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

< >
[231.] DE HOROLOGIIS ÆQVINOCTIALIBVS. PROBLEMA 49. PROPOSITIO 49.
Page: 289 (273)
[232.] SCHOLIVM.
Page: 290 (274)
[233.] PROBLEMA 50. PROPOSITIO 50.
Page: 290 (274)
[234.] SCHOLIVM.
Page: 292 (276)
[235.] PROBLEMA 51. PROPOSITIO 51.
Page: 293 (277)
[236.] PROBLEMA 52. PROPOSITIO 52.
Page: 293 (277)
[237.] SCHOLIVM.
Page: 294 (278)
[238.] PROBLEMA 53. PROPOSITIO 53.
Page: 295 (279)
[239.] SCHOLIVM.
Page: 297 (281)
[240.] PROBLEMA 54. PROPOSITIO 54.
Page: 297 (281)
[241.] PROBLEMA 55. PROPOSITIO 55.
Page: 298 (282)
[242.] PROBLEMA 56. PROPOSITIO 56.
Page: 298 (282)
[243.] SCHOLIVM.
Page: 300 (284)
[244.] PROBLEMA 57. PROPOSITIO 57.
Page: 300 (284)
[245.] SCHOLIVM.
Page: 301 (285)
[246.] PROBLEMA 58. PROPOSITIO 58. HOROLOGIVM Italicum æquinoctiale conſtruere.
Page: 302 (286)
[247.] PROBLEMA 59. PROPOSITIO 59. HOROLOGIVM Babylonicum ęquinoctiale componere.
Page: 305 (289)
[248.] SCHOLIVM.
Page: 305 (289)
[249.] PROBLEMA 60. PROPOSITIO 60. HOROLOGIVM Antiquum æquinoctiale conſtituere.
Page: 307 (291)
[250.] SCHOLIVM.
Page: 308 (292)
[251.] FINIS SECVNDI LIBRI.
Page: 308 (292)
[252.] GNOMONICES LIBER TERTIVS.
Page: 309 (293)
[253.] AVCTORE CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
Page: 309 (293)
[254.] DE HOROLOGIIS, QVAE A VER-ticali circulo declinant. PROBLEMA 1. PROPOSITIO 1.
Page: 310 (294)
[255.] SCHOLIVM.
Page: 318 (302)
[256.] PROBLEMA 2. PROPOSITIO 2.
Page: 328 (312)
[257.] SCHOLIVM.
Page: 334 (318)
[258.] PROBLEMA 3. PROPOSITIO 3.
Page: 336 (320)
[259.] SCHOLIVM.
Page: 336 (320)
[260.] PROBLEMA 4. PROPOSITIO 4.
Page: 336 (320)
< >
page |< < (219) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div749" type="section" level="1" n="180">
          <p style="it">
            <s xml:id="echoid-s14980" xml:space="preserve">
              <pb o="219" file="0239" n="239" rhead="LIBER SECVNDVS."/>
            ſim & </s>
            <s xml:id="echoid-s14981" xml:space="preserve">Horizon ad eadem rectus, ac proinde & </s>
            <s xml:id="echoid-s14982" xml:space="preserve">per polos eorundem horologiorum tranſibit, ex propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s14983" xml:space="preserve">13. </s>
            <s xml:id="echoid-s14984" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14985" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14986" xml:space="preserve">Theodoſii, & </s>
            <s xml:id="echoid-s14987" xml:space="preserve">ob id etiam per stylos eorundem, nempe per axem illorum. </s>
            <s xml:id="echoid-s14988" xml:space="preserve">Eundem autem Ho-
              <lb/>
            rizontem ad circulum quoque maximum per A E, ductum eſſe rectum, perſpicuum eſt; </s>
            <s xml:id="echoid-s14989" xml:space="preserve">propterea quòd
              <lb/>
            in illis horologiis dictus circulus vnus est ex Verticalibus, qui omnes recti ſunt ad Horizontem, & </s>
            <s xml:id="echoid-s14990" xml:space="preserve">viciſ-
              <lb/>
            ſim Horizon ad eoſdem rectus. </s>
            <s xml:id="echoid-s14991" xml:space="preserve">Hinc fit, rectas A G, C H, eſſe lineas horizontales in dictis horologiis. </s>
            <s xml:id="echoid-s14992" xml:space="preserve">
              <lb/>
            In reliquis antem horologijs ille circulus nullo modo eſſe poteſt Horizon; </s>
            <s xml:id="echoid-s14993" xml:space="preserve">quia Horizon ad eorum plana
              <lb/>
            rectus non est, cum huiuſmodi plana ad Horizontem ponantur eſſe inclinata: </s>
            <s xml:id="echoid-s14994" xml:space="preserve">quare neque rectę A G,
              <lb/>
            C H, horizontales erunt lineæ. </s>
            <s xml:id="echoid-s14995" xml:space="preserve">Sed in polari quidẽ horologio circulus ille erit Aequator, & </s>
            <s xml:id="echoid-s14996" xml:space="preserve">lineæ A G,
              <lb/>
            C H, æquinoctiales erunt: </s>
            <s xml:id="echoid-s14997" xml:space="preserve">In æquinoctiali vero horologio idem circulus erit horæ 6. </s>
            <s xml:id="echoid-s14998" xml:space="preserve">à meridie vel me-
              <lb/>
              <note position="left" xlink:label="note-0239-01" xlink:href="note-0239-01a" xml:space="preserve">10</note>
            dia nocte, & </s>
            <s xml:id="echoid-s14999" xml:space="preserve">lineæ A G, C H, horam 6. </s>
            <s xml:id="echoid-s15000" xml:space="preserve">à meridie, vel media nocte monstrabunt, vt patet poſitionem
              <lb/>
            horum circulorum diligenter contemplanti, & </s>
            <s xml:id="echoid-s15001" xml:space="preserve">ex ſequentibus planum fiet, ac manifeſtum. </s>
            <s xml:id="echoid-s15002" xml:space="preserve">In cæteris de-
              <lb/>
            nique horologiis dictus circulus erit alius, atque alius; </s>
            <s xml:id="echoid-s15003" xml:space="preserve">ſemper tamen rectæ A G, C H, parallelæ erunt
              <lb/>
            horizontali lineæ vtriuſque horologii. </s>
            <s xml:id="echoid-s15004" xml:space="preserve">Cum enim circulus hic maximus, de quo poſteriori loco diximus, re
              <lb/>
            ctus ſit ad priorem circulum maximum per rectas A E, C F, & </s>
            <s xml:id="echoid-s15005" xml:space="preserve">ſtylos A B, C D, ductum, hic autem ad
              <lb/>
            Horizontem rectus ſit poſitus, atque adeo & </s>
            <s xml:id="echoid-s15006" xml:space="preserve">Horizon viciſſim ad eundem rectus ſit, tranſibit tam Hori-
              <lb/>
            zon, quàm maximus ille circulus per rectas A G, C H, ductus, per polos huius circuli maximi per re-
              <lb/>
            ctas A E, C F, ducti, ex propoſ. </s>
            <s xml:id="echoid-s15007" xml:space="preserve">13. </s>
            <s xml:id="echoid-s15008" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15009" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15010" xml:space="preserve">Theodoſii; </s>
            <s xml:id="echoid-s15011" xml:space="preserve">ac proinde axis eiuſdem huius circuli per rectas
              <lb/>
            A E, C F, ducti erit communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s15012" xml:space="preserve">alterius illius circuli maximi, qui per rectas A G,
              <lb/>
            C H, ducitur. </s>
            <s xml:id="echoid-s15013" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s15014" xml:space="preserve">circulus maximus, cui horologium æquidiſtat, per eoſdem polos circuli maximi per
              <lb/>
            rectas A E, C F, ducti tranſit. </s>
            <s xml:id="echoid-s15015" xml:space="preserve">(Quia enim circulus maximus per rectas A E, C F, & </s>
            <s xml:id="echoid-s15016" xml:space="preserve">ſtylos A B, C D,
              <lb/>
              <note position="left" xlink:label="note-0239-02" xlink:href="note-0239-02a" xml:space="preserve">20</note>
            ductus rectus eſt, per conſtructionem, ad planum horologij, hoc eſt, ad circulum, quem in ſphæra facit horo
              <lb/>
            logij planum, tranſibit idem per polos huius circuli in ſphęra procreati, per propoſ. </s>
            <s xml:id="echoid-s15017" xml:space="preserve">13. </s>
            <s xml:id="echoid-s15018" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15019" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15020" xml:space="preserve">Theodoſii.
              <lb/>
            </s>
            <s xml:id="echoid-s15021" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s15022" xml:space="preserve">per polos circuli maximi, cui horologium ęquidiſtat, quòd circuli paralleli eoſdem habeant
              <lb/>
            polos, ex propoſ. </s>
            <s xml:id="echoid-s15023" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15024" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15025" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15026" xml:space="preserve">Thcodoſii. </s>
            <s xml:id="echoid-s15027" xml:space="preserve">Quare viciſſim circulus hic maximus, cui horologium æquidistat, per
              <lb/>
            polos illius, qui per rectas A E, C F, ducitur, tranſibit, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s15028" xml:space="preserve">15 lib. </s>
            <s xml:id="echoid-s15029" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15030" xml:space="preserve">Theodoſii.) </s>
            <s xml:id="echoid-s15031" xml:space="preserve">Habent
              <lb/>
            ergo Horizon, circulus maximus per rectas A G, C H, & </s>
            <s xml:id="echoid-s15032" xml:space="preserve">ſtylos A B, C D, ductus, & </s>
            <s xml:id="echoid-s15033" xml:space="preserve">circulus maxi-
              <lb/>
            mus, cui horologium æquidiſtat, eandem communem ſectionem, nempe axem circuli maximi per rectas
              <lb/>
            A E, C G, & </s>
            <s xml:id="echoid-s15034" xml:space="preserve">ſtylos A B, C D, ducti. </s>
            <s xml:id="echoid-s15035" xml:space="preserve">Quamobrem cum planum horologii huic poſtremo circulo æquidiſtet,
              <lb/>
            erunt per propoſ. </s>
            <s xml:id="echoid-s15036" xml:space="preserve">18. </s>
            <s xml:id="echoid-s15037" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s15038" xml:space="preserve">communes ſectiones aliorum, (nempe Horizontis, & </s>
            <s xml:id="echoid-s15039" xml:space="preserve">eius, qui per
              <lb/>
              <note position="left" xlink:label="note-0239-03" xlink:href="note-0239-03a" xml:space="preserve">30</note>
            rectas A G, C H, & </s>
            <s xml:id="echoid-s15040" xml:space="preserve">per ſtylos A B, C D, ducitur, & </s>
            <s xml:id="echoid-s15041" xml:space="preserve">plani horologii illos ſecantis) parallelę; </s>
            <s xml:id="echoid-s15042" xml:space="preserve">Ac pro-
              <lb/>
            inde cum ſectio, quam facit Horizon, ſit linea horizõtalis in horologio, ſectio autem alterius circuli maxi
              <lb/>
            mi ſit recta A G, in vno horologio, & </s>
            <s xml:id="echoid-s15043" xml:space="preserve">recta C H, in altero, parallelæ erunt rectæ A G, C H, horizontali
              <lb/>
            lineæ vtriuſque horologij.</s>
            <s xml:id="echoid-s15044" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15045" xml:space="preserve">IAM verò circulus aliquis maximus, ſiue horarius is ſit, ſiue alius quiſpiam, in horologio Auſtrali,
              <lb/>
            vel ſuperiori per centrum mundi, id eſt, per B, vel D, (duo enim hæc puncta vnum punctum conficiunt)
              <lb/>
            verticem ſtyli tranſiens faciat ſectionem E G, quę ſecet rectam A E, infra ſtylum in E, & </s>
            <s xml:id="echoid-s15046" xml:space="preserve">rectam A G,
              <lb/>
            ad dextram in G. </s>
            <s xml:id="echoid-s15047" xml:space="preserve">Secabit idem hic circulus in horologio boreali, vel inferiori, cum per ſtyli verticem
              <lb/>
            tranſeat, rectas C F, C H, in partibus oppoſitis, vt perſpicuum eſt, ſi planum horologij vtriuſque, & </s>
            <s xml:id="echoid-s15048" xml:space="preserve">pla-
              <lb/>
            num circuli ſectionem E G, facientis in proprijs poſitionibus conſiderentur; </s>
            <s xml:id="echoid-s15049" xml:space="preserve">ſecabit, inquam, rectam C F,
              <lb/>
            ſupra ſtylum, & </s>
            <s xml:id="echoid-s15050" xml:space="preserve">rectam C H, ad partem dextram. </s>
            <s xml:id="echoid-s15051" xml:space="preserve">Superior enim pars borealis horologij, vel inferioris,
              <lb/>
              <note position="left" xlink:label="note-0239-04" xlink:href="note-0239-04a" xml:space="preserve">40</note>
            parti inferiori Auſtralis, vel ſuperioris horologij opponitur, atque inferior ſuperiori, & </s>
            <s xml:id="echoid-s15052" xml:space="preserve">dextra dextræ,
              <lb/>
            ſiniſtra{q́ue} ſiniſtrę. </s>
            <s xml:id="echoid-s15053" xml:space="preserve">Appellamus autem partem dextram, ſiniſtramve, quæ nobis ad horologium conuerſis
              <lb/>
            ad dexteram eſt, vel ad ſiniſtram. </s>
            <s xml:id="echoid-s15054" xml:space="preserve">Vnde cum duo illa horologia ſe mutuo reſpiciant, reſpondebit dextra
              <lb/>
            pars vnius parti ſiniſtr æ alterius, & </s>
            <s xml:id="echoid-s15055" xml:space="preserve">contra; </s>
            <s xml:id="echoid-s15056" xml:space="preserve">dextra autem dextræ, & </s>
            <s xml:id="echoid-s15057" xml:space="preserve">ſiniſtra ſiniſtræ opponetur, cum
              <lb/>
            inter has partes medio loco ponatur ſtylus. </s>
            <s xml:id="echoid-s15058" xml:space="preserve">Sit ergo communis ſectio dicti circuli, & </s>
            <s xml:id="echoid-s15059" xml:space="preserve">plani horologij in
              <lb/>
            boreali horologio, ſeu inferiori, recta F H, ſecans C F, in F, ſupra ſtylum, & </s>
            <s xml:id="echoid-s15060" xml:space="preserve">C H, in H, ad partem eius
              <lb/>
            dextram. </s>
            <s xml:id="echoid-s15061" xml:space="preserve">Erunt autem ambæ ſectiones E G, F H, parallelæ, cum eas idem circulus in planis parallelis
              <lb/>
              <note position="right" xlink:label="note-0239-05" xlink:href="note-0239-05a" xml:space="preserve">16. vndec.</note>
            horologiorum efficiat. </s>
            <s xml:id="echoid-s15062" xml:space="preserve">Itaque quoniam rectæ A E, C F, parallelæ ſunt, vt demonſtratum eſt, erunt æqua-
              <lb/>
            les inter ſe anguli alterni in punctis E, & </s>
            <s xml:id="echoid-s15063" xml:space="preserve">F, rectarum E A, F C, facti à communi ſectione maximorum
              <lb/>
              <note position="right" xlink:label="note-0239-06" xlink:href="note-0239-06a" xml:space="preserve">29. primi.</note>
            circulorum ſectiones A E, C F, & </s>
            <s xml:id="echoid-s15064" xml:space="preserve">E G, C H, facientium, quæ quidem communis ſectio per puncta E, B,
              <lb/>
              <note position="left" xlink:label="note-0239-07" xlink:href="note-0239-07a" xml:space="preserve">50</note>
            D, F, tranſit, cum per hæc eadem ipſi circuli maximi tranſeant. </s>
            <s xml:id="echoid-s15065" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s15066" xml:space="preserve">anguli recti A, C, quos
              <lb/>
            ſtyli cum rectis A E, C F, per defin. </s>
            <s xml:id="echoid-s15067" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15068" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15069" xml:space="preserve">11. </s>
            <s xml:id="echoid-s15070" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s15071" xml:space="preserve">conſtituunt, æquales; </s>
            <s xml:id="echoid-s15072" xml:space="preserve">Item & </s>
            <s xml:id="echoid-s15073" xml:space="preserve">ſtyli A B, C D, æquales,
              <lb/>
            qui æqualibus angulis E, F, ſubtenduntur in triangulis A B E, C D F, quorum baſes ſunt partes commu
              <lb/>
            nis ſectionis maximorum circulorum ſectiones A E, C F, & </s>
            <s xml:id="echoid-s15074" xml:space="preserve">E G, C H, in horologio vtroque facientium.
              <lb/>
            </s>
            <s xml:id="echoid-s15075" xml:space="preserve">Erunt igitur latera quoque A E, C F, æqualia. </s>
            <s xml:id="echoid-s15076" xml:space="preserve">Tantum ergo abest ſectio E G, in recta A E, à ſtylo
              <lb/>
              <note position="right" xlink:label="note-0239-08" xlink:href="note-0239-08a" xml:space="preserve">26. primi.</note>
            deorſum verſus, quantum ſectio F H, in recta C F, à ſtylo ſurſum verſus diſtat. </s>
            <s xml:id="echoid-s15077" xml:space="preserve">Rurſus quia rectæ E K,
              <lb/>
            E I, rectis F C, F H, parallelæ ſunt, vt ostendimus, erit angulus K E I, angulo C F H, æqualis. </s>
            <s xml:id="echoid-s15078" xml:space="preserve">Cum er-
              <lb/>
              <note position="right" xlink:label="note-0239-09" xlink:href="note-0239-09a" xml:space="preserve">10. vndec.</note>
            go angulo K E I, æqualis ſit angulus A E G, ad verticem, eruntin triangulis A E G, C F H, anguli ad
              <lb/>
              <note position="right" xlink:label="note-0239-10" xlink:href="note-0239-10a" xml:space="preserve">15. primi.</note>
            E, F, æquales. </s>
            <s xml:id="echoid-s15079" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s15080" xml:space="preserve">anguli E A G, F C H, æquales, vtpotè recti; </s>
            <s xml:id="echoid-s15081" xml:space="preserve">& </s>
            <s xml:id="echoid-s15082" xml:space="preserve">latera A E, C F, dictis
              <lb/>
            angulis adiacentia, oſtenſa ſunt æqualia. </s>
            <s xml:id="echoid-s15083" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s15084" xml:space="preserve">latera A G, C H, æqualia erunt. </s>
            <s xml:id="echoid-s15085" xml:space="preserve">Aequalibus ergo
              <lb/>
              <note position="right" xlink:label="note-0239-11" xlink:href="note-0239-11a" xml:space="preserve">26. primi.</note>
            ſpatijs abſunt rectæ E G, F H, in rectis A G, C H, à ſtylis dextram verſus. </s>
            <s xml:id="echoid-s15086" xml:space="preserve">Quòd ſi recta E G, ſecet </s>
          </p>
        </div>
      </text>
    </echo>
Impressum