperiorẽ horologij auſtralis,
              <lb/>
            quam horizontalis linea abſcindit, exhibere nobis horologium boreale, ſi omnes eius partes ita permuten-
              <lb/>
            tur, vt ſuperior vertatur in inferiorem, hoc eſt, horizontalis linea occupet ſuperiorem locum, & </s>
            <s xml:id="echoid-s14910" xml:space="preserve">pars,
              <lb/>
            quæ in eo ſitu nobis ad horologiũ conuerſis dextra eſt, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s14911" xml:space="preserve">contra: </s>
            <s xml:id="echoid-s14912" xml:space="preserve">operætamen pretium me fa
              <lb/>
            cturum exiſtimaui, idem vniuerſe hoc loco oſtendere, nimirum non ſolum in Verticali horologia auſtrali,
              <lb/>
            ſed in alijs etiam omnibus (vt in meridiano, polari, in eo quod à Verticali declinat, & </s>
            <s xml:id="echoid-s14913" xml:space="preserve">in eo quod ab Hori
              <lb/>
            zonte, in inclinato ad Horizontem, & </s>
            <s xml:id="echoid-s14914" xml:space="preserve">in eo quod à Verticali declinat, ſimulq́, ad Horizontem inclinatũ
              <lb/>
            eſt) lineam horizontalem ad partes ſuperiores portionem auferre, quæ in facie plani horologii </s>
          </p>
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