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-div16" type="section" level="1" n="12">
          <p style="it">
            <s xml:id="echoid-s454" xml:space="preserve">
              <pb o="6" file="0026" n="26" rhead="GNOMONICES"/>
            quia tã interdiu, quàm noctu ex ipſis horas cognoſcim{us}; </s>
            <s xml:id="echoid-s455" xml:space="preserve">qualia ſunt Aſtrolabia, ſeu Planiſphæria, annuli
              <lb/>
            aſtronomici, & </s>
            <s xml:id="echoid-s456" xml:space="preserve">c. </s>
            <s xml:id="echoid-s457" xml:space="preserve">Pariratione alia horas indicant per dimidij anni ſpatium, cuiuſmodi est horologium
              <lb/>
            Aequinoctiale ſuperi{us}, horas eo anni tempore indicãs, quo ſol à principio ♈, ad principiũ ♎ mouetur:
              <lb/>
            </s>
            <s xml:id="echoid-s458" xml:space="preserve">Alia per reliquam partem anni, quale eſt A Equinoctiale inferius, quod horas monſirat, dum ſol à princi-
              <lb/>
            pio ♎, ad principium ♈, mouetur. </s>
            <s xml:id="echoid-s459" xml:space="preserve">Rurſus quædam indicant horas mane duntaxat & </s>
            <s xml:id="echoid-s460" xml:space="preserve">veſperi, quale
              <lb/>
            eſt horologium verticale ad ſeptentrionem ſpectans, & </s>
            <s xml:id="echoid-s461" xml:space="preserve">Polare inferius, & </s>
            <s xml:id="echoid-s462" xml:space="preserve">nonnulla alia declinantia, & </s>
            <s xml:id="echoid-s463" xml:space="preserve">
              <lb/>
            inclinata inferiora: </s>
            <s xml:id="echoid-s464" xml:space="preserve">quædam reliquas horas diei, quale eſt Verticale ad meridiem vergens, & </s>
            <s xml:id="echoid-s465" xml:space="preserve">Polare ſupe-
              <lb/>
            rius, nec non aliqua declinantia, & </s>
            <s xml:id="echoid-s466" xml:space="preserve">inclinata ſuperiora. </s>
            <s xml:id="echoid-s467" xml:space="preserve">Sic etiam horologiorum alia horas antemeridia-
              <lb/>
            nas ſolum indicant, cuiuſmodi cſt Meridianum Orientale; </s>
            <s xml:id="echoid-s468" xml:space="preserve">alia pomeridianas, quale cſt Meridianum occi-
              <lb/>
            dentale. </s>
            <s xml:id="echoid-s469" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s470" xml:space="preserve">hac ratione plura alia genera horologiorum excogitari poterunt.</s>
            <s xml:id="echoid-s471" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
        </div>
        <div xml:id="echoid-div25" type="section" level="1" n="13">
          <head xml:id="echoid-head15" style="it" xml:space="preserve">DE QV ADRVPLICI HORARVM,
            <lb/>
          atque ex ipſis horologiorum varietate.</head>
          <p style="it">
            <s xml:id="echoid-s472" xml:space="preserve">RETVLIMVS varia horologiorum genera ex uario duntaxat planorum, in quibus deſcribuntur,
              <lb/>
            ſitu, nunc de quatuor horarum generibus, ex quibus ſingulæ prædictæ horologiorum ſpecies quadrupli
              <lb/>
            cantur, dicam{us}. </s>
            <s xml:id="echoid-s473" xml:space="preserve">Principio autem horarum duo prima ſunt genera inter ſe diſtincta, vnæ quidem inæqua-
              <lb/>
              <note position="left" xlink:label="note-0026-02" xlink:href="note-0026-02a" xml:space="preserve">Horarum di
                <lb/>
              u
                <unsure/>
              iſio.</note>
            les dicuntur, æquales alteræ. </s>
            <s xml:id="echoid-s474" xml:space="preserve">Hora inæqualis eſt pars duodecima tam diei, quàm noctis artificialis. </s>
            <s xml:id="echoid-s475" xml:space="preserve">Diuide-
              <lb/>
              <note position="left" xlink:label="note-0026-03" xlink:href="note-0026-03a" xml:space="preserve">Hora inæ
                <lb/>
              qualis.</note>
            batur enim olim quæuis artificialis dies, & </s>
            <s xml:id="echoid-s476" xml:space="preserve">quælibet nox in 12 particulas æquales inter ſe, quæ horæ inæ-
              <lb/>
            quales, & </s>
            <s xml:id="echoid-s477" xml:space="preserve">antiquæ à ſcriptorib{us} dicuntur: </s>
            <s xml:id="echoid-s478" xml:space="preserve">Antiquæ quidem, quoniam apud omnes antiquos earum vſus
              <lb/>
            extitit. </s>
            <s xml:id="echoid-s479" xml:space="preserve">Inæquales autem, non quòd horæ vnius diei vel noctis inter ſe ſint inæquales; </s>
            <s xml:id="echoid-s480" xml:space="preserve">hoc enim falſum eſt,
              <lb/>
              <note position="left" xlink:label="note-0026-04" xlink:href="note-0026-04a" xml:space="preserve">Cur dictæ ſint
                <lb/>
              horæ antiquæ@
                <lb/>
              & inæquales.</note>
              <note position="left" xlink:label="note-0026-05" xlink:href="note-0026-05a" xml:space="preserve">20</note>
            cum quamlibet diem, ac noctem in 12 partes æquales diſtribui aſſeruerimus; </s>
            <s xml:id="echoid-s481" xml:space="preserve">ſed quia cũ dies artificiales,
              <lb/>
            & </s>
            <s xml:id="echoid-s482" xml:space="preserve">noctes ſint inæquales, horæ diei vel noctis longioris maiores ſunt horis diei, vel noctis breuioris. </s>
            <s xml:id="echoid-s483" xml:space="preserve">Quan-
              <lb/>
            do enim duæ magnitudines inæquales in partes numero æquales diuiduntur, efficiuntur ſingulæ partes ma-
              <lb/>
            ioris magnitudinis ſingulis partibus minoris inæquales, puta maiores. </s>
            <s xml:id="echoid-s484" xml:space="preserve">Rurſus dicuntur huiuſmodi partes
              <lb/>
            duodecimæ diei vel noctis, horæ inæquales, quoniam cum tam dies, quàm nox artificialis æqualib{us} duo-
              <lb/>
            decim horis conſtet, ſit autem in ſphæra obliqua perpetuo dies ſuæ nocti inæqualis, excepto tempore æqui-
              <lb/>
            noctiorum, ſole in principio ♈, vel ♎ exiſtente, neceſſario efficitur, hor{as} diurn{as} inæquales eſſe no-
              <lb/>
            cturnis horis. </s>
            <s xml:id="echoid-s485" xml:space="preserve">Deniq; </s>
            <s xml:id="echoid-s486" xml:space="preserve">nominatæ ſunt huiuſmodi horæ inæquales, quia nunquam, niſi in æquinoctijs, conue-
              <lb/>
            niunt cum horis æquinoctialibus, quæ æquales dicuntur, vt mox docebim{us}, ſed ſemper aut minores ſunt,
              <lb/>
            vt diurnæ in hyeme, & </s>
            <s xml:id="echoid-s487" xml:space="preserve">nocturnæ in æſtate, aut maiores, vt ſunt diurnæ in æſtate, & </s>
            <s xml:id="echoid-s488" xml:space="preserve">nocturnæ in hyeme.
              <lb/>
            </s>
            <s xml:id="echoid-s489" xml:space="preserve">
              <note position="left" xlink:label="note-0026-06" xlink:href="note-0026-06a" xml:space="preserve">30</note>
            Cur autem duodecim hor{as} diurn{as}, totidem{q́ue} nocturnas conſtituerint veteres, partim ſupra cõmemora-
              <lb/>
              <note position="left" xlink:label="note-0026-07" xlink:href="note-0026-07a" xml:space="preserve">Cur Antiqui
                <lb/>
              diem, & noctẽ
                <lb/>
              quãlibet in 12.
                <lb/>
              horas ſecuerint.</note>
            uim{us}, cum de etymologia hui{us} nominis, hora, diſſereremus, partim etiam hoc loco aperiemus. </s>
            <s xml:id="echoid-s490" xml:space="preserve">@eteres
              <lb/>
            magnam ſemper rationem habuiſſe temporis, quo ſingulæ partes zodiaci ſupra Horizontem exoriuntur,
              <lb/>
            perſpicuè conſtat. </s>
            <s xml:id="echoid-s491" xml:space="preserve">Vnde non temerè hor{as} à partib{us} zodiaci inſtituiſſe videntur. </s>
            <s xml:id="echoid-s492" xml:space="preserve">Sed quoniã 12 partes
              <lb/>
            ſunt præcipuæ in zodiaco, nempe 12. </s>
            <s xml:id="echoid-s493" xml:space="preserve">ſigna cœleſtia, quorum ſex qualibet die, & </s>
            <s xml:id="echoid-s494" xml:space="preserve">totidem quauis nocte oriũ-
              <lb/>
            tur, vt in ſphær a docuim{us}; </s>
            <s xml:id="echoid-s495" xml:space="preserve">ſi ſingulis ſignis horam tribuiſſent, ſex hor{as} duntaxat conſtituiſſent tam in
              <lb/>
            die, quàm in nocte qualibet, eaſ{q́ue} lõgiores, quàm par eſt, effeciſſent. </s>
            <s xml:id="echoid-s496" xml:space="preserve">Quocirca viſum eſt illis cuilibet medie
              <lb/>
            tati vnius ſigni ſupra Horizontem emergenti horam aſcribere. </s>
            <s xml:id="echoid-s497" xml:space="preserve">Vnde factum eſt, vt quemuis diem, & </s>
            <s xml:id="echoid-s498" xml:space="preserve">no-
              <lb/>
            ctem in 12 hor{as} partitiſint. </s>
            <s xml:id="echoid-s499" xml:space="preserve">Hiſce horis inæqualib{us} olim Iudæi vtebantur, vt ex ſacris literis conſtat,
              <lb/>
            nec non Romani, & </s>
            <s xml:id="echoid-s500" xml:space="preserve">tota ferme antiquit{as}, vt & </s>
            <s xml:id="echoid-s501" xml:space="preserve">hyſtoriæ, & </s>
            <s xml:id="echoid-s502" xml:space="preserve">libri veterum Mathematicorum teſtantur.
              <lb/>
            </s>
            <s xml:id="echoid-s503" xml:space="preserve">
              <note position="left" xlink:label="note-0026-08" xlink:href="note-0026-08a" xml:space="preserve">40</note>
            His enim noctem in quatuor vigili{as} diſtribuebant, ſingulis vigilijs tern{as} tribuendo hor{as}. </s>
            <s xml:id="echoid-s504" xml:space="preserve">Immo & </s>
            <s xml:id="echoid-s505" xml:space="preserve">Ec-
              <lb/>
            cleſia Romana laudes Deo Opt. </s>
            <s xml:id="echoid-s506" xml:space="preserve">Max. </s>
            <s xml:id="echoid-s507" xml:space="preserve">quæ ab horarum nomine quidem horæ canonicæ, numero autem Pri
              <lb/>
            ma, Tertia, Sexta, & </s>
            <s xml:id="echoid-s508" xml:space="preserve">Nona vocatę ſunt, ſecundum hoc gen{us} hor arum inſtituit decantand{as}.</s>
            <s xml:id="echoid-s509" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s510" xml:space="preserve">HORA verò æqualis eſt viceſima quarta pars dieinaturalis, qui ex die, nocte{q́ue} conficitur. </s>
            <s xml:id="echoid-s511" xml:space="preserve">Quia verò
              <lb/>
              <note position="left" xlink:label="note-0026-09" xlink:href="note-0026-09a" xml:space="preserve">Hora æqua-
                <lb/>
              lis.</note>
            circulus A Equinoctialis continens grad. </s>
            <s xml:id="echoid-s512" xml:space="preserve">360. </s>
            <s xml:id="echoid-s513" xml:space="preserve">ſemel in die cir cumagitur, ſupra{q́ue} Horizontem vbiuis gen-
              <lb/>
            tium totus aſcendit, (negligimus hic particulam illam, quæ portiunculæ illi zodiaci reſpondet, quam inte-
              <lb/>
            rim proprio motu ſol percurrit) neceſſe eſt ſingulis horis aſcendere grad. </s>
            <s xml:id="echoid-s514" xml:space="preserve">15. </s>
            <s xml:id="echoid-s515" xml:space="preserve">qua de cauſa hę horæ dictæ
              <lb/>
            ſunt æquinoctiales, quòd videlicet à cir cũuolutione æquinoctialis circuli efficiãtur. </s>
            <s xml:id="echoid-s516" xml:space="preserve">Dictæ quoq; </s>
            <s xml:id="echoid-s517" xml:space="preserve">ſunt æqua-
              <lb/>
              <note position="left" xlink:label="note-0026-10" xlink:href="note-0026-10a" xml:space="preserve">Cur dictæ
                <lb/>
              ſint horæ æqui-
                <lb/>
              noctiales, atq;
                <lb/>
              æquales.</note>
            les. </s>
            <s xml:id="echoid-s518" xml:space="preserve">Nam ſemper æquali temporis ſpatio emergunt grad. </s>
            <s xml:id="echoid-s519" xml:space="preserve">15. </s>
            <s xml:id="echoid-s520" xml:space="preserve">A Equatoris, qui cuiq; </s>
            <s xml:id="echoid-s521" xml:space="preserve">horæ tribuuntur, ſupra
              <lb/>
            Horizontem: </s>
            <s xml:id="echoid-s522" xml:space="preserve">Siquidem in omni regione vniformiter eleuatur, ac deprimitur infra Horizontem circulus
              <lb/>
              <note position="left" xlink:label="note-0026-11" xlink:href="note-0026-11a" xml:space="preserve">50</note>
            æquinoctialis, vt alibi oſtendim{us}.</s>
            <s xml:id="echoid-s523" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s524" xml:space="preserve">PORRO haſce hor{as} æquales olim non omnes nationes, ſicut ncc hodie, eodem modo numerabant;
              <lb/>
            </s>
            <s xml:id="echoid-s525" xml:space="preserve">quoniam non idem initium diei natur alis apud omnes erat conſtitutum. </s>
            <s xml:id="echoid-s526" xml:space="preserve">Babylonij etenim, teſte Plinio lib. </s>
            <s xml:id="echoid-s527" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0026-12" xlink:href="note-0026-12a" xml:space="preserve">Initium va-
                <lb/>
              rium diei apud
                <lb/>
              varias gentes.</note>
            2. </s>
            <s xml:id="echoid-s528" xml:space="preserve">& </s>
            <s xml:id="echoid-s529" xml:space="preserve">Macrobio lib. </s>
            <s xml:id="echoid-s530" xml:space="preserve">1. </s>
            <s xml:id="echoid-s531" xml:space="preserve">Saturnaliorum, diem appellabant motum ſolis ab vno ortu ad alterum ortum, quos
              <lb/>
            hac tempeſtate imitantur incolæ inſularum Balearium. </s>
            <s xml:id="echoid-s532" xml:space="preserve">Vnde hor{as} ab exortu ſolis ſupputabant, quæ Ba-
              <lb/>
            bylonicæ à pleriſ ſcriptoribus dicuntur, propterea quod apud Babylonios in vſu fuerunt. </s>
            <s xml:id="echoid-s533" xml:space="preserve">Athenienſes
              <lb/>
              <note position="left" xlink:label="note-0026-13" xlink:href="note-0026-13a" xml:space="preserve">Horæ Baby-
                <lb/>
              lonicæ.</note>
            autem, quos nunc ſequitur tota Italia vna cum Bohemia, diem definiebant ab uno ſolis occaſu ad occaſum
              <lb/>
            alterũ, inde{q́ue} hor{as} æquales numer abant: </s>
            <s xml:id="echoid-s534" xml:space="preserve">quæ iã Italicæ nuncupãtur ab Italia, vbi maxime earũ vſus vi-
              <lb/>
              <note position="left" xlink:label="note-0026-14" xlink:href="note-0026-14a" xml:space="preserve">Horę Italicę.</note>
            get. </s>
            <s xml:id="echoid-s535" xml:space="preserve">Vmbri deinde (quem etiam morem Aſtronomi omnes obſeruant) totum temp{us} à meridie ad ſequen-
              <lb/>
            tem meridiem vo
              <unsure/>
            cabant diem, hor{as}{q́ue} æquales 24. </s>
            <s xml:id="echoid-s536" xml:space="preserve">computabant à meridie, quę quoniam in motibus </s>
          </p>
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