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

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        <div xml:id="echoid-div319" type="section" level="1" n="121">
          <pb o="93" file="0113" n="113" rhead="LIBER PRIMVS."/>
          <p style="it">
            <s xml:id="echoid-s5183" xml:space="preserve">FEDER@CVS Commandinus hoc quoque problema proponit generalius, vt & </s>
            <s xml:id="echoid-s5184" xml:space="preserve">illud, quod ſupra
              <lb/>
            demonſtrauimus propoſ. </s>
            <s xml:id="echoid-s5185" xml:space="preserve">24. </s>
            <s xml:id="echoid-s5186" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s5187" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div321" type="section" level="1" n="122">
          <head xml:id="echoid-head125" xml:space="preserve">PROBLEMA 6. PROPOSITIO 27.</head>
          <p>
            <s xml:id="echoid-s5188" xml:space="preserve">PLANI cuiuslibet inclinationem ad Meridianum circulum in-
              <lb/>
            ueſtigare.</s>
            <s xml:id="echoid-s5189" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5190" xml:space="preserve">SIT Horizon A B C D, Meridianus A C G, planum ad Meridianũ inclinatũ E F, ecans Meri
              <lb/>
              <note position="right" xlink:label="note-0113-01" xlink:href="note-0113-01a" xml:space="preserve">Inclinatio pla-
                <lb/>
              ni propoſiti ad
                <lb/>
              Meridianum.
                <lb/>
              qua rati@one d@-
                <lb/>
              pr@hendatut.</note>
            dianũ in G, ſiue infra Horizontẽ, ſiue ſupra. </s>
            <s xml:id="echoid-s5191" xml:space="preserve">Intelligimus autẽ hic, & </s>
            <s xml:id="echoid-s5192" xml:space="preserve">in ſequẽtibus quinque proble
              <lb/>
              <note position="left" xlink:label="note-0113-02" xlink:href="note-0113-02a" xml:space="preserve">10</note>
              <figure xlink:label="fig-0113-01" xlink:href="fig-0113-01a" number="78">
                <image file="0113-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113-01"/>
              </figure>
            matibus, planum inclinatũ, quod
              <lb/>
            per centrũ ſphærę ducitur, ac pro-
              <lb/>
            inde in ſphera, ꝑ propoſ. </s>
            <s xml:id="echoid-s5193" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5194" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5195" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s5196" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s5197" xml:space="preserve">circulũ maximũ facit. </s>
            <s xml:id="echoid-s5198" xml:space="preserve">Quo
              <lb/>
            niam igitur in triangulo ſphærico
              <lb/>
            C F G, cuius angulus C, rectus eſt. </s>
            <s xml:id="echoid-s5199" xml:space="preserve">
              <lb/>
            (Nam Meridianus ad Horizõtem
              <lb/>
            rectus eſt) vt ſinus anguli F, inclina
              <lb/>
            tionis plani dati EF, ad Horizontẽ,
              <lb/>
            ad ſinũ anguli C, recti, hoc eſt, ad
              <lb/>
              <note position="left" xlink:label="note-0113-03" xlink:href="note-0113-03a" xml:space="preserve">20</note>
            ſinũ totũ, ita eſt, ꝑ propoſ. </s>
            <s xml:id="echoid-s5200" xml:space="preserve">18. </s>
            <s xml:id="echoid-s5201" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s5202" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5203" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s5204" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s5205" xml:space="preserve">de triangulis, vel
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s5206" xml:space="preserve">14. </s>
            <s xml:id="echoid-s5207" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5208" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5209" xml:space="preserve">Gebri, vel cer
              <lb/>
            tè ex propoſ. </s>
            <s xml:id="echoid-s5210" xml:space="preserve">42. </s>
            <s xml:id="echoid-s5211" xml:space="preserve">noſtrorum trian-
              <lb/>
            gulotum ſphæricorum, ſinus com-
              <lb/>
            plementi anguli G, inclinationis eiuſdem plani E F, ad Meridianum, ad ſinum complementi ar-
              <lb/>
            cus CF, hoc eſt, ad ſinum arcus D F, vel B F, declinationem à Verticali circulo metientis: </s>
            <s xml:id="echoid-s5212" xml:space="preserve">Erit quo
              <lb/>
            que conuertendo, vt ſinus totus anguli recti C, ad ſinum anguli F, inclinationis plani E F, ad Ho
              <lb/>
            rizontem, ita ſinus complementi arcus C F, hoc eſt, ſinus arcus D F, vel B F, declinationem à Ver
              <lb/>
            ticali metientis, ad ſinum complementi anguli G, inclinationis eiuſdem plani E F, ad Meridia-
              <lb/>
              <note position="left" xlink:label="note-0113-04" xlink:href="note-0113-04a" xml:space="preserve">30</note>
            num. </s>
            <s xml:id="echoid-s5213" xml:space="preserve">Quamobrem, inuenta per propoſ. </s>
            <s xml:id="echoid-s5214" xml:space="preserve">23. </s>
            <s xml:id="echoid-s5215" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s5216" xml:space="preserve">declinatione plani propoſiti à Verticali cir-
              <lb/>
            culo, nec non eiuſdem inclinationead Horizontem; </s>
            <s xml:id="echoid-s5217" xml:space="preserve">ſi fiat, vt ſinus totus ad ſinum inclinationis ad
              <lb/>
            Horizontem, ita ſinus declinationis à Verticali ad aliud, habebitur ſinus complementi inclinatio-
              <lb/>
            nis ad Meridianũ; </s>
            <s xml:id="echoid-s5218" xml:space="preserve">quo cõplemento detracto ex quadrante, inclinatio ad Meridianum nota fiet.</s>
            <s xml:id="echoid-s5219" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5220" xml:space="preserve">EXEMPLVM. </s>
            <s xml:id="echoid-s5221" xml:space="preserve">Ponatur declinatio plani à Verticali circulo grad. </s>
            <s xml:id="echoid-s5222" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5223" xml:space="preserve">inclinatio verò ad Ho
              <lb/>
            rizontem grad. </s>
            <s xml:id="echoid-s5224" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5225" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5226" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5227" xml:space="preserve">Si igitur fiat, vt 100000. </s>
            <s xml:id="echoid-s5228" xml:space="preserve">ſinus totus ad 78854. </s>
            <s xml:id="echoid-s5229" xml:space="preserve">ſinum inclinationis ad
              <lb/>
            Horizontem, nempead ſinum grad. </s>
            <s xml:id="echoid-s5230" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5231" xml:space="preserve">min. </s>
            <s xml:id="echoid-s5232" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5233" xml:space="preserve">ita 50000. </s>
            <s xml:id="echoid-s5234" xml:space="preserve">ſinus declinationis à Verticali, hoc eſt,
              <lb/>
            ſinus grad. </s>
            <s xml:id="echoid-s5235" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5236" xml:space="preserve">ad aliud, inuenietur hic ſinus 39427. </s>
            <s xml:id="echoid-s5237" xml:space="preserve">cuius arcus continet gradus 23. </s>
            <s xml:id="echoid-s5238" xml:space="preserve">min. </s>
            <s xml:id="echoid-s5239" xml:space="preserve">13. </s>
            <s xml:id="echoid-s5240" xml:space="preserve">quo
              <lb/>
            detracto ex quadrante, remanebit inclinatio ad Meridianũ grad. </s>
            <s xml:id="echoid-s5241" xml:space="preserve">66. </s>
            <s xml:id="echoid-s5242" xml:space="preserve">min. </s>
            <s xml:id="echoid-s5243" xml:space="preserve">47. </s>
            <s xml:id="echoid-s5244" xml:space="preserve">Quod eſt propoſitũ.</s>
            <s xml:id="echoid-s5245" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quando planũ
            <lb/>
          r@ctũ eſt ad Ver
            <lb/>
          ticalem.</note>
          <p>
            <s xml:id="echoid-s5246" xml:space="preserve">QVOD ſi planum inclinatum directè ad ortum, vel occaſum ſpectet, hoc eſt, ſi ad Vertica-
              <lb/>
              <note position="left" xlink:label="note-0113-06" xlink:href="note-0113-06a" xml:space="preserve">40</note>
            lem circulum ſit rectum, tranſeatque per communes ſectiones Horizontis, & </s>
            <s xml:id="echoid-s5247" xml:space="preserve">Meridiani, erit cõ-
              <lb/>
            plementum inclinationis ipſius ad Horizontẽ, inclinatio eiuſdem ad Meridianũ, vt perſpicuũ eſt.</s>
            <s xml:id="echoid-s5248" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quando planũ
            <lb/>
          inclinatum ad
            <lb/>
          Horizontem di
            <lb/>
          recto ſpectat ad
            <lb/>
          auſtrum, vel bo
            <lb/>
          ream.</note>
          <p>
            <s xml:id="echoid-s5249" xml:space="preserve">SI verò planum ad Horizontem inclinatum careat declinatione, hoc eſt, ſi tranſeat per com-
              <lb/>
            munes ſectiones Verticalis circuli & </s>
            <s xml:id="echoid-s5250" xml:space="preserve">Horizontis, vergatq́ue directò ad auſtrum, vel ſeptentrionẽ,
              <lb/>
            carebit huiuſmodi planum inclinationead Meridianum, hoc eſt, rectum erit ad Meridianum,
              <lb/>
            vt patet.</s>
            <s xml:id="echoid-s5251" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quando planũ
            <lb/>
          rectũ eſt ad Ho
            <lb/>
          rizontem.</note>
          <p>
            <s xml:id="echoid-s5252" xml:space="preserve">SI deniqueplanum ad Horizontem ſit rectum, hoc eſt, ſi tranſeat per verticem, erit comple-
              <lb/>
            mentum declinationis ipſius à Verticali circulo, inclinatio eiuſdem ad Meridianum, vt manife-
              <lb/>
            ſtum eſt. </s>
            <s xml:id="echoid-s5253" xml:space="preserve">Plani igitur cuiuslibet inclinationem ad Meridianum circulum inueſtigauimus. </s>
            <s xml:id="echoid-s5254" xml:space="preserve">Quod
              <lb/>
            erat faciendum.</s>
            <s xml:id="echoid-s5255" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
        </div>
        <div xml:id="echoid-div324" type="section" level="1" n="123">
          <head xml:id="echoid-head126" xml:space="preserve">PROBLEMA. 7. PROPOSITIO 28.</head>
          <p>
            <s xml:id="echoid-s5256" xml:space="preserve">DATO plano ad Horizontem & </s>
            <s xml:id="echoid-s5257" xml:space="preserve">Meridianum, vel ad Meridia-
              <lb/>
            num tantum, vel ad Horizontem tantum inclinato, quantus ſit arcus
              <lb/>
              <note position="right" xlink:label="note-0113-10" xlink:href="note-0113-10a" xml:space="preserve">Arcus Meridia
                <lb/>
              ni inter Hori-
                <lb/>
              zontem & pla-
                <lb/>
              nũ inclinatum
                <lb/>
              poſitus, qua ar-
                <lb/>
              te ſit inueſti
                <unsure/>
              -
                <lb/>
              gandus.</note>
            Meridiani circuli interipſum, & </s>
            <s xml:id="echoid-s5258" xml:space="preserve">Horizontem poſitus, inuenire.</s>
            <s xml:id="echoid-s5259" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5260" xml:space="preserve">SIT Horizon A B C D, cuius centrum E, communis ſectio ipſius, ac Meridiani A C; </s>
            <s xml:id="echoid-s5261" xml:space="preserve">eiuſdẽ
              <lb/>
            & </s>
            <s xml:id="echoid-s5262" xml:space="preserve">Verticalis B D; </s>
            <s xml:id="echoid-s5263" xml:space="preserve">declinatio plani tam ad Horizontem, quàm ad Meridianum inclinati, à Ver-
              <lb/>
            ticali circulo D F, vt recta F G, communis ſectio ſit Horizontis, ac plani inclinati. </s>
            <s xml:id="echoid-s5264" xml:space="preserve">Inuẽta </s>
          </p>
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