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

< >
[271.] PROBLEMA 12. PROPOSITIO 12.
Page: 348 (332)
[272.] SCHOLIVM.
Page: 350 (334)
[273.] DE HOROLOGIIS, QVAE ab Horizonte declinant. PROBLEMA 13. PROPOSITIO 13.
Page: 350 (334)
[274.] SCHOLIVM.
Page: 353 (337)
[275.] PROBLEMA 14. PROPOSITIO 14.
Page: 357 (341)
[276.] PROBLEMA 15. PROPOSITIO 15.
Page: 359 (343)
[277.] SCHOLIVM.
Page: 360 (344)
[278.] PROBLEMA 16. PROPOSITIO 16.
Page: 360 (344)
[279.] SCHOLIVM.
Page: 361 (345)
[280.] PROBLEMA 17. PROPOSITIO 17.
Page: 362 (346)
[281.] SCHOLIVM.
Page: 362 (346)
[282.] PROBLEMA 18. PROPOSITIO 18.
Page: 363 (347)
[283.] PROBLEMA 19. PROPOSITIO 19.
Page: 363 (347)
[284.] PROBLEMA 20. PROPOSITIO 20.
Page: 363 (347)
[285.] SCHOLIVM.
Page: 364 (348)
[286.] PROBLEMA 21. PROPOSITIO 21.
Page: 365 (349)
[287.] SCHOLIVM.
Page: 366 (350)
[288.] PROBLEMA 22. PROPOSITIO 22.
Page: 367 (351)
[289.] PROBLEMA 23. PROPOSITIO 23.
Page: 368 (352)
[290.] SCHOLIVM.
Page: 368 (352)
[291.] PROBLEMA 24. PROPOSITIO 24.
Page: 368 (352)
[292.] DE HOROLOGIIS ad Horizontem inclinatis.
Page: 369 (353)
[293.] PROBLEMA 25. PROPOSITIO 25.
Page: 369 (353)
[294.] PRÆCEPTVM I.
Page: 369 (353)
[295.] PRAECEPTVM II.
Page: 369 (353)
[296.] PRAECEPTVM III.
Page: 370 (354)
[297.] PRAECEPTVM IIII.
Page: 370 (354)
[298.] PRAECEPTVM V.
Page: 370 (354)
[299.] PRAECEPTVM VI.
Page: 370 (354)
[300.] SCHOLIVM.
Page: 372 (356)
< >
page |< < (333) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div1131" type="section" level="1" n="271">
          <p>
            <s xml:id="echoid-s22193" xml:space="preserve">
              <pb o="333" file="0349" n="349" rhead="LIBER TERTIVS."/>
            ſecat lineam æquinoctialem in puncto n, & </s>
            <s xml:id="echoid-s22194" xml:space="preserve">recta ex C, pern, ducta ſecat tropicum ♑, in p, pun-
              <lb/>
            cto horæ 9. </s>
            <s xml:id="echoid-s22195" xml:space="preserve">inæqualis, & </s>
            <s xml:id="echoid-s22196" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s22197" xml:space="preserve">Pro hora 11. </s>
            <s xml:id="echoid-s22198" xml:space="preserve">inæquali tropici ♑, quoniam non contine-
              <lb/>
            tur in ſemicirculo A N B, cuius vnius puncta in tropicis inueniuntur, vt ſupra dictum eſt, acci-
              <lb/>
            piemus punctum ei oppoſitum D, quod cadit in horam 11. </s>
            <s xml:id="echoid-s22199" xml:space="preserve">inæqualem arcus nocturni tropici ♋,
              <lb/>
            vt mox demonſtrabimus, ex quo ſi per L, ducamus rectam, ſecabit hæc lineam æquinoctialem in
              <lb/>
            puncto quodam, nempe in R, (quod, quia remotiſſimum eſt, in noſtro horologio nõ continetur)
              <lb/>
            per quod recta ex C, emiſſa dabit in arcu nocturno tropici ♋, punctũ horæ 11. </s>
            <s xml:id="echoid-s22200" xml:space="preserve">inæqualis reſpon-
              <lb/>
            dens puncto D, eadem verò recta vltra cẽtrum C, eiecta offeret in arcu diurno ♑, punctum aliud
              <lb/>
            pro hora 11. </s>
            <s xml:id="echoid-s22201" xml:space="preserve">diurna inæquali tropici ♑, vt ex demonſtratis conſtat. </s>
            <s xml:id="echoid-s22202" xml:space="preserve">Eadem ratione pro horis 11.
              <lb/>
            </s>
            <s xml:id="echoid-s22203" xml:space="preserve">10. </s>
            <s xml:id="echoid-s22204" xml:space="preserve">& </s>
            <s xml:id="echoid-s22205" xml:space="preserve">9. </s>
            <s xml:id="echoid-s22206" xml:space="preserve">inæqualibus tropici ♋, quoniam etiam extra dictum ſemicirculum A N D, cadunt, acci-
              <lb/>
              <note position="left" xlink:label="note-0349-01" xlink:href="note-0349-01a" xml:space="preserve">10</note>
            piemus puncta ipſis oppoſita E, F, G, quæ cadunt in horas inæquales 11. </s>
            <s xml:id="echoid-s22207" xml:space="preserve">10. </s>
            <s xml:id="echoid-s22208" xml:space="preserve">& </s>
            <s xml:id="echoid-s22209" xml:space="preserve">9. </s>
            <s xml:id="echoid-s22210" xml:space="preserve">arcus nocturni
              <lb/>
            tropici ♑, vt mox oſtendemus, & </s>
            <s xml:id="echoid-s22211" xml:space="preserve">ex ipſis rectas per L, ducemus, vt inueniamus in arcu nocturno
              <lb/>
            Capricorni puncta K, P, Q, reſpondẽtia punctis E, F, G, arcus nocturni tropici ♑. </s>
            <s xml:id="echoid-s22212" xml:space="preserve">Quòd ſi quãdo
              <lb/>
            hora aliqua cadat præcisè in punctum A, vel B, tum ducta recta per C, æquinoctiali lineæ æqui-
              <lb/>
            diſtãs, indicabit in tropico Capricorni duo puncta, quorũ illud, quod ad dextrã ipſius C L, exiſtet,
              <lb/>
            ad horam, quæ cadit in punctũ A, alterum verò, quod ad ſiniſtram ipſius CL, ſtatuetur, ad horam,
              <lb/>
            quæ in punctum B, cadit, pertinebit, vt conſtar ex ijs, quæ oſtendimus propoſ. </s>
            <s xml:id="echoid-s22213" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22214" xml:space="preserve">huius libri de
              <lb/>
            recta Cd, quæ per C, lineæ æquinoctiali ducta eſt parallela. </s>
            <s xml:id="echoid-s22215" xml:space="preserve">Ea enim refert illam horam, à cuius
              <lb/>
            puncto in circulo ex L, deſcripto, recta ducta per L, lineæ æquinoctiali æquidiſtat, vt ad finem de-
              <lb/>
            monſtrationis modi prioris conſtruendi horologii declinantis oſtendimus propoſ. </s>
            <s xml:id="echoid-s22216" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22217" xml:space="preserve">huius libri.
              <lb/>
            </s>
            <s xml:id="echoid-s22218" xml:space="preserve">
              <note position="left" xlink:label="note-0349-02" xlink:href="note-0349-02a" xml:space="preserve">20</note>
            Si igitur reſpondentia puncta in tropicis iungantur lineis rectis, deſcriptum erit horologium An-
              <lb/>
            tiquum; </s>
            <s xml:id="echoid-s22219" xml:space="preserve">tranſibuntq́ue omnes lineæ horarum inęqualium per horas à meridie, vel media nocte
              <lb/>
            in linea æquinoctiali, prout in tabulis 13. </s>
            <s xml:id="echoid-s22220" xml:space="preserve">& </s>
            <s xml:id="echoid-s22221" xml:space="preserve">14. </s>
            <s xml:id="echoid-s22222" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s22223" xml:space="preserve">33. </s>
            <s xml:id="echoid-s22224" xml:space="preserve">primi libri colligitur. </s>
            <s xml:id="echoid-s22225" xml:space="preserve">Quoniam verò
              <lb/>
            puncta horarum 11. </s>
            <s xml:id="echoid-s22226" xml:space="preserve">10. </s>
            <s xml:id="echoid-s22227" xml:space="preserve">& </s>
            <s xml:id="echoid-s22228" xml:space="preserve">9. </s>
            <s xml:id="echoid-s22229" xml:space="preserve">arcus ♑, non habent puncta reſpondentia in tropico ♋, iungemus
              <lb/>
            ea cum punctis arcus nocturni ♑, inuentis beneficio punctorum E, F, G, quæ eiſdem horis 11.
              <lb/>
            </s>
            <s xml:id="echoid-s22230" xml:space="preserve">10. </s>
            <s xml:id="echoid-s22231" xml:space="preserve">9. </s>
            <s xml:id="echoid-s22232" xml:space="preserve">arcus diurni ♋, opponuntur, caduntq́ue in horas inæquales 11. </s>
            <s xml:id="echoid-s22233" xml:space="preserve">10. </s>
            <s xml:id="echoid-s22234" xml:space="preserve">& </s>
            <s xml:id="echoid-s22235" xml:space="preserve">9. </s>
            <s xml:id="echoid-s22236" xml:space="preserve">arcus no-
              <lb/>
              <note position="right" xlink:label="note-0349-03" xlink:href="note-0349-03a" xml:space="preserve">Demonſtratio,
                <lb/>
              quòd horę di-
                <lb/>
              urnæ inæqua-
                <lb/>
              les in tropico
                <lb/>
              Caneri, oppo-
                <lb/>
              nuntur per dia
                <lb/>
              metrum eiſd@
                <lb/>
              horis inęquali-
                <lb/>
              bu@ nocturnis
                <lb/>
              in tropico Ca-
                <lb/>
              pricorni; & @
                <lb/>
              in horologio
                <lb/>
              horæ diurnę
                <lb/>
              tropici Capri-
                <lb/>
              corni, ducendæ
                <lb/>
              ſint per eaſdem
                <lb/>
              horas noctur-
                <lb/>
              nas eiuſdẽ tro-
                <lb/>
              pici.</note>
            cturni Capricorni.</s>
            <s xml:id="echoid-s22237" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22238" xml:space="preserve">QVOD autem hoc ita ſit, & </s>
            <s xml:id="echoid-s22239" xml:space="preserve">lineæ horarum diurnarum tropici ♑, ducendæ ſint per eaſdem
              <lb/>
            horas nocturnas eiuſdem tropici in horologio, ita demonſtrabimus. </s>
            <s xml:id="echoid-s22240" xml:space="preserve">Quoniam v. </s>
            <s xml:id="echoid-s22241" xml:space="preserve">g. </s>
            <s xml:id="echoid-s22242" xml:space="preserve">recta ex E,
              <lb/>
            puncto, quod opponitur horæ 11. </s>
            <s xml:id="echoid-s22243" xml:space="preserve">♋, contineturq́ue in arcu nocturno ♑, per L, ducta ſecat æqui
              <lb/>
              <note position="left" xlink:label="note-0349-04" xlink:href="note-0349-04a" xml:space="preserve">30</note>
            noctialem lineam in H, & </s>
            <s xml:id="echoid-s22244" xml:space="preserve">recta C H, arcum nocturnum ♑, ſecat in K, ſecabit circulus maximus
              <lb/>
            per polos mundi, & </s>
            <s xml:id="echoid-s22245" xml:space="preserve">horam 11. </s>
            <s xml:id="echoid-s22246" xml:space="preserve">inæqualem tropici ♋, nec non per punctum E, ductus, planum ho
              <lb/>
            rologii per rectam C H, atque adeo tropicum ♑, in K, vt conſtat ex demonſtratis propoſ. </s>
            <s xml:id="echoid-s22247" xml:space="preserve">10. </s>
            <s xml:id="echoid-s22248" xml:space="preserve">ſupe-
              <lb/>
            rioris libri. </s>
            <s xml:id="echoid-s22249" xml:space="preserve">Quoniam verò circulus ille maximus in circulo Ma Nb, neceſſario aufert arcum e E,
              <lb/>
            horæ 11. </s>
            <s xml:id="echoid-s22250" xml:space="preserve">inæqualis arcus nocturni tropici ♑, d Me, (Nam quia arcus a M, e N, æquales ſunt, cum
              <lb/>
            dimidiatæ partes ſint arcuum æqualium a M b, e N d; </s>
            <s xml:id="echoid-s22251" xml:space="preserve">ſi addatur communis arcus e M, fiet arcus
              <lb/>
            a M e, ſemicirculo M e N, ęqualis. </s>
            <s xml:id="echoid-s22252" xml:space="preserve">Igitur recta ex a, ad e, @producta per centrum L, tranſibit, atq;
              <lb/>
            </s>
            <s xml:id="echoid-s22253" xml:space="preserve">adeo in centro L, cum recta E L, ducta vſque ad horam 11. </s>
            <s xml:id="echoid-s22254" xml:space="preserve">tropici ♋, conſtituet angulos ad verti-
              <lb/>
              <note position="right" xlink:label="note-0349-05" xlink:href="note-0349-05a" xml:space="preserve">15. primi.</note>
            cem æquales; </s>
            <s xml:id="echoid-s22255" xml:space="preserve">propteraq́ue arcus a 11, e E, æquales erunt. </s>
            <s xml:id="echoid-s22256" xml:space="preserve">Sicut igitur a 11, eſt pars duodecima ar
              <lb/>
              <note position="right" xlink:label="note-0349-06" xlink:href="note-0349-06a" xml:space="preserve">26. tertij.</note>
            cus diurni tropici ♋, a N b, ita e E, pars duodecima erit arcus nocturni tropici ♑, e M d; </s>
            <s xml:id="echoid-s22257" xml:space="preserve">quando-
              <lb/>
              <note position="left" xlink:label="note-0349-07" xlink:href="note-0349-07a" xml:space="preserve">40</note>
            quidem arcus a N b, e M d, æquales ſunt; </s>
            <s xml:id="echoid-s22258" xml:space="preserve">ac proindee E, arcus erit horæ 11. </s>
            <s xml:id="echoid-s22259" xml:space="preserve">inæqualis in arcu no-
              <lb/>
            cturno ♑) ſit, vt tranſeat per horam 11. </s>
            <s xml:id="echoid-s22260" xml:space="preserve">nocturnam tropici ♑. </s>
            <s xml:id="echoid-s22261" xml:space="preserve">Cum enim dictus circulus maxi-
              <lb/>
            mus, & </s>
            <s xml:id="echoid-s22262" xml:space="preserve">Meridianus auferant ex Aequatore, & </s>
            <s xml:id="echoid-s22263" xml:space="preserve">tropico ♑, per propoſ. </s>
            <s xml:id="echoid-s22264" xml:space="preserve">10. </s>
            <s xml:id="echoid-s22265" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22266" xml:space="preserve">2. </s>
            <s xml:id="echoid-s22267" xml:space="preserve">Theod arcus ſimi
              <lb/>
            les, contineat autem arcus M E, qui ſimilis eſt arcui Aequatoris inter dictum circulum maximũ,
              <lb/>
            & </s>
            <s xml:id="echoid-s22268" xml:space="preserve">Meridianum interiecto, quinque ſextas partes arcus Me, qui ſimilis eſt arcui ſeminocturno tro
              <lb/>
            pici ♑, comprehendet quoque arcus tropici ♑, inter eundem circulum maximum, & </s>
            <s xml:id="echoid-s22269" xml:space="preserve">Meridia-
              <lb/>
            num interpoſitus quinque ſextas partes ſui arcus ſeminocturni, atque adeo dictus maximus circu-
              <lb/>
            lus per horam 11. </s>
            <s xml:id="echoid-s22270" xml:space="preserve">inæqualem nocturnam tropici ♑, tranſibit. </s>
            <s xml:id="echoid-s22271" xml:space="preserve">Et quoniam hora 11. </s>
            <s xml:id="echoid-s22272" xml:space="preserve">inæqualis in
              <lb/>
            arcu diurno tropici ♋, & </s>
            <s xml:id="echoid-s22273" xml:space="preserve">hora 11. </s>
            <s xml:id="echoid-s22274" xml:space="preserve">inæqualis in arcu nocturno tropici ♑, intercipiunt ex circulo
              <lb/>
            illo maximo per vtramque horam ducto ſemicirculum, (quoniam enim arcus ipſius inter paral-
              <lb/>
              <note position="left" xlink:label="note-0349-08" xlink:href="note-0349-08a" xml:space="preserve">50</note>
            lelum ♋, & </s>
            <s xml:id="echoid-s22275" xml:space="preserve">Aequatorem poſitus ſupra Horizontem) æqualis eſt arcui eiuſdem inter parallelum
              <lb/>
            ♑, & </s>
            <s xml:id="echoid-s22276" xml:space="preserve">Aequatorem collocato infra Horizontem, quòd vterque per propoſ. </s>
            <s xml:id="echoid-s22277" xml:space="preserve">10. </s>
            <s xml:id="echoid-s22278" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22279" xml:space="preserve">2. </s>
            <s xml:id="echoid-s22280" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s22281" xml:space="preserve">æqua-
              <lb/>
            lis ſit arcui maximæ declinationis; </s>
            <s xml:id="echoid-s22282" xml:space="preserve">ſi addatur communis arcus eiuſdem inter Aequatorem, & </s>
            <s xml:id="echoid-s22283" xml:space="preserve">tro-
              <lb/>
            picum ♑, poſitus, tranſiensq́ue per polum antarcticum, fient arcus eiuſdem æquales, quorũ vnus
              <lb/>
            quidem inter tropicum ♋, & </s>
            <s xml:id="echoid-s22284" xml:space="preserve">tropicum ♑, alter verò inter Aequatorem ponitur tranſiens per po
              <lb/>
            lum antarcticum. </s>
            <s xml:id="echoid-s22285" xml:space="preserve">Cum ergo Aequator ex illo auferat ſemicirculum ex propol. </s>
            <s xml:id="echoid-s22286" xml:space="preserve">11. </s>
            <s xml:id="echoid-s22287" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22288" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22289" xml:space="preserve">Theod.
              <lb/>
            </s>
            <s xml:id="echoid-s22290" xml:space="preserve">erit quoque alter arcus ſemicirculus) ſit, vt neceſſario circulus alius maximus qui vnus eſt ex cir-
              <lb/>
            culis horarum inæqualium, & </s>
            <s xml:id="echoid-s22291" xml:space="preserve">per polos mundi non tranſit, & </s>
            <s xml:id="echoid-s22292" xml:space="preserve">qui dictum circulum maximũ per
              <lb/>
            polos mundi, & </s>
            <s xml:id="echoid-s22293" xml:space="preserve">horam 11. </s>
            <s xml:id="echoid-s22294" xml:space="preserve">tropici ♋, diurnam ductum ſecat in hora 11. </s>
            <s xml:id="echoid-s22295" xml:space="preserve">diurna tropici ♋, ſecet
              <lb/>
            eundem in puncto oppoſito, hoc eſt, in hora 11. </s>
            <s xml:id="echoid-s22296" xml:space="preserve">nocturna tropici ♑; </s>
            <s xml:id="echoid-s22297" xml:space="preserve">quandoquidem illum per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s22298" xml:space="preserve">11. </s>
            <s xml:id="echoid-s22299" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22300" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22301" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s22302" xml:space="preserve">ſecat biſariam, oſtenſumq́ue eſt, circulum dictum maximum in hora 11.</s>
            <s xml:id="echoid-s22303" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum