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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[21.] SCHOLIVM.
Page: 41 (21)
[22.] THEOREMA 3. PROPOSITIO 4.
Page: 41 (21)
[23.] COROLLARIVM.
Page: 41 (21)
[24.] THEQREMA 4. PROPOSITIQ 5.
Page: 42 (22)
[25.] COROLLARIVM.
Page: 42 (22)
[26.] THEOREMA 5. PROPOSITIO 6.
Page: 43 (23)
[27.] SCHOLIVM.
Page: 44 (24)
[28.] COROLLARIVM.
Page: 44 (24)
[29.] THEOREMA 6. PROPOSITIO 7.
Page: 44 (24)
[30.] COROLLARIVM.
Page: 45 (25)
[31.] PROBLEMA 2. PROPOSITIO 8.
Page: 46 (26)
[32.] SCHOLIVM.
Page: 49 (29)
[33.] LEMMA.
Page: 49 (29)
[34.] LEMMA PRIMVM.
Page: 51 (31)
[35.] LEMMA II.
Page: 51 (31)
[36.] LEMMA PRIMVM.
Page: 53 (33)
[37.] LEMMA II.
Page: 53 (33)
[38.] THEOREMA 7. PROPOSITIO 9.
Page: 57 (37)
[39.] SCHOLIVM.
Page: 58 (38)
[40.] THEOREMA 8. PROPOSITIQ 10.
Page: 59 (39)
[41.] COROLLARIVM.
Page: 60 (40)
[42.] SCHOLIVM.
Page: 60 (40)
[43.] THEOREMA 9. PROPOSITIO 11.
Page: 62 (42)
[44.] SCHOLIVM.
Page: 63 (43)
[45.] COROLLARIVM PRIMVM.
Page: 63 (43)
[46.] COROLLARIVM II.
Page: 63 (43)
[47.] THEOREMA 10. PROPOSITIO 12.
Page: 63 (43)
[48.] COROLLARIVM.
Page: 64 (44)
[49.] THEOREMA 11. PROPOSITIO 13.
Page: 64 (44)
[50.] THEOREMA 12. PROPOSITIO 14.
Page: 65 (45)
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        <div xml:id="echoid-div25" type="section" level="1" n="13">
          <p style="it">
            <s xml:id="echoid-s536" xml:space="preserve">
              <pb o="7" file="0027" n="27" rhead="LIBER PRIMVS."/>
            rum ſupputandis ab Aſtronomis vſurpantur, Aſtronomicæ dici conſueuerunt. </s>
            <s xml:id="echoid-s537" xml:space="preserve">Aegyptij deniq;</s>
            <s xml:id="echoid-s538" xml:space="preserve">, & </s>
            <s xml:id="echoid-s539" xml:space="preserve">teſte
              <lb/>
              <note position="right" xlink:label="note-0027-01" xlink:href="note-0027-01a" xml:space="preserve">Horæ Aſtro-
                <lb/>
              nomicæ.</note>
            Macrobio lib. </s>
            <s xml:id="echoid-s540" xml:space="preserve">1. </s>
            <s xml:id="echoid-s541" xml:space="preserve">Saturnaliorum, popul{us} Roman{us}, diẽ numer abant à media nocte in proximè ſequentem
              <lb/>
            mediam noctem, atq; </s>
            <s xml:id="echoid-s542" xml:space="preserve">hinc horas elapſas obſeruabant. </s>
            <s xml:id="echoid-s543" xml:space="preserve">Id quod Eccleſia quoq; </s>
            <s xml:id="echoid-s544" xml:space="preserve">Romana obſeruat in celebra-
              <lb/>
            tione ſolennitatum & </s>
            <s xml:id="echoid-s545" xml:space="preserve">ieiuniorum. </s>
            <s xml:id="echoid-s546" xml:space="preserve">Cæterum ab horis, quæ Vmbris, Aſtronomis, Aegyptijs, atq; </s>
            <s xml:id="echoid-s547" xml:space="preserve">Romanis
              <lb/>
              <note position="right" xlink:label="note-0027-02" xlink:href="note-0027-02a" xml:space="preserve">Horæ vulga-
                <lb/>
              res, ſiue commu
                <lb/>
              nes quo modo
                <lb/>
              diffe ant ab ho
                <lb/>
              ris Aſtronomi-
                <lb/>
              ci@.</note>
            in vſu fuerunt, non multum diſcrepant horæ vulgares, ſiue communes, quibus Germania, Gallia, Hiſpa-
              <lb/>
            nia, & </s>
            <s xml:id="echoid-s548" xml:space="preserve">tota fermè Europa hodie vtitur. </s>
            <s xml:id="echoid-s549" xml:space="preserve">Numer ant enim harum regionum populi hor{as} æquales 12 à me-
              <lb/>
            ridie vſq; </s>
            <s xml:id="echoid-s550" xml:space="preserve">ad noctem mediam, totidem{q́ue} hinc ad proximum meridiem. </s>
            <s xml:id="echoid-s551" xml:space="preserve">Quo fit, vt in numer atione hor arum
              <lb/>
            à meridie in mediam noctem nulla in re differant ab Vmbris, Aſtronomiſve; </s>
            <s xml:id="echoid-s552" xml:space="preserve">à media verò nocte in meri-
              <lb/>
            diẽ vſq; </s>
            <s xml:id="echoid-s553" xml:space="preserve">ab ijſdẽ diſſentiant in numer atione duntaxat horarum. </s>
            <s xml:id="echoid-s554" xml:space="preserve">Nam quæ Vmbris, Aſtronomiſ{q́ue} dicitur
              <lb/>
            hora 13. </s>
            <s xml:id="echoid-s555" xml:space="preserve">à meridie, apud vulgus Europæum appellatur prima poſt mediam noctem, & </s>
            <s xml:id="echoid-s556" xml:space="preserve">quæ apud illos eſt
              <lb/>
            14. </s>
            <s xml:id="echoid-s557" xml:space="preserve">à meridie, his dicitur ſecunda poſt mediam noctem, & </s>
            <s xml:id="echoid-s558" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s559" xml:space="preserve">Pari ratione in numer atione ho-
              <lb/>
              <note position="left" xlink:label="note-0027-03" xlink:href="note-0027-03a" xml:space="preserve">10</note>
            rarũ à media nocte in meridiẽ vſq; </s>
            <s xml:id="echoid-s560" xml:space="preserve">cum Aegyptijs, & </s>
            <s xml:id="echoid-s561" xml:space="preserve">Romanis conueniũt, at à meridie in mediã noctem
              <lb/>
            ab ijſdem in ſola numer atione diſcrepant. </s>
            <s xml:id="echoid-s562" xml:space="preserve">Quæ enim hora apud Romanos, vel A Egyptios appellatur 13.
              <lb/>
            </s>
            <s xml:id="echoid-s563" xml:space="preserve">poſt mediam noctem, hodie apud Europæos dicitur prima poſt meridiem, & </s>
            <s xml:id="echoid-s564" xml:space="preserve">quam illi vocant 14. </s>
            <s xml:id="echoid-s565" xml:space="preserve">à media
              <lb/>
            nocte, dicitur Europęis ſecunda à meridie, & </s>
            <s xml:id="echoid-s566" xml:space="preserve">c. </s>
            <s xml:id="echoid-s567" xml:space="preserve">Hinc efficitur, vnum idem{q́ue} horologium oſtẽdere & </s>
            <s xml:id="echoid-s568" xml:space="preserve">horas
              <lb/>
            à meridie, & </s>
            <s xml:id="echoid-s569" xml:space="preserve">hor{as} à media nocte numer atas, dummodo horarum numeros commutes, vt dictum est. </s>
            <s xml:id="echoid-s570" xml:space="preserve">So-
              <lb/>
            lent tamen in huiuſmodi horologijs apponi numeri horarum iuxta numerationem vulgi, vt 12. </s>
            <s xml:id="echoid-s571" xml:space="preserve">à meridie
              <lb/>
            ad mediam noctem, & </s>
            <s xml:id="echoid-s572" xml:space="preserve">totidem à media nocte in meridiem, vt ex ſequentibus erit manifeſtum. </s>
            <s xml:id="echoid-s573" xml:space="preserve">Itaque vt
              <lb/>
              <note position="right" xlink:label="note-0027-04" xlink:href="note-0027-04a" xml:space="preserve">In quolibe@
                <lb/>
              horologio ſola-
                <lb/>
              ri quatuor hora
                <lb/>
              rum genera de-
                <lb/>
              ſcribi poſſunt.</note>
            omnia paucis comprehendamus, quoniam duo ſunt horarum genera, inæqualium vnum, & </s>
            <s xml:id="echoid-s574" xml:space="preserve">alterum æqua-
              <lb/>
            lium; </s>
            <s xml:id="echoid-s575" xml:space="preserve">æquales verò horæ initium habent vel ab ortu ſolis, vel ab occaſu, vel à meridie, ſeu media nocte, fit
              <lb/>
            vt in quouis horologio ſiue penſili, ſiue concauo, conuexove, ſiue plano, quatuor horarum genera deſcribi
              <lb/>
              <note position="left" xlink:label="note-0027-05" xlink:href="note-0027-05a" xml:space="preserve">20</note>
              <note position="right" xlink:label="note-0027-06" xlink:href="note-0027-06a" xml:space="preserve">Horologiot
                <unsure/>
              ũ
                <lb/>
              quatuor gene-
                <lb/>
              ra ex varietate
                <lb/>
              horarum orta.</note>
            poſſint, puta horæ inæquales, ſiue antiquæ, horæ æquales ab ortu ſolis, horæ æquales à ſolis occaſu, & </s>
            <s xml:id="echoid-s576" xml:space="preserve">horæ
              <lb/>
            æquales à meridie & </s>
            <s xml:id="echoid-s577" xml:space="preserve">media nocte ſupputatæ: </s>
            <s xml:id="echoid-s578" xml:space="preserve">Quareratione horarum quodcunq; </s>
            <s xml:id="echoid-s579" xml:space="preserve">horologium quadruplex
              <lb/>
            erit, habebit{q́ue}, hæc nomina.</s>
            <s xml:id="echoid-s580" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Horologium
            <lb/>
          Antiquum.</note>
          <p style="it">
            <s xml:id="echoid-s581" xml:space="preserve">ANTIQVVM, quod hor{as} inæquales, quibus antiqui vtebantur, continet.</s>
            <s xml:id="echoid-s582" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s583" xml:space="preserve">BABYLONICVM, quod indicat hor{as} ab ortu ſolis, quæ apud Babylonios in vſu fuerunt.</s>
            <s xml:id="echoid-s584" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Horologium
            <lb/>
          Babylo@@cum.</note>
          <p style="it">
            <s xml:id="echoid-s585" xml:space="preserve">ITALICVM, quod hor{as} complectitur à ſolis occaſu, quibus Itali vtuntur.</s>
            <s xml:id="echoid-s586" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Horologium
            <lb/>
          Italicum.</note>
          <p style="it">
            <s xml:id="echoid-s587" xml:space="preserve">ASTRONOMICVM, quod hor{as} notat à meridie in mediam noctem, & </s>
            <s xml:id="echoid-s588" xml:space="preserve">à medianocte in me-
              <lb/>
            ridiem, quæ non ſolum Europæ ferè vniuerſæ, ſed omnibus Aſtronomis etiam communes ſunt.</s>
            <s xml:id="echoid-s589" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Horologium
            <lb/>
          Aſtronomicũ.</note>
        </div>
        <div xml:id="echoid-div29" type="section" level="1" n="14">
          <head xml:id="echoid-head16" style="it" xml:space="preserve">DE INVENTORIBVS SCIOTHERI-
            <lb/>
          corum horologiorum, eorum{q́ue} ſcriptoribus.</head>
          <p style="it">
            <s xml:id="echoid-s590" xml:space="preserve">SCIOTHERICORVM horologiorum primus inuentor perhibetur fuiſſe Anaximenes Mileſi{us},
              <lb/>
              <note position="right" xlink:label="note-0027-12" xlink:href="note-0027-12a" xml:space="preserve">Anaximenes
                <lb/>
              Mileſius horo-
                <lb/>
              logiorum ſola-
                <lb/>
              rium primus
                <unsure/>
                <lb/>
              inuentor.</note>
            de quo habentur hæc verba apud Plinium lib. </s>
            <s xml:id="echoid-s591" xml:space="preserve">2, cap. </s>
            <s xml:id="echoid-s592" xml:space="preserve">76. </s>
            <s xml:id="echoid-s593" xml:space="preserve">Vmbrarum rationem, & </s>
            <s xml:id="echoid-s594" xml:space="preserve">quam vocant Gno-
              <lb/>
            monicen, inuenit Anaximenes Mileſius Anaximandri diſcipulus, primus{q́ue} horologium, quod appellant
              <lb/>
            Sciothericum Lacedæmone oſtendit. </s>
            <s xml:id="echoid-s595" xml:space="preserve">hæc Plini{us}. </s>
            <s xml:id="echoid-s596" xml:space="preserve">Verum horologiorũ vſum antiquiorem multo fuiſſe, ſa-
              <lb/>
            tis euidentib{us} argumentis compertum eſt. </s>
            <s xml:id="echoid-s597" xml:space="preserve">Legimus enim in ſacris literis, Achaz Regem habuiſſe ſolare
              <lb/>
              <note position="right" xlink:label="note-0027-13" xlink:href="note-0027-13a" xml:space="preserve">4. Reg. cap.
                <lb/>
              20.</note>
            horologium, qui multo antiquior Anaximene fuit. </s>
            <s xml:id="echoid-s598" xml:space="preserve">Regnauit enim Achaz circa olympiadem primam, hoc
              <lb/>
            eſt, anno 775. </s>
            <s xml:id="echoid-s599" xml:space="preserve">ante Chriſtum natum, vel minimum, vt alijs placet, circa olympiadem ſeptimam, id eſt, anno
              <lb/>
            ante Chriſtum 751. </s>
            <s xml:id="echoid-s600" xml:space="preserve">Anaximenes autem floruit circa olympiadem quinquageſimã, id eſt, circa annũ 579.
              <lb/>
            </s>
            <s xml:id="echoid-s601" xml:space="preserve">
              <note position="left" xlink:label="note-0027-14" xlink:href="note-0027-14a" xml:space="preserve">40</note>
            ante Chriſtum; </s>
            <s xml:id="echoid-s602" xml:space="preserve">vt hic illo fuerit iunior annis fere 196. </s>
            <s xml:id="echoid-s603" xml:space="preserve">vel 172. </s>
            <s xml:id="echoid-s604" xml:space="preserve">Quare rationem hanc horologiorum à pri-
              <lb/>
            mis illis Patrib{us} (quod & </s>
            <s xml:id="echoid-s605" xml:space="preserve">de alijs ſcientijs affirmat Ioſeph{us} in lib. </s>
            <s xml:id="echoid-s606" xml:space="preserve">de antiquitate.) </s>
            <s xml:id="echoid-s607" xml:space="preserve">originem traxiſſe
              <lb/>
            crediderim, eam{q́ue}, ſenſim ad A Egyptios, ab his ad Græcos, à Græcis deniq; </s>
            <s xml:id="echoid-s608" xml:space="preserve">ad Latinos perueniſſe. </s>
            <s xml:id="echoid-s609" xml:space="preserve">In-
              <lb/>
            uentores autem alij aliorum horologiorum Sciothericorum cõmemor antur à Vitruuio lib. </s>
            <s xml:id="echoid-s610" xml:space="preserve">9. </s>
            <s xml:id="echoid-s611" xml:space="preserve">Beroſ{us} enim
              <lb/>
              <note position="right" xlink:label="note-0027-15" xlink:href="note-0027-15a" xml:space="preserve">Inuentores
                <lb/>
              varij variorum
                <lb/>
              horologiorum.</note>
            Chaldæus inueniſſe fertur hemicyclium excauatum ex quadrato, in quo lineæ hor{as} indicantes deſcriptæ
              <lb/>
            erant. </s>
            <s xml:id="echoid-s612" xml:space="preserve">Ariſtarch{us} Sami{us} Scaphen, ſeu hemiſphærium, qualia fortaſſis nunc ſunt horologia hemiſphęrica
              <lb/>
            concaua. </s>
            <s xml:id="echoid-s613" xml:space="preserve">Idem excogitaſſe dicitur Diſcum, horologium videlicet parum excauatum in modum diſci, ſeu pa
              <lb/>
            tinæ, ita vt interior pars non fuerit perfecte ſphærica. </s>
            <s xml:id="echoid-s614" xml:space="preserve">Eudox{us} Aſtrologus fertur reperiſſe Arachnen, id
              <lb/>
            eſt, ar aneam, horologium videlicet in modum araneæ, quale nunc eſt horologium horizontale continens ho-
              <lb/>
            r{as} aſtronomic{as}, & </s>
            <s xml:id="echoid-s615" xml:space="preserve">cir culos altitudinũ ſolis, quos Almucantarath Arabes dicunt. </s>
            <s xml:id="echoid-s616" xml:space="preserve">Vel etiam quodcũq;
              <lb/>
            </s>
            <s xml:id="echoid-s617" xml:space="preserve">
              <note position="left" xlink:label="note-0027-16" xlink:href="note-0027-16a" xml:space="preserve">50</note>
            horologium, in quo deſcriptæ ſint & </s>
            <s xml:id="echoid-s618" xml:space="preserve">lineæ horariæ, & </s>
            <s xml:id="echoid-s619" xml:space="preserve">arc{us} ſignorum zodiaci. </s>
            <s xml:id="echoid-s620" xml:space="preserve">Sunt qui huiuſce horologij
              <lb/>
            Apollonium faciant inuentorem. </s>
            <s xml:id="echoid-s621" xml:space="preserve">Scop{as} Syracuſius prædicatur inuentor Plinthi, ſiue lacunaris, inſtar
              <lb/>
            trabis cuiuſdam quadratę, in qua tam horologium Verticale auſtrale, boreale{q́ue}, quàm Meridianũ Orien-
              <lb/>
            tale, & </s>
            <s xml:id="echoid-s622" xml:space="preserve">Occidentale, nec non in plano ſuperiori Horizontale deſcribi poterat, quale in circo Flaminio po-
              <lb/>
            ſitum erat. </s>
            <s xml:id="echoid-s623" xml:space="preserve">Parmenionem faciunt inuentorem horologiorum, quę vocabantur πρὸς τὰ ἱςοροὐμενα, quę qua-
              <lb/>
            lia fuerint, difficile iudicare poſſumus, niſi fortè dicam{us}, in illis contentas fuiſſe non ſolum line{as} hora-
              <lb/>
            ri{as}, verum etiam ſigna zodiaci, menſes, & </s>
            <s xml:id="echoid-s624" xml:space="preserve">dies, quę omnia per indicem monſtr abantur, ita vt horologia
              <lb/>
            illa fuerint inſtar hyſtorię cuiuſdam. </s>
            <s xml:id="echoid-s625" xml:space="preserve">Theodoſium aſſerunt excogitaſſc horologium dictum πρὸς πᾶν κλῖμα
              <lb/>
            quia omnibus ſeruiebat climatib{us} mundi. </s>
            <s xml:id="echoid-s626" xml:space="preserve">Patrocles reperiſſe narratur πελέκινον, id est, horarium figurã
              <lb/>
            habens ſecuris, ſeu bipennis, qualem formam nũc pene gerit horologium Meridianum, in quo ſigna </s>
          </p>
        </div>
      </text>
    </echo>
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