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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[Item 1.]
[2.] GNOMONICES LIBRI OCTO, IN QVIB VS
[3.] AV CTORE CHRIST OPHORO CLAVIO BAMBERGENSI Societatis Ie sv
[4.] STEPHANO POLONIAE REGI POTENTISSIMO, MAGNOQ. LITHVANIAE DVCI, ETC. CHRISTOPHORVS CLAVIVS SOCIET AT IS IESV PERPETVAM FELICITATEM.
[5.] IN GNOMONICEN PR AE FATIO.
[6.] INDEX EORVM, QVAE TOTO HOC OPERE CONTINENTVR.
[7.] FINIS.
[8.] AD LECTOREM.
[9.] GNOMONICES LIBER PRIMVS.
[10.] AVCTORE CHRISTOPHORO CLAVIO BAMBERGENSI SOCIETATISIESV.
[11.] DE HOROLOGIIS IN VNIVERSVM, eorumque neceſſitate, atque inuentione.
[12.] DE HOROLOGIIS SCIOTHERICIS eorum{q́ue} varijs generibus.
[13.] DE QV ADRVPLICI HORARVM, atque ex ipſis horologiorum varietate.
[14.] DE INVENTORIBVS SCIOTHERI- corum horologiorum, eorum{q́ue} ſcriptoribus.
[15.] PROBLEMA PRIMVM. PROPOSITIO PRIMA.
[16.] LEMMA.
[17.] COROLLARIVM.
[18.] SCHOLIVM.
[19.] THEOREMA PRIMVM. PROPOSITIO SECVNDA.
[20.] THEOREMA 2. PROPOSITIO 3.
[21.] SCHOLIVM.
[22.] THEOREMA 3. PROPOSITIO 4.
[23.] COROLLARIVM.
[24.] THEQREMA 4. PROPOSITIQ 5.
[25.] COROLLARIVM.
[26.] THEOREMA 5. PROPOSITIO 6.
[27.] SCHOLIVM.
[28.] COROLLARIVM.
[29.] THEOREMA 6. PROPOSITIO 7.
[30.] COROLLARIVM.
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        <div xml:id="echoid-div83" type="section" level="1" n="25">
          <p>
            <s xml:id="echoid-s1608" xml:space="preserve">
              <pb o="23" file="0043" n="43" rhead="LIBER PRIMVS."/>
            tioni prædicti paralleli. </s>
            <s xml:id="echoid-s1609" xml:space="preserve">Sic quoque ſectio coni, cuius baſis parallelus eſt ♏, & </s>
            <s xml:id="echoid-s1610" xml:space="preserve">♓, & </s>
            <s xml:id="echoid-s1611" xml:space="preserve">horologii Hori-
              <lb/>
            zontalis ad latitudinem borealem grad. </s>
            <s xml:id="echoid-s1612" xml:space="preserve">78. </s>
            <s xml:id="echoid-s1613" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1614" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1615" xml:space="preserve">Parabole erit; </s>
            <s xml:id="echoid-s1616" xml:space="preserve">quippe cum huiuſce latitudinis com-
              <lb/>
            plementum, hoc eſt, grad. </s>
            <s xml:id="echoid-s1617" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1618" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1619" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1620" xml:space="preserve">æquale ſit declinationi paralleli ♏ & </s>
            <s xml:id="echoid-s1621" xml:space="preserve">♓. </s>
            <s xml:id="echoid-s1622" xml:space="preserve">Idem dic de conis,
              <lb/>
            quorum baſes ſunt paralleli boreales prædictis oppoſiti, nempe parallelus ♋; </s>
            <s xml:id="echoid-s1623" xml:space="preserve">♊, & </s>
            <s xml:id="echoid-s1624" xml:space="preserve">♌; </s>
            <s xml:id="echoid-s1625" xml:space="preserve">♉ υ, & </s>
            <s xml:id="echoid-s1626" xml:space="preserve">♍, vbi
              <lb/>
            tamen polus antarcticus ſupra Horizontem eleuatur. </s>
            <s xml:id="echoid-s1627" xml:space="preserve">Ex his facile erit iudicare, quænam plana horolo-
              <lb/>
            giorum Parabolas faciant, Sole quemcunque parallelum poſſidente. </s>
            <s xml:id="echoid-s1628" xml:space="preserve">Si enim Sol exiſtat in parallelo ſe-
              <lb/>
            ptentrionali, quem circulus maximus plano horologii æquidiſtãs tangit, erit communis ſectio horologij,
              <lb/>
            & </s>
            <s xml:id="echoid-s1629" xml:space="preserve">coni vmbræ baſim habentis parallelum auſtralem oppoſitum, Parabole; </s>
            <s xml:id="echoid-s1630" xml:space="preserve">vbi videlicet polus arcticus ſu-
              <lb/>
            pra horologii planum extollitur. </s>
            <s xml:id="echoid-s1631" xml:space="preserve">At vero ſi antarcticus polus ſupra planum horologii conſpiciatur, & </s>
            <s xml:id="echoid-s1632" xml:space="preserve">Sol
              <lb/>
            obtineat parallelum auſtralem, quem circulus maximus horologii plano æquidiftans contingit, fiet Pa-
              <lb/>
            rabole in cono vmbræ, cuius baſis eſt parallelus ſeptentrionalis oppoſitus, vt ex dictis patet. </s>
            <s xml:id="echoid-s1633" xml:space="preserve">Nam in figu-
              <lb/>
              <note position="left" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">10</note>
            ra ſuperiore, ſi B, ponatur polus arcticus, & </s>
            <s xml:id="echoid-s1634" xml:space="preserve">Sol exiſtat in parallelo ſeptentrionali D E, deſcribet quidem
              <lb/>
            radius Solis conos A D E, A F G, ſed horologii planum H I, in cono vmbræ A F G, cuius baſis F G, paral-
              <lb/>
            lelo Solis D E, opponitur, faciet parabolen K L M. </s>
            <s xml:id="echoid-s1635" xml:space="preserve">Si uerò B, ponatur polus antarcticus, & </s>
            <s xml:id="echoid-s1636" xml:space="preserve">Sol percur-
              <lb/>
            rat parallelum auſtralem D E, faciet eodem modo planum horologii parabolen in cono vmbræ ſepten-
              <lb/>
            trionali A F G, &</s>
            <s xml:id="echoid-s1637" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1638" xml:space="preserve">In eadem quoque figura vides polum arcticum B, tantum eleuari ſupra planum F E,
              <lb/>
            tangens parallelum D E, Borealem, quantum eſt cõplementum declinationis paralleli oppoſiti auſtralis
              <lb/>
            F G, &</s>
            <s xml:id="echoid-s1639" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1640" xml:space="preserve">cum altitudo poli ſit arcus B E, complementum uero declinationis arcus C F, qui illi æqualis
              <lb/>
              <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">26. tertij.</note>
            eſt, propter æquales angulos ad verticem in centro E, quibus inſiſtunt. </s>
            <s xml:id="echoid-s1641" xml:space="preserve">In vniuerſum enim circulus qui-
              <lb/>
            libet maximus tangit illum parallelum, cuius declinatio æqualis eſt complemento altitudinis poli ſupra
              <lb/>
            illum circulum maximum, vel quod idem eſt, cuius declinationis complementum æquale eſt altitudi-
              <lb/>
            ni poli ſupra circulum maximum. </s>
            <s xml:id="echoid-s1642" xml:space="preserve">id quod figura ſatis indicat.</s>
            <s xml:id="echoid-s1643" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
        </div>
        <div xml:id="echoid-div86" type="section" level="1" n="26">
          <head xml:id="echoid-head29" xml:space="preserve">THEOREMA 5. PROPOSITIO 6.</head>
          <p>
            <s xml:id="echoid-s1644" xml:space="preserve">SECTIONES communes earundem ſuperficierum conicarum,
              <lb/>
              <note position="right" xlink:label="note-0043-04" xlink:href="note-0043-04a" xml:space="preserve">Planum horolo
                <lb/>
              gii æquidiſtans
                <lb/>
              maximo circu-
                <lb/>
              lo baſes conica
                <lb/>
              rum ſuperficie-
                <lb/>
              rum ſecanti fa-
                <lb/>
              @it duas hyper-
                <lb/>
              bolas oppoſitas
                <lb/>
              & æquales.</note>
            & </s>
            <s xml:id="echoid-s1645" xml:space="preserve">plani horologij æquidiſtantis circulo maximo, qui baſes conicarum
              <lb/>
            ſuperficierum ſecat, Hyperbolę ſunt oppoſitæ, & </s>
            <s xml:id="echoid-s1646" xml:space="preserve">ęquales.</s>
            <s xml:id="echoid-s1647" xml:space="preserve"/>
          </p>
          <figure number="21">
            <image file="0043-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0043-01"/>
          </figure>
          <note position="left" xml:space="preserve">30</note>
          <note position="left" xml:space="preserve">40</note>
          <note position="left" xml:space="preserve">50</note>
          <p>
            <s xml:id="echoid-s1648" xml:space="preserve">SINT in eadem Sphæra duæ ſuperficies conicæ, quæ prius; </s>
            <s xml:id="echoid-s1649" xml:space="preserve">& </s>
            <s xml:id="echoid-s1650" xml:space="preserve">H I, circulus maximus ſecans
              <lb/>
            vtramque baſim: </s>
            <s xml:id="echoid-s1651" xml:space="preserve">Cui circulo æquidiſtet planum horologii K L, faciens in ſuperficiebus conicis
              <lb/>
            ſectiones M N O, P Q R. </s>
            <s xml:id="echoid-s1652" xml:space="preserve">Dico ſectiones M N O, P Q R, Hyperbolas eſſe oppoſitas, & </s>
            <s xml:id="echoid-s1653" xml:space="preserve">æquales.
              <lb/>
            </s>
            <s xml:id="echoid-s1654" xml:space="preserve">Cum enim ſuperficies conicæ A D E, A F G, ad verticem A, coniunctæ, ſecentur plano K L, non
              <lb/>
            per verticem; </s>
            <s xml:id="echoid-s1655" xml:space="preserve">erit in vtraque ſuperficierum, per propoſ. </s>
            <s xml:id="echoid-s1656" xml:space="preserve">14. </s>
            <s xml:id="echoid-s1657" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1658" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1659" xml:space="preserve">Apollonij, ſectio, quæ appella-
              <lb/>
            tur Hyperbole, & </s>
            <s xml:id="echoid-s1660" xml:space="preserve">duarum ſectionum eadem erit diameter K L, &</s>
            <s xml:id="echoid-s1661" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1662" xml:space="preserve">Hyperbolæ igitur ſunt MNO,
              <lb/>
            P Q R, oppoſitæ, & </s>
            <s xml:id="echoid-s1663" xml:space="preserve">æquales quoque, vt ex dicta propoſ. </s>
            <s xml:id="echoid-s1664" xml:space="preserve">14. </s>
            <s xml:id="echoid-s1665" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1666" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1667" xml:space="preserve">Apoll. </s>
            <s xml:id="echoid-s1668" xml:space="preserve">elicitur. </s>
            <s xml:id="echoid-s1669" xml:space="preserve">Sectiones ergo
              <lb/>
            communes earundem ſuperficierum conicarum, &</s>
            <s xml:id="echoid-s1670" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1671" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1672" xml:space="preserve"/>
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