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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[121.] COROLLARIVM.
Page: 112 (92)
[122.] PROBLEMA 6. PROPOSITIO 27.
Page: 113 (93)
[123.] PROBLEMA. 7. PROPOSITIO 28.
Page: 113 (93)
[124.] SCHOLIVM I.
Page: 115 (95)
[125.] COROLLARIVM.
Page: 115 (95)
[126.] SCHOLIVM II.
Page: 116 (96)
[127.] PROBLEMA 8. PROPOSITIO 29.
Page: 119 (99)
[128.] PROBLEMA. 9. PROPOSITIO 30.
Page: 121 (101)
[129.] PROBLEMA 10. PROPOSITIO 31.
Page: 123 (103)
[130.] PROBLEMA 11. PROPOSITIO 32.
Page: 125 (105)
[131.] SCHOLIVM.
Page: 125 (105)
[132.] PROBLEMA 12. PROPOSITIO 33.
Page: 126 (106)
[133.] SCHOLIVM.
Page: 129 (109)
[134.] PROBLEMA 13. PROPOSITIO 34.
Page: 134 (114)
[135.] SCHOLIVM.
Page: 137 (117)
[136.] PROBLEMA 14. PROPOSITIO 35.
Page: 138 (118)
[137.] SCHOLIVM.
Page: 140 (120)
[138.] PROBLEMA 15. PROPOSITIO 36.
Page: 144 (124)
[139.] SCHOLIVM.
Page: 158 (138)
[140.] FINIS PRIMI LIBRI.
Page: 160 (140)
[141.] GNOMONICES LIBER SECVNDVS.
Page: 161 (141)
[142.] AVCTORE CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
Page: 161 (141)
[143.] DE HOROLOGIIS HORIZONTALIBVS. PROBLEMA 1. PROPOSITIO 1.
Page: 162 (142)
[144.] SCHOLIVM.
Page: 165 (145)
[145.] PROBLEMA 2. PROPOSITIO 2.
Page: 177 (157)
[146.] SCHOLIVM.
Page: 186 (166)
[147.] PROBLEMA 3. PROPOSITIO 3.
Page: 189 (169)
[148.] SCHOLIVM.
Page: 190 (170)
[149.] PROBLEMA. 4. PROPOSITIO 4.
Page: 190 (170)
[150.] SCHOLIVM.
Page: 191 (171)
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          <p>
            <s xml:id="echoid-s11036" xml:space="preserve">
              <pb o="171" file="0191" n="191" rhead="LIBER SECVNDVS."/>
            ex Analemmate conſtat) quàm planum horologii horizontalis, ad Meridianum rectum eſt, erit & </s>
            <s xml:id="echoid-s11037" xml:space="preserve">
              <lb/>
            communis eorum ſectio ad eundem Meridianum recta; </s>
            <s xml:id="echoid-s11038" xml:space="preserve">atque adeò, per defin. </s>
            <s xml:id="echoid-s11039" xml:space="preserve">3. </s>
            <s xml:id="echoid-s11040" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11041" xml:space="preserve">11. </s>
            <s xml:id="echoid-s11042" xml:space="preserve">Euclidis,
              <lb/>
              <note position="right" xlink:label="note-0191-01" xlink:href="note-0191-01a" xml:space="preserve">19. vndec.</note>
            ad lineam meridianam in puncto G, perpendicularis. </s>
            <s xml:id="echoid-s11043" xml:space="preserve">Recta igitur A B, quæ per G, ducta eſt ad
              <lb/>
            meridianam lineam perpendicularis, communis ſectio eſt plani horologii, & </s>
            <s xml:id="echoid-s11044" xml:space="preserve">Verticalis propriè
              <lb/>
            dicti. </s>
            <s xml:id="echoid-s11045" xml:space="preserve">Et quia circuli omnes Verticales ſecant Horizontem in partes 360. </s>
            <s xml:id="echoid-s11046" xml:space="preserve">ęquales, atque adeo & </s>
            <s xml:id="echoid-s11047" xml:space="preserve">
              <lb/>
            circulum, quem planum horologii Horizonti ęquidiſtans in ſphęra, per propoſ. </s>
            <s xml:id="echoid-s11048" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11049" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11050" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11051" xml:space="preserve">Theodo-
              <lb/>
            ſii, facit; </s>
            <s xml:id="echoid-s11052" xml:space="preserve">propterea quòd per Zenith, ſeu polum Horizontis tranſeuntes diuidant, per propoſ. </s>
            <s xml:id="echoid-s11053" xml:space="preserve">10.
              <lb/>
            </s>
            <s xml:id="echoid-s11054" xml:space="preserve">lib.</s>
            <s xml:id="echoid-s11055" xml:space="preserve">
              <unsure/>
            2. </s>
            <s xml:id="echoid-s11056" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s11057" xml:space="preserve">Horizontem, & </s>
            <s xml:id="echoid-s11058" xml:space="preserve">circulos Horizonti parallelos, in ſegmenta ſimilia; </s>
            <s xml:id="echoid-s11059" xml:space="preserve">fit vt omnes Ver-
              <lb/>
            ticales circuli, atque adeò & </s>
            <s xml:id="echoid-s11060" xml:space="preserve">communes ipſorum, ac plani horologij ſectiones, tranſeant per pun-
              <lb/>
            cta, quibus dictus circulus à plano horologij in ſphęra factus in 360. </s>
            <s xml:id="echoid-s11061" xml:space="preserve">partes ęquales diuiditur. </s>
            <s xml:id="echoid-s11062" xml:space="preserve">Sed
              <lb/>
              <note position="left" xlink:label="note-0191-02" xlink:href="note-0191-02a" xml:space="preserve">10</note>
            eędem ſectiones ducuntur quoque per punctum G, ex propoſ. </s>
            <s xml:id="echoid-s11063" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11064" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s11065" xml:space="preserve">in quo nimirum
              <lb/>
            communis ſectio circulorum Verticalium plano horologij occurrit. </s>
            <s xml:id="echoid-s11066" xml:space="preserve">Igitur eędem ſectiones tran-
              <lb/>
            ſibunt quoque per puncta diuiſionum circuli ex G, deſcripti. </s>
            <s xml:id="echoid-s11067" xml:space="preserve">Cum enim G, punctum, in quod
              <lb/>
            cadit axis Horizontis, & </s>
            <s xml:id="echoid-s11068" xml:space="preserve">circuli à plano horologii in ſphęra facti, centrum ſit, per propoſ. </s>
            <s xml:id="echoid-s11069" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11070" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s11071" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11072" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s11073" xml:space="preserve">dicti circuli ab horologij plano in ſphęra procreati, efficitur, vt circulus hic, & </s>
            <s xml:id="echoid-s11074" xml:space="preserve">ille, quẽ
              <lb/>
            ex G, deſcripſimus, in arcus ſimiles diuidantur à rectis lineis è centro G, egredientibus, per ea, quę
              <lb/>
            in commentarijs in ſphæram ad finem cap. </s>
            <s xml:id="echoid-s11075" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11076" xml:space="preserve">demonſtrauimus: </s>
            <s xml:id="echoid-s11077" xml:space="preserve">Ac proinde cum prior ſecetur
              <lb/>
            in partes æquales, ſecabitur & </s>
            <s xml:id="echoid-s11078" xml:space="preserve">poſterior, quem ex G, deſcripſimus, in æquales partes. </s>
            <s xml:id="echoid-s11079" xml:space="preserve">Sunt ergo re-
              <lb/>
            ctę illę ex G, emiſſæ per puncta, quibus circulus ex G, deſcriptus in partes ęquales eſt diuiſus, com
              <lb/>
            munes ſectiones plani horologii, & </s>
            <s xml:id="echoid-s11080" xml:space="preserve">circulorum Verticalium. </s>
            <s xml:id="echoid-s11081" xml:space="preserve">Circulos igitur Verticales, &</s>
            <s xml:id="echoid-s11082" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11083" xml:space="preserve">in eo-
              <lb/>
              <note position="left" xlink:label="note-0191-03" xlink:href="note-0191-03a" xml:space="preserve">20</note>
            dem horizontali horologio deſcripſimus. </s>
            <s xml:id="echoid-s11084" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s11085" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div598" type="section" level="1" n="150">
          <head xml:id="echoid-head153" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="right" xml:space="preserve">Vſus Vertica-
            <lb/>
          lium circulor@
            <lb/>
          in hotologio
            <lb/>
          deſcriptorum,
            <lb/>
          quibus cogno-
            <lb/>
          ſcimus, quonã
            <lb/>
          in quadrãte he-
            <lb/>
          miſphærii ſupe
            <lb/>
          ri Sol exiſtat.</note>
          <p style="it">
            <s xml:id="echoid-s11086" xml:space="preserve">EX circulis Verticalibus addiſcimus quolibet momento temporis, quanam in parte ex quatuor illis,
              <lb/>
            in quas hemiſphærium ſuperum à Verticali proprio, ac Meridiano dirimitur, Sol verſetur. </s>
            <s xml:id="echoid-s11087" xml:space="preserve">Nam in eaſ-
              <lb/>
            dem quatuor partes diuiditur planum horologij à recta A B, quæ communis ſectio eſt ipſius plani horolo
              <lb/>
            gij, & </s>
            <s xml:id="echoid-s11088" xml:space="preserve">Verticalis propriè dicti, & </s>
            <s xml:id="echoid-s11089" xml:space="preserve">à linea meridiana, ſiue ſectione communi eiuſdem plani horologij, & </s>
            <s xml:id="echoid-s11090" xml:space="preserve">
              <lb/>
            Meridiani; </s>
            <s xml:id="echoid-s11091" xml:space="preserve">ita vt pars contenta intra rectas G B, G C, dicatur Quarta occidentalis, & </s>
            <s xml:id="echoid-s11092" xml:space="preserve">borea; </s>
            <s xml:id="echoid-s11093" xml:space="preserve">pars au-
              <lb/>
              <note position="right" xlink:label="note-0191-05" xlink:href="note-0191-05a" xml:space="preserve">Quatuor qua-
                <lb/>
              drantes hemi-
                <lb/>
              ſphęrii ſuperi in
                <lb/>
              horologio hori-
                <lb/>
              zontali qui ſint.</note>
            tem intra rectas G B, G H, comprehenſa, Quarta occidentalis, & </s>
            <s xml:id="echoid-s11094" xml:space="preserve">auſtrina; </s>
            <s xml:id="echoid-s11095" xml:space="preserve">pars deinde, quam continẽt
              <lb/>
              <note position="left" xlink:label="note-0191-06" xlink:href="note-0191-06a" xml:space="preserve">30</note>
            rectę G A, G C, Quarta orientalis, ac borea; </s>
            <s xml:id="echoid-s11096" xml:space="preserve">pars denique, quam rectæ G A, G H, complectuntur, Quar-
              <lb/>
            ta orientalis, & </s>
            <s xml:id="echoid-s11097" xml:space="preserve">auſtrina. </s>
            <s xml:id="echoid-s11098" xml:space="preserve">Vnde cum Sol proijciat ſemper vmbram ſtyli in contrariam partem ei,
              <lb/>
            in qua exiſtit, facile iudicabimus ex vmbra, quanam in Quarta hemiſphærij commoretur. </s>
            <s xml:id="echoid-s11099" xml:space="preserve">Nam ſi vm-
              <lb/>
            bra ſtyli cadat in Quartam occidentalem, boream{q́ue}, quam intra lineas G B, G C, contineri dixi-
              <lb/>
            mus, dicemus Solem tunc exiſtere in Quarta oppoſita, nempe in Quarta orientali, atque auſtrina, & </s>
            <s xml:id="echoid-s11100" xml:space="preserve">
              <lb/>
            ſic de cæteris.</s>
            <s xml:id="echoid-s11101" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11102" xml:space="preserve">PRAETEREA ex eiſdem Verticalibus cognoſcimus, quanta ſit Solis diſtantia Verticalis,
              <lb/>
              <note position="right" xlink:label="note-0191-07" xlink:href="note-0191-07a" xml:space="preserve">Quo pacto e@
                <lb/>
              circulis Vertica
                <lb/>
              libus cognoſca-
                <lb/>
              tur, quantus ſit
                <lb/>
              arcus Horizon-
                <lb/>
              tis inter Ver-
                <lb/>
              ticalem propriè
                <lb/>
              dictum, & Ver-
                <lb/>
              ticalem, qui per
                <lb/>
              Solem ducitur:
                <unsure/>
                <lb/>
              qui quidem ar-
                <lb/>
              cus dici ſolet di
                <lb/>
              ſtantia Vertica
                <lb/>
              lis.</note>
            hoc eſi, quantum Verticalis ille circulus, in quo Sol quouis momento temporis exiſtit, recedat in Ho-
              <lb/>
            rizonte à Verticali proprie dicto, ſiue à puncto veri ortus, occaſusve. </s>
            <s xml:id="echoid-s11103" xml:space="preserve">Nam ſi, exempli gratia, Sol
              <lb/>
            deprehenſus fuerit, per ea, quæ proximè tradidimus, exiſtere in Quarta orientali, & </s>
            <s xml:id="echoid-s11104" xml:space="preserve">auſtrina, cadat
              <lb/>
              <note position="left" xlink:label="note-0191-08" xlink:href="note-0191-08a" xml:space="preserve">40</note>
            autem vmbra tunc temporis in Verticalem lineam, cui aſcriptus eſt numerus hic, 30. </s>
            <s xml:id="echoid-s11105" xml:space="preserve">diſtabit Vertica-
              <lb/>
            lis, in quo Sol tunc eſt, à puncto veri ortus verſus auſtrum grad. </s>
            <s xml:id="echoid-s11106" xml:space="preserve">30. </s>
            <s xml:id="echoid-s11107" xml:space="preserve">hoc eſt, ar cus Horizontis inter Ver-
              <lb/>
            ticalem propriè dictum, & </s>
            <s xml:id="echoid-s11108" xml:space="preserve">Verticalem, qui tunc per centrum Solis incedit, interpoſitus orientalis eſt, & </s>
            <s xml:id="echoid-s11109" xml:space="preserve">
              <lb/>
            austrinus, complectitur{q́ue} grad. </s>
            <s xml:id="echoid-s11110" xml:space="preserve">30. </s>
            <s xml:id="echoid-s11111" xml:space="preserve">atque ita de cæteris erit iudicandum.</s>
            <s xml:id="echoid-s11112" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div601" type="section" level="1" n="151">
          <head xml:id="echoid-head154" xml:space="preserve">PROBLEMA 5. PROPOSITIO 5.</head>
          <p>
            <s xml:id="echoid-s11113" xml:space="preserve">PARALLELOS Horizontis, hoc eſt, circulos minores al-
              <lb/>
            titudinum aſtrorum, quos Almucantarath vocant, in eodem horolo-
              <lb/>
              <note position="left" xlink:label="note-0191-09" xlink:href="note-0191-09a" xml:space="preserve">50</note>
            gio horizontali deſcribere.</s>
            <s xml:id="echoid-s11114" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11115" xml:space="preserve">DESCRIBATVR quadrans circuli A B C, qui in 90. </s>
            <s xml:id="echoid-s11116" xml:space="preserve">partes ęquales diſtribuatur, initio
              <lb/>
              <note position="right" xlink:label="note-0191-10" xlink:href="note-0191-10a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              rallelorum Ho
                <lb/>
              rizontis, qui Al
                <lb/>
              mucantarath di
                <unsure/>
                <lb/>
              cuntur, in eodẽ
                <lb/>
              horologio hori-
                <lb/>
              zon tali.</note>
            facto à ſemidiametro A B. </s>
            <s xml:id="echoid-s11117" xml:space="preserve">(Nos eundem in 9. </s>
            <s xml:id="echoid-s11118" xml:space="preserve">partes tantum diuiſimus, ob ſpatii anguſtias, ita
              <lb/>
            vt ſingulæ denos complectantur gradus.) </s>
            <s xml:id="echoid-s11119" xml:space="preserve">Sumpta deinde A D, longitudine ſtyli in ſemidiametro
              <lb/>
            A C, ducatur per D, alteri ſemidiametro A B, parallela D E. </s>
            <s xml:id="echoid-s11120" xml:space="preserve">Poſtremo eductis è centro A, per
              <lb/>
            diuiſionum puncta rectis, ſi in horologio ex G, loco gnomonis, tanquam centro, ad interualla re-
              <lb/>
            ctarum inter D, & </s>
            <s xml:id="echoid-s11121" xml:space="preserve">rectas ex A, emiſſas, comprehenſarum, circuli deſcribantur, vt in figura pręce-
              <lb/>
            dentis propoſ. </s>
            <s xml:id="echoid-s11122" xml:space="preserve">qui tamen tropicos horologii non tranſcendant, deſcripti erunt paralleli Hori-
              <lb/>
            zontis, ſeu circuli altitudinum; </s>
            <s xml:id="echoid-s11123" xml:space="preserve">qui quidem omnes conicę ſectiones ſunt, in quas, ex coroll. </s>
            <s xml:id="echoid-s11124" xml:space="preserve"/>
          </p>
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