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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[111.] THEOREMA 20. PROPOSITIO 22.
Page: 97 (77)
[112.] COROLLARIVM.
Page: 97 (77)
[113.] SCHOLIVM.
Page: 98 (78)
[114.] PROBLEMA 3. PROPOSITIO 23.
Page: 99 (79)
[115.] SCHOLIVM.
Page: 102 (82)
[116.] THEOREMA 21. PROPOSITIO 24.
Page: 109 (89)
[117.] SCHOLIVM.
Page: 110 (90)
[118.] PROBLEMA 4. PROPOSITIO 25.
Page: 110 (90)
[119.] COROLLARIVM.
Page: 111 (91)
[120.] PROBLEMA 5. PROPOSITIO 26.
Page: 111 (91)
[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)
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            auſtrali, ſi arcus inter planum, & </s>
            <s xml:id="echoid-s5443" xml:space="preserve">Horizontem ad partes boreales fuerit ſub Horizonte. </s>
            <s xml:id="echoid-s5444" xml:space="preserve">In ea
              <unsure/>
            dem enim fi-
              <lb/>
            gura cernis, arcum D I, vel D L, ex quadrante D A, ablatum relinquere arcum I A, vel L A, inter planum,
              <lb/>
            & </s>
            <s xml:id="echoid-s5445" xml:space="preserve">verticem ad partes boreales. </s>
            <s xml:id="echoid-s5446" xml:space="preserve">Item arcum B H, vel B N, (Eſt autem arcus B H, arcui G D, & </s>
            <s xml:id="echoid-s5447" xml:space="preserve">arcus
              <lb/>
            B N, arcui O D, inter planum & </s>
            <s xml:id="echoid-s5448" xml:space="preserve">Horizontem ſub Horizonte æqualis) ex quadrante B A, detractum re-
              <lb/>
              <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">26. tertij.</note>
            linquere arcum H A, uel N A, inter planum, & </s>
            <s xml:id="echoid-s5449" xml:space="preserve">verticem ex parte auſtrali.</s>
            <s xml:id="echoid-s5450" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div338" type="section" level="1" n="126">
          <head xml:id="echoid-head129" xml:space="preserve">SCHOLIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s5451" xml:space="preserve">SED tradamus iam modum illum inueniendæ altitudinis poli ſupra Horizontem per Analemma,
              <lb/>
            quem in ſcholio propoſ. </s>
            <s xml:id="echoid-s5452" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5453" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5454" xml:space="preserve">polliciti ſumus, quem quidem ex Ioanne Baptiſta Benedicto in lib.
              <lb/>
            </s>
            <s xml:id="echoid-s5455" xml:space="preserve">
              <note position="left" xlink:label="note-0116-02" xlink:href="note-0116-02a" xml:space="preserve">10</note>
            de Gnomonum, vmbrarum ſolarium vſu accepimus. </s>
            <s xml:id="echoid-s5456" xml:space="preserve">Eum tamen clarius nos proponentes ad talem for-
              <lb/>
            mam redegimus.</s>
            <s xml:id="echoid-s5457" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Altitudo poli
            <lb/>
          ſupta Horizon-
            <lb/>
          ze@, quo artifi-
            <lb/>
          c@@ per Analem
            <lb/>
          c@a
            <unsure/>
          ieperiatur.</note>
          <p style="it">
            <s xml:id="echoid-s5458" xml:space="preserve">IN plano, quod Horizonti æquidiſtet, deſcribatur circulus A B C D, cuius centrum E, in quo linea
              <lb/>
            meridiana ſit B D, id est, communis ſectio Meridiani circuli, & </s>
            <s xml:id="echoid-s5459" xml:space="preserve">circuli A B C D, ita vt B, ad auſtrũ,
              <lb/>
              <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a" number="82">
                <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0116-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s5460" xml:space="preserve">D, ad Boream vergat; </s>
            <s xml:id="echoid-s5461" xml:space="preserve">AC,
              <lb/>
            communis ſectio Verticalis, et
              <lb/>
            eiuſdem circuli. </s>
            <s xml:id="echoid-s5462" xml:space="preserve">Infixo autem
              <lb/>
            ſtylo cuiuſcunque magnitu
              <unsure/>
            di-
              <lb/>
            nis in centro E, ad planum cir-
              <lb/>
            culi A B C D, recto, obſeruc-
              <lb/>
              <note position="left" xlink:label="note-0116-04" xlink:href="note-0116-04a" xml:space="preserve">20</note>
            tur vel antemeridiẽ, vel poſt,
              <lb/>
            vmbra ſtyli, in cuius medio pro
              <lb/>
            pe extremitatem (nam punctũ
              <lb/>
            extremum uix in plano depre-
              <lb/>
            hendi poteſt ſine errore) pun-
              <lb/>
            ctum notetur, per quod & </s>
            <s xml:id="echoid-s5463" xml:space="preserve">per
              <lb/>
            centrum E, ducatur recta F G.
              <lb/>
            </s>
            <s xml:id="echoid-s5464" xml:space="preserve">Commode etiam hic vti pote-
              <lb/>
            rimus inſtrumento, quod ad
              <lb/>
            principium ſcholij propoſ. </s>
            <s xml:id="echoid-s5465" xml:space="preserve">23. </s>
            <s xml:id="echoid-s5466" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0116-05" xlink:href="note-0116-05a" xml:space="preserve">30</note>
            huius lib. </s>
            <s xml:id="echoid-s5467" xml:space="preserve">conſtruxim{us}. </s>
            <s xml:id="echoid-s5468" xml:space="preserve">Nam
              <lb/>
            ſi regula A B, in plano circuli
              <lb/>
            A B C D, collocetur, ita vt
              <lb/>
            punctum D, in centro E, pona-
              <lb/>
            tur, obſeruabimus vmbram la-
              <lb/>
            teris H D, loco vmbrę styli,
              <lb/>
            in qua punctum not abimus,
              <lb/>
            per quod & </s>
            <s xml:id="echoid-s5469" xml:space="preserve">per centrum E,
              <lb/>
            (amoto prius inſtrumento,)
              <lb/>
            rectam ducem{us} F G. </s>
            <s xml:id="echoid-s5470" xml:space="preserve">Hoc eo-
              <lb/>
              <note position="left" xlink:label="note-0116-06" xlink:href="note-0116-06a" xml:space="preserve">40</note>
            dem instrumento vtemur in a-
              <lb/>
            lijs quoque obſeruationibus, in
              <lb/>
            quibus ſtyl{us} ad proiectionem vmbræ aſſumi ſolet. </s>
            <s xml:id="echoid-s5471" xml:space="preserve">Sumpta autem tunc altitudine Solis ſine mora, an-
              <lb/>
            tequam recta F G, ducatur, ſumatur ei è regione vmbræ arcus æqualis G H, & </s>
            <s xml:id="echoid-s5472" xml:space="preserve">ex H, ad F G, perpen-
              <lb/>
            dicularis demittatur H I. </s>
            <s xml:id="echoid-s5473" xml:space="preserve">Deinde ex I, ad B D, perpendicularis ducatur I O Q, vel ipſi A C, paral-
              <lb/>
            lela, abſcindatur{q́ue}, O Q, ipſi H I, æqualis. </s>
            <s xml:id="echoid-s5474" xml:space="preserve">Rurſus poſt aliquod ſpatium temporis elapſis
              <unsure/>
            m obſeruetur ite-
              <lb/>
            rum vmbra ſtyli, in cuius medio prope extremitatem aliud punctum ſignetur, ex quo per centrum E,
              <lb/>
            emittatur recta K L; </s>
            <s xml:id="echoid-s5475" xml:space="preserve">ſumptaq́, eo tempore altitudine Solis, accipiatur ei è regione vmbræ arcus L M,
              <lb/>
            æqualis, & </s>
            <s xml:id="echoid-s5476" xml:space="preserve">ex M, ad K L, deducatur perpendicularis M N; </s>
            <s xml:id="echoid-s5477" xml:space="preserve">atque ex N, ad B D, excitetur perpendicu-
              <lb/>
            laris N P R, vel ipſi AC, parallela, auferaturq́, P R, ipſi M N, æqualis. </s>
            <s xml:id="echoid-s5478" xml:space="preserve">Poſtremo per puncta R, Q,
              <lb/>
              <note position="left" xlink:label="note-0116-07" xlink:href="note-0116-07a" xml:space="preserve">50</note>
            ducatur recta R Q. </s>
            <s xml:id="echoid-s5479" xml:space="preserve">Dico angulum P R Q, angulum eſſe altitudinis poli, & </s>
            <s xml:id="echoid-s5480" xml:space="preserve">arcum π ρ, ex R, deſcri-
              <lb/>
            ptum continere gradus eiuſdem altitudinis. </s>
            <s xml:id="echoid-s5481" xml:space="preserve">Quod nos hac ratione demonſtr abimus. </s>
            <s xml:id="echoid-s5482" xml:space="preserve">Quoniam tempore
              <lb/>
            primæ obſeruationis extremum vmbræ cadit in rectam E F, erit recta F G, communis ſectio circuli
              <lb/>
            A B C D, & </s>
            <s xml:id="echoid-s5483" xml:space="preserve">Verticalis illius, in quo tunc Sol exiſtit, vt ex propoſitione 11. </s>
            <s xml:id="echoid-s5484" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5485" xml:space="preserve">conſtat. </s>
            <s xml:id="echoid-s5486" xml:space="preserve">Vnde
              <lb/>
            cum Verticalis propriè dictus per rectam A C, ductus, & </s>
            <s xml:id="echoid-s5487" xml:space="preserve">Verticalis per centrum Solis, & </s>
            <s xml:id="echoid-s5488" xml:space="preserve">per rectam
              <lb/>
            F G, tranſiens, auferant ex Horizonte, & </s>
            <s xml:id="echoid-s5489" xml:space="preserve">circulo A B C D, (qui Horizonti æquidiſtat tanto interual-
              <lb/>
            lo ab eo remotus, quanta eſt ſtyli longitudo, vt ex propoſ. </s>
            <s xml:id="echoid-s5490" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5491" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5492" xml:space="preserve">perſpicuum eſt) arcus ſimiles, ex
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s5493" xml:space="preserve">10. </s>
            <s xml:id="echoid-s5494" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5495" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5496" xml:space="preserve">Theodoſii, quòd per eorum polos ducantur; </s>
            <s xml:id="echoid-s5497" xml:space="preserve">fit vt ſi circulus A B C D, pro Horizonte
              <lb/>
            accipiatur, recta F G, ſit quoque communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s5498" xml:space="preserve">Verticalis per centrum Solis tranſeun-
              <lb/>
            tis. </s>
            <s xml:id="echoid-s5499" xml:space="preserve">Quia verò G H, arcus eſt altitudinis Solis; </s>
            <s xml:id="echoid-s5500" xml:space="preserve">ſi ſemicircul{us} F H G, intelligatur circa diametrum
              <lb/>
            F G, moueri, donec rect{us} ſit ad Horizontem, & </s>
            <s xml:id="echoid-s5501" xml:space="preserve">ideo recta, H I, ad eundem perpendicularis, ex </s>
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