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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            <s xml:id="echoid-s4539" xml:space="preserve">
              <pb o="83" file="0103" n="103" rhead="LIBER PRIMVS."/>
            hoc inſtrumentum percommodum ad examinandum quodcunque planum propoſitum, ſit ne Horizonti
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            parallelum nec ne. </s>
            <s xml:id="echoid-s4540" xml:space="preserve">Filo enim radente planum C D, per rectam F G, erit planim, in quo iacet regula
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            A B, Horizonti æquidiſtans. </s>
            <s xml:id="echoid-s4541" xml:space="preserve">I am in vmbra ſiue fili, ſiue lateris H D, duo pur cta A, B, aliquantulum
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            inter ſe distantia notentur, quę recta linea A B, iungantur. </s>
            <s xml:id="echoid-s4542" xml:space="preserve">Erit hęc communis ſectio plani ſubiecti, & </s>
            <s xml:id="echoid-s4543" xml:space="preserve">
              <lb/>
            Verticalis circuli, qui tempore obſeruatio-
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              <figure xlink:label="fig-0103-01" xlink:href="fig-0103-01a" number="67">
                <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103-01"/>
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            nis per centrum Solis deſcribicur. </s>
            <s xml:id="echoid-s4544" xml:space="preserve">Obſerua-
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            ta autem vmbra, accipiatur ſine mora qua-
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            drante, vel Aſtrolabio, altitudo Solis; </s>
            <s xml:id="echoid-s4545" xml:space="preserve">quæ
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            quidem altitudo Solis obſeruanda eſt ſta-
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            tim poſt ſignationem duorum punctorum in
              <lb/>
              <note position="left" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">10</note>
            vmbra, antequam recta linea per illa duca-
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            tur, ne periculum ſit in mora, quòd propter
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            aſcenſum Solis ante meridiem, vel deſcen-
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            ſum poſt meridiem, hoc eſt, propter motum
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            Solis diurnum, vmbra neceſſario mutetur,
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            at que Sol in alio statim Verticali exiſtat.
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            </s>
            <s xml:id="echoid-s4546" xml:space="preserve">Poſt hęc in Aſtrolabio, in quo Aequator
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            C D E F, circa centrum G, vbi duę dia-
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            metri C E, D F, ſeſe ad angulos rectos ſe-
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            cant, & </s>
            <s xml:id="echoid-s4547" xml:space="preserve">Verticalis proprie dictus HIKL,
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              <note position="left" xlink:label="note-0103-02" xlink:href="note-0103-02a" xml:space="preserve">20</note>
            circa centrum M, per quod recta I L, du-
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            cta rectam C E, ad angulos rectos ſecat,
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            deſcribatur parallelus Solis N O, quem
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            exempli gratia ponamus tranſire per grad.
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            </s>
            <s xml:id="echoid-s4548" xml:space="preserve">15. </s>
            <s xml:id="echoid-s4549" xml:space="preserve">♌, habereq́, declinationem grad. </s>
            <s xml:id="echoid-s4550" xml:space="preserve">16. </s>
            <s xml:id="echoid-s4551" xml:space="preserve">
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            min. </s>
            <s xml:id="echoid-s4552" xml:space="preserve">23. </s>
            <s xml:id="echoid-s4553" xml:space="preserve">quem in puncto O, ex parte orien-
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            tis (ponamus enim nunc obſeruationem fie-
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            ri ante meridiem) ſecet parallelus Horizon
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            tis P O, per altitudinem Solis, quam nunc
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            ponamus eſſe grad. </s>
            <s xml:id="echoid-s4554" xml:space="preserve">30. </s>
            <s xml:id="echoid-s4555" xml:space="preserve">tranſiens. </s>
            <s xml:id="echoid-s4556" xml:space="preserve">Per hoc
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              <note position="left" xlink:label="note-0103-03" xlink:href="note-0103-03a" xml:space="preserve">30</note>
            enim punctum O, deſcribendus eſt Vertica-
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            lis eo tempore per centrum Solis incedens.
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            </s>
            <s xml:id="echoid-s4557" xml:space="preserve">Huius autem centrum, quod in recta I L, existit, vt in Aſtrolabio à nobis demonſtratum eſt, ita inue-
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            niemus. </s>
            <s xml:id="echoid-s4558" xml:space="preserve">Ex H, & </s>
            <s xml:id="echoid-s4559" xml:space="preserve">O, bini arcus tam ſupra puncta H, & </s>
            <s xml:id="echoid-s4560" xml:space="preserve">O, quàm infra, deſcribantur ad quodcunque
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            interuallum ſeſe interſecantes in duobus punctis, per quę recta ducatur ſecans I L, in Q. </s>
            <s xml:id="echoid-s4561" xml:space="preserve">Erit enim Q,
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            centrum Verticalis per H, & </s>
            <s xml:id="echoid-s4562" xml:space="preserve">O, deſcribendi. </s>
            <s xml:id="echoid-s4563" xml:space="preserve">Nam vt conſtat exijs, quę in ſcholio propoſ. </s>
            <s xml:id="echoid-s4564" xml:space="preserve">25. </s>
            <s xml:id="echoid-s4565" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4566" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4567" xml:space="preserve">
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            Euclidis demonſtrauimas, recta coniungens illa puncta tranſit per centrum circuli deſcribendi per H, O. </s>
            <s xml:id="echoid-s4568" xml:space="preserve">
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            Si igitur ex Q, & </s>
            <s xml:id="echoid-s4569" xml:space="preserve">ad interuallum Q H, vel Q O, circulus deſcribatur, erit hic Verticalis per centrũ
              <lb/>
            Solis incedens tempore obſeruationis, qui quidem à Verticali proprie dicto H I K L, ex parte orient ali
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            deflectet in Auſtrum, ſi centrum Q, in rectam E I, ceciderit, & </s>
            <s xml:id="echoid-s4570" xml:space="preserve">obſeruatio fiat ante meridiem; </s>
            <s xml:id="echoid-s4571" xml:space="preserve">in Bo-
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              <note position="left" xlink:label="note-0103-04" xlink:href="note-0103-04a" xml:space="preserve">40</note>
            ream verò, ſi extiterit in E L, & </s>
            <s xml:id="echoid-s4572" xml:space="preserve">ante meridiem fiat obſeruatio. </s>
            <s xml:id="echoid-s4573" xml:space="preserve">At ſi obſeruatio fiat poſt meridiem,
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            quoniam tunc punctum O, ſumendũ eſt ex parte occidentis, ſi cẽtrum Q, extiterit in recta E L, deflectet
              <lb/>
            Verticalis H O, à proprio Verticali in Auſtrum ex parte occidentali, in boream vero, ſi centrum Q, in
              <lb/>
            rectam E I, ceciderit. </s>
            <s xml:id="echoid-s4574" xml:space="preserve">Sed quantum deflectat, ita deprehendemus. </s>
            <s xml:id="echoid-s4575" xml:space="preserve">Ex H, vertice per Q, recta duca-
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            tur ſecans Verticalem H I k L, in R. </s>
            <s xml:id="echoid-s4576" xml:space="preserve">Nam K S, dimidium arcus K R, erit declinatio Verticalis H O,
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            à Verticali propriè dicto H I K L, vt perſpicuum eſt ex ijs, quæ in Aſtrolabio demonſtrauimus. </s>
            <s xml:id="echoid-s4577" xml:space="preserve">Comple-
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            mentum igitur I S, erit declinatio eiuſdem à Meridiano circulo. </s>
            <s xml:id="echoid-s4578" xml:space="preserve">Itaque ſi ex quocunque puncto A, lineę
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            vmbrę circulus deſeribatur B T, ęqualis Verticali H I K L, ſumatur{q́ue} arcus B T, ęqualis arcui I S, ab
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            ortu quidem verſus auſtrum, ſi obſeruatio fiat ante meridiem, & </s>
            <s xml:id="echoid-s4579" xml:space="preserve">Verticalis H O, deftectat verſus au-
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            ſtrum ex parte orientali, vt in exemplo; </s>
            <s xml:id="echoid-s4580" xml:space="preserve">vel ab ortu verſus boream, ſi obſeruatio ante meridiem fiat, & </s>
            <s xml:id="echoid-s4581" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0103-05" xlink:href="note-0103-05a" xml:space="preserve">50</note>
            Verticalis H O, ex parte orient ali deflectat verſus boream: </s>
            <s xml:id="echoid-s4582" xml:space="preserve">Ab occaſu vero eodem modo verſus au-
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            ſtrum vel boream, ſi obſeruatio poſt meridiem fiat, & </s>
            <s xml:id="echoid-s4583" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4584" xml:space="preserve">crit recta ducta A T, linea meridiana, nimirum
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            communis ſectio plani propoſiti, & </s>
            <s xml:id="echoid-s4585" xml:space="preserve">Meridiani circuli.</s>
            <s xml:id="echoid-s4586" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s4587" xml:space="preserve">EADEM hęc declinatio K S, Verticalis H O, à Verticali proprie dicto H I K L, ex calculo ſi-
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              <note position="right" xlink:label="note-0103-06" xlink:href="note-0103-06a" xml:space="preserve">Inuentio lineæ
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              meridianæ per
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              ſinus.</note>
            nuum inueniri, atque adeo & </s>
            <s xml:id="echoid-s4588" xml:space="preserve">ipſa linea meridiana duci poteſt. </s>
            <s xml:id="echoid-s4589" xml:space="preserve">Si enim ex declinatione Solis, & </s>
            <s xml:id="echoid-s4590" xml:space="preserve">altitu-
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            dine, quam habet Sol tempore obſeruationis, ex ſinubus inueniatur diſtantia Solis à Meridiano circulo,
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            vt propoſ. </s>
            <s xml:id="echoid-s4591" xml:space="preserve">36. </s>
            <s xml:id="echoid-s4592" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s4593" xml:space="preserve">docebimus, & </s>
            <s xml:id="echoid-s4594" xml:space="preserve">per hanc diſtantiam, ex eiſdem ſinubus inueſtigetur circunferen-
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            tia horizontalis, id eſt, arcus Horizontis interiectus inter Verticalem propriè dictum, & </s>
            <s xml:id="echoid-s4595" xml:space="preserve">Verticalem
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            qui per centrum Solis tempore obſeruationis tranſit, vt propoſ. </s>
            <s xml:id="echoid-s4596" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4597" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4598" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4599" xml:space="preserve">oſtendemus, erit hæc circunfe-
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            rentia circunferentiæ K S, æqualis, & </s>
            <s xml:id="echoid-s4600" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4601" xml:space="preserve"/>
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            <s xml:id="echoid-s4602" xml:space="preserve">IMMO ſine deſcriptione Aſtrolabij per ſolum Analemma eandem meridianam lineam </s>
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