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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[311.] PROBLEMA 34. PROPOSITIO 34.
Page: 383 (367)
[312.] PROBLEMA 35. PROPOSITIO 35.
Page: 385 (369)
[313.] SCHOLIVM.
Page: 385 (369)
[314.] PROBLEMA 36. PROPOSITIO 36.
Page: 385 (369)
[315.] DE HOROLOGIIS ET A VERTICALI declinantibus, & ad Horizontem inclinatis.
Page: 386 (370)
[316.] PROBLEMA 37. PROPOSITIO 37.
Page: 386 (370)
[317.] SCHOLIVM.
Page: 403 (387)
[318.] PROBLEMA 38. PROPOSITIO 38.
Page: 411 (395)
[319.] SCHOLIVM.
Page: 415 (399)
[320.] PROBLEMA 39. PROPOSITIQ 39.
Page: 415 (399)
[321.] SCHOLIVM.
Page: 416 (400)
[322.] PROBLEMA 40. PROPOSITIO 40.
Page: 416 (400)
[323.] SCHOLIVM.
Page: 417 (401)
[324.] PROBLEMA 41. PROPOSITIO 41.
Page: 419 (403)
[325.] PROBLEMA 42. PROPOSITIO 42.
Page: 421 (405)
[326.] PROBLEMA 43. PROPOSITIO 43.
Page: 422 (406)
[327.] PROBLEMA 44. PROPOSITIO 44.
Page: 422 (406)
[328.] SCHOLIVM.
Page: 423 (407)
[329.] PROBLEMA 45. PROPOSITIO 45.
Page: 424 (408)
[330.] SCHOLIVM.
Page: 426 (410)
[331.] PROBLEMA 46. PROPOSITIO 46.
Page: 427 (411)
[332.] PROBLEMA 47. PROPOSITIO 47.
Page: 429 (413)
[333.] PROBLEMA 48. PROPOSITIO 48.
Page: 429 (413)
[334.] FINIS TERTII LIBRI.
Page: 429 (413)
[335.] GNOMONICES LIBER QVARTVS.
Page: 430 (414)
[336.] AVCTORE
Page: 430 (414)
[337.] CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
Page: 430 (414)
[338.] PROBLEMA 1. PROPOSITIO 1.
Page: 430 (414)
[339.] I. SOLE EXISTENTE IN PRINCIPIO ♈.
Page: 432 (416)
[340.] II. SOLE EXISTENTE IN PRINCIPIO ♎.
Page: 432 (416)
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          <p>
            <s xml:id="echoid-s34109" xml:space="preserve">
              <pb o="530" file="0546" n="546" rhead="GNOMONICES"/>
            ſingulis; </s>
            <s xml:id="echoid-s34110" xml:space="preserve">tres quidem in tribus circulis immobilibus, & </s>
            <s xml:id="echoid-s34111" xml:space="preserve">in mobilibus totidem: </s>
            <s xml:id="echoid-s34112" xml:space="preserve">quæ omnes à cir-
              <lb/>
            culis, quorum ſunt partes, nomen accipiunt, ita vt ea, quæ in Horizonte ſumitur, dicatur circun-
              <lb/>
            ferentia horizontalis; </s>
            <s xml:id="echoid-s34113" xml:space="preserve">quæ in Deſcenſiuo, deſcenſiua; </s>
            <s xml:id="echoid-s34114" xml:space="preserve">quæ in Verticali, Verticalis; </s>
            <s xml:id="echoid-s34115" xml:space="preserve">quæ in Horario,
              <lb/>
            horatia; </s>
            <s xml:id="echoid-s34116" xml:space="preserve">quę in Meridiano, meridiana; </s>
            <s xml:id="echoid-s34117" xml:space="preserve">quæ denique in Hectemorio, hectemoria. </s>
            <s xml:id="echoid-s34118" xml:space="preserve">Horizontalis
              <lb/>
              <figure xlink:label="fig-0546-01" xlink:href="fig-0546-01a" number="333">
                <image file="0546-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0546-01"/>
              </figure>
            circunferentia interiicitur
              <lb/>
            in Horizonte inter Verti-
              <lb/>
            calem circulum, & </s>
            <s xml:id="echoid-s34119" xml:space="preserve">Deſcen
              <lb/>
            ſiuum, qualis eſt circunfe-
              <lb/>
            rentia Horizõtis F N: </s>
            <s xml:id="echoid-s34120" xml:space="preserve">De-
              <lb/>
              <note position="left" xlink:label="note-0546-01" xlink:href="note-0546-01a" xml:space="preserve">Hurizõ@@lis cir-
                <lb/>
              cunfer@ntia.</note>
            ſcenſiua in Deſcenſiuo cir
              <lb/>
              <note position="left" xlink:label="note-0546-02" xlink:href="note-0546-02a" xml:space="preserve">10</note>
            culo comprehenditur in-
              <lb/>
            ter centrum Solis, & </s>
            <s xml:id="echoid-s34121" xml:space="preserve">verti-
              <lb/>
            cem capitis, cuiuſmodi eſt
              <lb/>
            circunferentia Deſcenſiui
              <lb/>
              <note position="left" xlink:label="note-0546-03" xlink:href="note-0546-03a" xml:space="preserve">Defcenſiuz.</note>
            circuli D H: </s>
            <s xml:id="echoid-s34122" xml:space="preserve">Verticalis
              <lb/>
            clauditur inter Meridia-
              <lb/>
            num, & </s>
            <s xml:id="echoid-s34123" xml:space="preserve">Horarium circu-
              <lb/>
            lum in circulo Verticali,
              <lb/>
            qualis eſt circunferentis
              <lb/>
              <note position="left" xlink:label="note-0546-04" xlink:href="note-0546-04a" xml:space="preserve">Ve@tieali@.</note>
            circuli Verticalis D K: </s>
            <s xml:id="echoid-s34124" xml:space="preserve">Ho
              <lb/>
              <note position="left" xlink:label="note-0546-05" xlink:href="note-0546-05a" xml:space="preserve">20</note>
            raria intercipitur in Hora-
              <lb/>
            rio circulo inter centrum
              <lb/>
            Solis, & </s>
            <s xml:id="echoid-s34125" xml:space="preserve">alterutrum polo-
              <lb/>
            rũ Verticalis circuli, qua-
              <lb/>
            lis eſt circunſerentia cir-
              <lb/>
            culi Horarij A H: </s>
            <s xml:id="echoid-s34126" xml:space="preserve">Meri-
              <lb/>
              <note position="left" xlink:label="note-0546-06" xlink:href="note-0546-06a" xml:space="preserve">H@rati@.</note>
            diana cõtinetur inter Ho-
              <lb/>
            rizontem, atque Hectemo
              <lb/>
            rion in Meridiano circu-
              <lb/>
            lo, cuiuſmodi eſt circun-
              <lb/>
              <note position="left" xlink:label="note-0546-07" xlink:href="note-0546-07a" xml:space="preserve">Meridiana.</note>
              <note position="left" xlink:label="note-0546-08" xlink:href="note-0546-08a" xml:space="preserve">30</note>
            ferentia Meridiani A L:
              <lb/>
            </s>
            <s xml:id="echoid-s34127" xml:space="preserve">Hectemoria denique in-
              <lb/>
            teriacet in Hectemorio circulo inter centrum Solis, & </s>
            <s xml:id="echoid-s34128" xml:space="preserve">punctum ortus æquinoctialis, vel occaſus,
              <lb/>
            qualis eſt circunferentia Hectemorii F H. </s>
            <s xml:id="echoid-s34129" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0546-09" xlink:href="note-0546-09a" xml:space="preserve">Hectemoria.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s34130" xml:space="preserve">CÆTERVM cùm dictæ circunferentiæ aliquando ſint quadrantes, interdum vero qua-
              <lb/>
              <note position="left" xlink:label="note-0546-10" xlink:href="note-0546-10a" xml:space="preserve">Nulla dictarú
                <lb/>
              circunferentia -
                <lb/>
              rum quadrani@
                <lb/>
              ſuperare debet.</note>
            drante maiores, minoresve; </s>
            <s xml:id="echoid-s34131" xml:space="preserve">quando quadrantem ſuperant, accipiendæ erunt eæ, quæ cum illis ſe-
              <lb/>
            micircuſum conſtituunt: </s>
            <s xml:id="echoid-s34132" xml:space="preserve">non quod omnino hoc ſit neceſſarium, ſed quòd expeditius hac ratio-
              <lb/>
            ne horologia deſcribantur. </s>
            <s xml:id="echoid-s34133" xml:space="preserve">Vt ſi v. </s>
            <s xml:id="echoid-s34134" xml:space="preserve">g. </s>
            <s xml:id="echoid-s34135" xml:space="preserve">Sol exiſtat poſt meridiem, non erit ſumenda illa circunfe-
              <lb/>
            rentia horizontalis, quæ inter Verticalem circulum ex parte orientis, & </s>
            <s xml:id="echoid-s34136" xml:space="preserve">Deſcenſiuum ex parteoc-
              <lb/>
            cidentis poſita eſt, quoniam ea quadrantem ſuperat, ſed illa, quæ inter Verticalem ex parte occi-
              <lb/>
              <note position="left" xlink:label="note-0546-11" xlink:href="note-0546-11a" xml:space="preserve">40</note>
            dentis, Deſcenſiuumq́ue interijcitur, quoniam hæc quadrante minor eſt. </s>
            <s xml:id="echoid-s34137" xml:space="preserve">atque ita de cæteris di-
              <lb/>
            cendum eſt. </s>
            <s xml:id="echoid-s34138" xml:space="preserve">Vnde quoniam omnes dictæ circunferentiæ initium ſumuntà tribus illis ſectioni-
              <lb/>
              <note position="left" xlink:label="note-0546-12" xlink:href="note-0546-12a" xml:space="preserve">Vnde initium
                <lb/>
              habeant ſex di-
                <lb/>
              ctæ circunferen
                <lb/>
              tiæ.</note>
            bus communibus trium circulorum immobilium, vt horizontalis, atque hectemoria à ſectione
              <lb/>
            æquinoctiali F G, quæ axis eſt Meridiani, cum per eius polos ducatur, Verticalis, & </s>
            <s xml:id="echoid-s34139" xml:space="preserve">deſcenſiua
              <lb/>
            à gnomone D B, qui axis eſt Horizontis per illius polos incedens, meridiana denique, & </s>
            <s xml:id="echoid-s34140" xml:space="preserve">horaria
              <lb/>
            à linea meridiana A B, quæ axis eſt Verticalis, cum per eius polos tranſeat: </s>
            <s xml:id="echoid-s34141" xml:space="preserve">fit, vt tempore anteme
              <lb/>
            ridiano tam horizontalis circunferentia, quàm hectemoria initium ſumat à diametro æquino-
              <lb/>
            ctiali ex parte orientis, puta ab ortu æquinoctiali; </s>
            <s xml:id="echoid-s34142" xml:space="preserve">pomeridiano vero tempore ex parte occidentis,
              <lb/>
            ſiue ab occaſu æquinoctiali. </s>
            <s xml:id="echoid-s34143" xml:space="preserve">Pari ratione efficitur, tam Verticalem circunferentiam, quàm deſcen
              <lb/>
            ſiuam principium habere in gnomone à vertice capitis, vbicunque Sol ſupra Horizontem exiſtat,
              <lb/>
              <note position="left" xlink:label="note-0546-13" xlink:href="note-0546-13a" xml:space="preserve">50</note>
            quia femper minor eſt quadrante, alia vero inchoata ab oppoſito verticis, quadrãte maior. </s>
            <s xml:id="echoid-s34144" xml:space="preserve">Perſpi-
              <lb/>
            cuum denique eſt, Sole exiſtente in parte hemiſphærii auſtrali, quæ vergit à Verticali circulo ver-
              <lb/>
            ſus polum antarcticum, tam circunferentiam meridianam, quàm horariam initium habere à li-
              <lb/>
            nea meridiana ex parte auſtrali; </s>
            <s xml:id="echoid-s34145" xml:space="preserve">Sole vero exiſtente in parte hemiſphærii boreali, quæ à Verticali
              <lb/>
            circulo verſus polum arcticum porrigitur, ab eadem linea ex parte ſeptentrionali. </s>
            <s xml:id="echoid-s34146" xml:space="preserve">Quòd ſi quan
              <lb/>
            do circunferentia aliqua quadranti ſit æqualis, nihil intereſt, ab vtro ſectionis extremo initium
              <lb/>
            ſumatur,</s>
          </p>
          <p>
            <s xml:id="echoid-s34147" xml:space="preserve">EX his autem ſex circunferentiis determinatur radii ſolaris poſitio in planis, quæ Horizon-
              <lb/>
            ti, Verticali, & </s>
            <s xml:id="echoid-s34148" xml:space="preserve">Meridiano æquidiſtant, quam qualibet hora habet. </s>
            <s xml:id="echoid-s34149" xml:space="preserve">Nam horizontalis circunfe-
              <lb/>
              <note position="left" xlink:label="note-0546-14" xlink:href="note-0546-14a" xml:space="preserve">Oſſcia dictatũ
                <lb/>
              ſex circunferen-
                <lb/>
              tiarum.</note>
            rentia indicat vmbræ latitudinem in plano, quod Horizonti æquidiſtat, id eſt, demonſtrat, quan-
              <lb/>
            tum vmbra declinat à communi ſectione Verticalis circuli, & </s>
            <s xml:id="echoid-s34150" xml:space="preserve">illius plani, quæ ab ortu in </s>
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