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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        <div xml:id="echoid-div324" type="section" level="1" n="123">
          <p>
            <s xml:id="echoid-s5362" xml:space="preserve">
              <pb o="95" file="0115" n="115" rhead="LIBER PRIMVS."/>
            nationis ad Horizontem, ad aliud, inuenietur hic ferè ſinus 74306. </s>
            <s xml:id="echoid-s5363" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s5364" xml:space="preserve">48. </s>
            <s xml:id="echoid-s5365" xml:space="preserve">ferè inter
              <lb/>
            Horizontem, & </s>
            <s xml:id="echoid-s5366" xml:space="preserve">planum inclinatum eſt poſitus. </s>
            <s xml:id="echoid-s5367" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s5368" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5369" xml:space="preserve">QVOD ſi planum tam ad Horizontem, quàm ad Meridianum inclinatum directo ad ortũ
              <lb/>
              <note position="right" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve">Quando planũ
                <lb/>
              rectũ eſt ad Ver
                <lb/>
              ticalem.</note>
            vel occaſum ſpectet, hoc eſt, ſi ad Verticalem ſit rectum, nullus intercipietur arcus Meridiani inter
              <lb/>
            ipſum planum, & </s>
            <s xml:id="echoid-s5370" xml:space="preserve">Horizontem, quia tunc planum per communes ſectiones Meridiani, & </s>
            <s xml:id="echoid-s5371" xml:space="preserve">Hori-
              <lb/>
            zontis incedit, vt conſtat.</s>
            <s xml:id="echoid-s5372" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5373" xml:space="preserve">SI verò planum ad Horizontem tantum inclinatum fuerit, hoc eſt, ſi per communes ſectio-
              <lb/>
              <note position="right" xlink:label="note-0115-02" xlink:href="note-0115-02a" xml:space="preserve">Quando planũ
                <lb/>
              rectũ eſt ad Me
                <lb/>
              tidianum.</note>
            nes Horizontis, ac Verticalis, ſeu polos Meridiani tranſierit, atque adeo ad Meridianum ſuerit re-
              <lb/>
            ctum, erit ipſa inclinatio ad Horizontem arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5374" xml:space="preserve">Horizontem poſitus:
              <lb/>
            </s>
            <s xml:id="echoid-s5375" xml:space="preserve">quia tunc Meridianus inclinationem metitur, vt patet.</s>
            <s xml:id="echoid-s5376" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p>
            <s xml:id="echoid-s5377" xml:space="preserve">SI denique planum inclinatum tantum fuerit ad Meridianum, hoc eſt, ſi per verticem, ſeu
              <lb/>
              <note position="right" xlink:label="note-0115-04" xlink:href="note-0115-04a" xml:space="preserve">Quando planũ
                <lb/>
              rectũ eſt ad Ho
                <lb/>
              rizontem.</note>
            polum Horizontis tranſierit, ideoq́uead Horizontem fuerit rectum, intercipietur inter ipſum pla
              <lb/>
            num, & </s>
            <s xml:id="echoid-s5378" xml:space="preserve">Horizontem quarta pars Meridiani circuli, vt manifeſtum eſt. </s>
            <s xml:id="echoid-s5379" xml:space="preserve">Dato ergo plano velad Ho
              <lb/>
            rizontem & </s>
            <s xml:id="echoid-s5380" xml:space="preserve">Meridianum, vel ad Meridianum tantum, &</s>
            <s xml:id="echoid-s5381" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5382" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s5383" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div331" type="section" level="1" n="124">
          <head xml:id="echoid-head127" xml:space="preserve">SCHOLIVM I.</head>
          <note position="right" xml:space="preserve">Quando arcus
            <lb/>
          Meridiani in-
            <lb/>
          ter Horizontẽ
            <lb/>
          & planũ incli-
            <lb/>
          natũ reperiatur
            <lb/>
          ſupra Horizon
            <lb/>
          tem, & quando
            <lb/>
          infra.</note>
          <p style="it">
            <s xml:id="echoid-s5384" xml:space="preserve">SI inclinatio plani ad Horizontem cadat in partem hemiſphærij ſuperni Borealem, iuxta ea, quæ
              <lb/>
            propoſitione 23. </s>
            <s xml:id="echoid-s5385" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5386" xml:space="preserve">docuimus, ſecabitur Meridianus ex parte poli arctici ſupra Horizontem, at-
              <lb/>
            que arcus inter Horizontem & </s>
            <s xml:id="echoid-s5387" xml:space="preserve">planum poſitus ſupra Horizontem extabit ex parte poli arctici. </s>
            <s xml:id="echoid-s5388" xml:space="preserve">Si ve-
              <lb/>
              <note position="left" xlink:label="note-0115-06" xlink:href="note-0115-06a" xml:space="preserve">20</note>
            ro inclinatio in partem eiuſdem hemiſphærij auſtralem cadat, ſecabit planum circulum Meridianum ex
              <lb/>
            parte poli arctici infra Horizontem, arcus{q́ue} propterea Meridiani inter planum, ac Horizontem interie-
              <lb/>
            ctus ſub Horizonte occultabitur. </s>
            <s xml:id="echoid-s5389" xml:space="preserve">Ratio hui{us} rei eſt, quia cum inter circulum maximum metientem in-
              <lb/>
            clinationem plani, & </s>
            <s xml:id="echoid-s5390" xml:space="preserve">planum ipſum intercipiatur quadrans Horizontis, quòd dictus circulus ſegmentum
              <lb/>
            Horizontis inter planum inclinatum, quod quidem ſemicirculus est, ſecet bifariam, per propoſ. </s>
            <s xml:id="echoid-s5391" xml:space="preserve">9. </s>
            <s xml:id="echoid-s5392" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5393" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s5394" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s5395" xml:space="preserve">fit vt cadente inclinatione in partem borealem, Meridianus ex eadem parte boreali ſecet planum
              <lb/>
            inclinatum ſupra Horizontem. </s>
            <s xml:id="echoid-s5396" xml:space="preserve">Eodem modo, cadente inclinatione ad partes auſtrales, ſecabit Meridia-
              <lb/>
            nus ex eadem parte australi planum inclinatum ſupra Horizontem, ac proinde ſub Horizonte ex parte
              <lb/>
            boreali. </s>
            <s xml:id="echoid-s5397" xml:space="preserve">Id quod facile intelligetur, ſi diligenter expendatur ſitus ac poſitio circulorum in ſphæra.</s>
            <s xml:id="echoid-s5398" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
        </div>
        <div xml:id="echoid-div333" type="section" level="1" n="125">
          <head xml:id="echoid-head128" xml:space="preserve">COROLLARIVM.</head>
          <note position="right" xml:space="preserve">Arcus Meridia
            <lb/>
          ni inter planũ
            <lb/>
          inclinatũ, & po
            <lb/>
          lum arcticũ po-
            <lb/>
          ſitus, quo pacto
            <lb/>
          cognoſcat@@.</note>
          <p>
            <s xml:id="echoid-s5399" xml:space="preserve">EX his non difficile erit, quantus ſit arcus Meridiani inter planum inclinatum, & </s>
            <s xml:id="echoid-s5400" xml:space="preserve">polum mundi ar-
              <lb/>
            cticum interpoſitus, inuenire. </s>
            <s xml:id="echoid-s5401" xml:space="preserve">Nam ſi arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5402" xml:space="preserve">Horizontem fuerit ſub Horizon-
              <lb/>
            te ex parte poli arctici, erit arcus, qui ex ipſo, & </s>
            <s xml:id="echoid-s5403" xml:space="preserve">arcu altitudinem poli ſupra Horizontem metiente com-
              <lb/>
              <figure xlink:label="fig-0115-01" xlink:href="fig-0115-01a" number="81">
                <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0115-01"/>
              </figure>
            ponitur, interiectus inter planum inclinatum, & </s>
            <s xml:id="echoid-s5404" xml:space="preserve">polum mundi arcti-
              <lb/>
            cum, ſi quadratem non exceſſerit; </s>
            <s xml:id="echoid-s5405" xml:space="preserve">ſi enim exceſſerit quadrantem,
              <lb/>
            erit eius cõplementum ad ſemicirculũ dictus arcus, qui quidem ſupra
              <lb/>
            Horizontẽ cõtinetur verſus auſtrũ, quemadmodum ille partim ſupra
              <lb/>
            Horizontẽ & </s>
            <s xml:id="echoid-s5406" xml:space="preserve">partim infra. </s>
            <s xml:id="echoid-s5407" xml:space="preserve">Si verò ſupra Horizontẽ extiterit, erit ar-
              <lb/>
            cus, quo ipſe differt ab arcu altitudinẽ poli ſupra Horizõtem metien
              <lb/>
            te, inter planũ ipſum, & </s>
            <s xml:id="echoid-s5408" xml:space="preserve">polum mundi arcticũ interceptus, cõtinebi-
              <lb/>
            turq́; </s>
            <s xml:id="echoid-s5409" xml:space="preserve">ſupra Horizontem modo verſus boream, modo verſus auſtrum.
              <lb/>
            </s>
            <s xml:id="echoid-s5410" xml:space="preserve">Quę quidem omnia ex hac appoſita figura perſpicua fient, in qua
              <lb/>
            Meridianus A B C D; </s>
            <s xml:id="echoid-s5411" xml:space="preserve">axis mundi E F; </s>
            <s xml:id="echoid-s5412" xml:space="preserve">polus arcticus E, antarcti-
              <lb/>
            cus F; </s>
            <s xml:id="echoid-s5413" xml:space="preserve">communis ſectio Horizontis ac Meridiani
              <unsure/>
            B D; </s>
            <s xml:id="echoid-s5414" xml:space="preserve">communis ſe-
              <lb/>
              <note position="left" xlink:label="note-0115-09" xlink:href="note-0115-09a" xml:space="preserve">40</note>
            ctio Verticalis, & </s>
            <s xml:id="echoid-s5415" xml:space="preserve">Meridiani A C; </s>
            <s xml:id="echoid-s5416" xml:space="preserve">communis ſectio plani inclinati,
              <lb/>
            & </s>
            <s xml:id="echoid-s5417" xml:space="preserve">Meridiani G H, vel I k, vel L M, vel N O. </s>
            <s xml:id="echoid-s5418" xml:space="preserve">Vides igitur arcum
              <lb/>
            G E, compoſitum ex arcu G D, inter planum inclinatum, ac Horizon
              <lb/>
            tem ſub Horizonte, & </s>
            <s xml:id="echoid-s5419" xml:space="preserve">arcu D E, altitudinis poli ſupra Horizontem; </s>
            <s xml:id="echoid-s5420" xml:space="preserve">arcum item I E, vel L E, quo differt
              <lb/>
            arcus D I, vel D L, inter planum inclinatum & </s>
            <s xml:id="echoid-s5421" xml:space="preserve">Horizontem ſupra Horizontẽ ab arcu D E, altitudinis
              <lb/>
            poli ſupra Horizontem, interceptum eſſe inter planum inclinatum, & </s>
            <s xml:id="echoid-s5422" xml:space="preserve">polum arcticum E. </s>
            <s xml:id="echoid-s5423" xml:space="preserve">Item arcum
              <lb/>
            E N, inter planum N O, & </s>
            <s xml:id="echoid-s5424" xml:space="preserve">polum eſſe ſumendum, quamuis arcus D O, inter planum, & </s>
            <s xml:id="echoid-s5425" xml:space="preserve">Horizontem ſit
              <lb/>
              <note position="left" xlink:label="note-0115-10" xlink:href="note-0115-10a" xml:space="preserve">50</note>
            ſub Horizonte, quia totus arcus E O, quadrantem ſuperat.</s>
            <s xml:id="echoid-s5426" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5427" xml:space="preserve">QVOD ſi planum inclinatum, fuerit rectum ad Verticalem circulum, hoc eſt, ſi directè ad ortum,
              <lb/>
              <note position="right" xlink:label="note-0115-11" xlink:href="note-0115-11a" xml:space="preserve">Quando planũ
                <lb/>
              rectũ eſt ad Ver
                <lb/>
              ticalem.</note>
            vel occaſum ſpectet, tranſeatq́; </s>
            <s xml:id="echoid-s5428" xml:space="preserve">per communes ſectiones Horizontis ac Meridiani, ita vt eius, & </s>
            <s xml:id="echoid-s5429" xml:space="preserve">Meridia-
              <lb/>
            ni communis ſectio ſit recta B D, non differet arcus inter planum ipſum, & </s>
            <s xml:id="echoid-s5430" xml:space="preserve">polum E, ab arcu D E, altitu
              <lb/>
            dinem poli ſupra Horizontem metiente, vt conſtat.</s>
            <s xml:id="echoid-s5431" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5432" xml:space="preserve">SI verò planum inclinatum rectum fuerit ad Horizontem, hoc eſt, ſi per verticem A, tranſierit, ita vt
              <lb/>
              <note position="right" xlink:label="note-0115-12" xlink:href="note-0115-12a" xml:space="preserve">Quando planũ
                <lb/>
              recũ eſt ad Ho
                <lb/>
              rizontem.</note>
            communis ſectio ipſius, ac Meridiani ſit recta A C, non differet arcus inter ipſum planum, & </s>
            <s xml:id="echoid-s5433" xml:space="preserve">polum E,
              <lb/>
            ab arcu A E, qui complementum altitudinis poli ſupra Horizontem dimetitur, vt manifeſtum eſt.</s>
            <s xml:id="echoid-s5434" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5435" xml:space="preserve">PARI ratione comperiemus, quantus ſit arcus Meridiani inter planum inclinatum, & </s>
            <s xml:id="echoid-s5436" xml:space="preserve">verticem ca-
              <lb/>
              <note position="right" xlink:label="note-0115-13" xlink:href="note-0115-13a" xml:space="preserve">Quantus ſit ar-
                <lb/>
              cus Meridiani
                <lb/>
              inter planũ in-
                <lb/>
              clinatũ, & ver-
                <lb/>
              ticem capitis.</note>
            pitis interiectus. </s>
            <s xml:id="echoid-s5437" xml:space="preserve">Nam ſi arcum Meridiani inter planum & </s>
            <s xml:id="echoid-s5438" xml:space="preserve">Horizontem auſeramus ex quadrante, reli-
              <lb/>
            quus erit arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s5439" xml:space="preserve">verticem capitis; </s>
            <s xml:id="echoid-s5440" xml:space="preserve">continebiturq́ arcus hic in parte boreali,
              <lb/>
            ſi arcus inter planum, & </s>
            <s xml:id="echoid-s5441" xml:space="preserve">Horizontem fuerit ſupra Horizontem ex eadem parte boreali; </s>
            <s xml:id="echoid-s5442" xml:space="preserve">in parte </s>
          </p>
        </div>
      </text>
    </echo>
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