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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      <text xml:lang="it" type="free">
        <div xml:id="echoid-div659" type="section" level="1" n="170">
          <p style="it">
            <s xml:id="echoid-s12369" xml:space="preserve">
              <pb o="190" file="0210" n="210" rhead="GNOMONICES"/>
            ſinum complementi arcus E G, Eclipticæ dati, ita ſinus totus ad ſinum complementi arcus B G, aſcenſio-
              <lb/>
            nis rectæ. </s>
            <s xml:id="echoid-s12370" xml:space="preserve">Quocirca ſi fiat, vt ſinus complementi declinationis puncti Eclipticæ propoſiti ad ſinum com-
              <lb/>
            plementi arcus Eclipticæ inter datum punctum, & </s>
            <s xml:id="echoid-s12371" xml:space="preserve">principium ♈, ita ſinus totus ad aliud, proueniet ſi-
              <lb/>
            nus complementi aſcenſionis rectæ. </s>
            <s xml:id="echoid-s12372" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s12373" xml:space="preserve">Ponatur punctum E, grad. </s>
            <s xml:id="echoid-s12374" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12375" xml:space="preserve">♊, ita vt arcus Ecli-
              <lb/>
              <figure xlink:label="fig-0210-01" xlink:href="fig-0210-01a" number="149">
                <image file="0210-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0210-01"/>
              </figure>
              <note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">10</note>
            pticæ G E, complectatur grad. </s>
            <s xml:id="echoid-s12376" xml:space="preserve">70. </s>
            <s xml:id="echoid-s12377" xml:space="preserve">& </s>
            <s xml:id="echoid-s12378" xml:space="preserve">arcus B E, declinationis, ex coroll. </s>
            <s xml:id="echoid-s12379" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12380" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12381" xml:space="preserve">pręcedentis libri in-
              <lb/>
              <note position="left" xlink:label="note-0210-02" xlink:href="note-0210-02a" xml:space="preserve">20</note>
            uentus, grad. </s>
            <s xml:id="echoid-s12382" xml:space="preserve">22. </s>
            <s xml:id="echoid-s12383" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12384" xml:space="preserve">0. </s>
            <s xml:id="echoid-s12385" xml:space="preserve">Itaque ſi fiat, vt 92718. </s>
            <s xml:id="echoid-s12386" xml:space="preserve">ſinus complementi declinationis ad 34202. </s>
            <s xml:id="echoid-s12387" xml:space="preserve">ſinum cõ-
              <lb/>
            plementi arcus Eclipticę B E, dati, ita 100000. </s>
            <s xml:id="echoid-s12388" xml:space="preserve">ſinus totus ad aliud, inuenietur hic ferme ſinus 36888.
              <lb/>
            </s>
            <s xml:id="echoid-s12389" xml:space="preserve">cui reſpondet arcus grad. </s>
            <s xml:id="echoid-s12390" xml:space="preserve">21. </s>
            <s xml:id="echoid-s12391" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12392" xml:space="preserve">39. </s>
            <s xml:id="echoid-s12393" xml:space="preserve">cuius complementum grad. </s>
            <s xml:id="echoid-s12394" xml:space="preserve">68. </s>
            <s xml:id="echoid-s12395" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12396" xml:space="preserve">21. </s>
            <s xml:id="echoid-s12397" xml:space="preserve">dabit aſcenſionem rectam
              <lb/>
            grad. </s>
            <s xml:id="echoid-s12398" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12399" xml:space="preserve">♊. </s>
            <s xml:id="echoid-s12400" xml:space="preserve">atque ita de cęteris. </s>
            <s xml:id="echoid-s12401" xml:space="preserve">Hac arte ſupputari poſſunt aſcenſiones rectæ omnium arcuum Eclipti
              <lb/>
            cæ à principio ♈, vſque ad finem ♊.</s>
            <s xml:id="echoid-s12402" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12403" xml:space="preserve">QVOD ſi arcus Eclipticę G E, ſit quadrans, hoc eſt, E, ſit principium ♋, erit quoque eius aſcenſio
              <lb/>
              <note position="left" xlink:label="note-0210-03" xlink:href="note-0210-03a" xml:space="preserve">Quando arcus
                <lb/>
              E
                <unsure/>
              c
                <unsure/>
              lipticæ eſt
                <lb/>
              @uadrans.</note>
            recta G B, quadrans. </s>
            <s xml:id="echoid-s12404" xml:space="preserve">Quoniam enim in triangulo B E G, angulus B, rectus eſt, & </s>
            <s xml:id="echoid-s12405" xml:space="preserve">arcus G E, quadrans,
              <lb/>
            erit per propoſ. </s>
            <s xml:id="echoid-s12406" xml:space="preserve">36. </s>
            <s xml:id="echoid-s12407" xml:space="preserve">noſtrorum triangulorum ſphęricorum, ſaltem alter reliquorum quadrans. </s>
            <s xml:id="echoid-s12408" xml:space="preserve">Cum ergo
              <lb/>
            B E, minor ſit quadrante, nempe declinationi maxime
              <unsure/>
            Solis æqualis, erit G B, quadrans. </s>
            <s xml:id="echoid-s12409" xml:space="preserve">Quod etiam ita
              <lb/>
            confirmari poteſt. </s>
            <s xml:id="echoid-s12410" xml:space="preserve">Quoniam arcus Eclipticæ G E, quadrans eſt, & </s>
            <s xml:id="echoid-s12411" xml:space="preserve">G, principium ♈, tranſibit per punctũ
              <lb/>
              <note position="left" xlink:label="note-0210-04" xlink:href="note-0210-04a" xml:space="preserve">30</note>
            E, colurus ſolſtitiorum, cum arcus Eclipticæ inter principium ♈, & </s>
            <s xml:id="echoid-s12412" xml:space="preserve">colurum ſolstitiorum ſit quadrans.
              <lb/>
            </s>
            <s xml:id="echoid-s12413" xml:space="preserve">Cum ergo idem colurus per polos mundi ducatur, non differet à circulo maximo A B C D; </s>
            <s xml:id="echoid-s12414" xml:space="preserve">ac proinde,
              <lb/>
            cum arcus Aequatoris inter principium ♈, & </s>
            <s xml:id="echoid-s12415" xml:space="preserve">colurum ſolſtitiorum ſit quadrans, erit omnino arcus
              <lb/>
            G B, quadrans.</s>
            <s xml:id="echoid-s12416" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12417" xml:space="preserve">SI arcus datus Eclipticæ ſit quadrante maior, minor autem ſemicirculo, ita vt v.</s>
            <s xml:id="echoid-s12418" xml:space="preserve">g. </s>
            <s xml:id="echoid-s12419" xml:space="preserve">punctum E, ſit
              <lb/>
              <note position="left" xlink:label="note-0210-05" xlink:href="note-0210-05a" xml:space="preserve">Quando arcus
                <lb/>
              Eclipticę maior
                <lb/>
              eſt quadrante,
                <lb/>
              at ſemicirculo
                <lb/>
              minor.</note>
            grad. </s>
            <s xml:id="echoid-s12420" xml:space="preserve">20. </s>
            <s xml:id="echoid-s12421" xml:space="preserve">♋, & </s>
            <s xml:id="echoid-s12422" xml:space="preserve">arcus datus comprehendat grad. </s>
            <s xml:id="echoid-s12423" xml:space="preserve">110. </s>
            <s xml:id="echoid-s12424" xml:space="preserve">Detrahemus ipſum ex ſemicirculo, & </s>
            <s xml:id="echoid-s12425" xml:space="preserve">reliqui ar-
              <lb/>
            cus grad. </s>
            <s xml:id="echoid-s12426" xml:space="preserve">70. </s>
            <s xml:id="echoid-s12427" xml:space="preserve">ab altero ęquinoctio inchoati aſcenſionem rectam inuestigabimus, vt prius, eam{q́ue} ex ſemi-
              <lb/>
            circulo auferemus. </s>
            <s xml:id="echoid-s12428" xml:space="preserve">Remanebit enim aſcenſio recta arcus propoſiti, cum totus ſemicir culus ab ♈, vſque
              <lb/>
            ad ♎, habeat reſpondentem ſemicirculum Aequatoris pro aſcenſione recta. </s>
            <s xml:id="echoid-s12429" xml:space="preserve">Vt quoniam grad. </s>
            <s xml:id="echoid-s12430" xml:space="preserve">70. </s>
            <s xml:id="echoid-s12431" xml:space="preserve">ha-
              <lb/>
            bent aſcenſionem rectam grad. </s>
            <s xml:id="echoid-s12432" xml:space="preserve">68. </s>
            <s xml:id="echoid-s12433" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12434" xml:space="preserve">21. </s>
            <s xml:id="echoid-s12435" xml:space="preserve">quę ablata ex grad. </s>
            <s xml:id="echoid-s12436" xml:space="preserve">180. </s>
            <s xml:id="echoid-s12437" xml:space="preserve">relinquit aſcenſionem rectam grad.
              <lb/>
            </s>
            <s xml:id="echoid-s12438" xml:space="preserve">
              <note position="left" xlink:label="note-0210-06" xlink:href="note-0210-06a" xml:space="preserve">40</note>
            111. </s>
            <s xml:id="echoid-s12439" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12440" xml:space="preserve">39. </s>
            <s xml:id="echoid-s12441" xml:space="preserve">reſpondentem arcui Eclipticæ grad. </s>
            <s xml:id="echoid-s12442" xml:space="preserve">110. </s>
            <s xml:id="echoid-s12443" xml:space="preserve">hoc eſt, gradui 20. </s>
            <s xml:id="echoid-s12444" xml:space="preserve">♋.</s>
            <s xml:id="echoid-s12445" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12446" xml:space="preserve">AT ſi arcus Eclipticæ à principio ♈, inchoatus ſit ſemicirculus, ita vt in principio ♎, finiatur, erit
              <lb/>
              <note position="left" xlink:label="note-0210-07" xlink:href="note-0210-07a" xml:space="preserve">Quando arcus
                <unsure/>
                <lb/>
              Eclipticæ ſemi-
                <lb/>
              circulus eſt.</note>
            quoque eius recta aſcenſio ſemicirculus, vt patet.</s>
            <s xml:id="echoid-s12447" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12448" xml:space="preserve">ARCV Eclipticę ſemicirculum ſuperante, ita tamen, vt tribus quadrantibus minor ſit, auferemus
              <lb/>
              <note position="left" xlink:label="note-0210-08" xlink:href="note-0210-08a" xml:space="preserve">Quando arcus
                <lb/>
              Eclipticæ ſemi-
                <lb/>
              circulo maior
                <lb/>
              eſt, minor autẽ
                <lb/>
              tribus quadran
                <lb/>
              tibus.</note>
            ex eo ſemicirculum, & </s>
            <s xml:id="echoid-s12449" xml:space="preserve">reliqui arcus à principio ♎, inchoati aſcenſionem rectam inuentam, vt prius, ſe-
              <lb/>
            micirculo adijciemus, vt habeamus aſcenſionem rectam dati arcus. </s>
            <s xml:id="echoid-s12450" xml:space="preserve">Vt ſi quęratur recta aſcenſio grad.
              <lb/>
            </s>
            <s xml:id="echoid-s12451" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12452" xml:space="preserve">♐, ita vt totus arcus Eclipticę à principio ♈, computatus contineat grad. </s>
            <s xml:id="echoid-s12453" xml:space="preserve">250. </s>
            <s xml:id="echoid-s12454" xml:space="preserve">Detracto ſemicir-
              <lb/>
            culo ex grad. </s>
            <s xml:id="echoid-s12455" xml:space="preserve">250. </s>
            <s xml:id="echoid-s12456" xml:space="preserve">reliqui fiunt grad. </s>
            <s xml:id="echoid-s12457" xml:space="preserve">70. </s>
            <s xml:id="echoid-s12458" xml:space="preserve">huius arcus aſcenſio recta grad. </s>
            <s xml:id="echoid-s12459" xml:space="preserve">68. </s>
            <s xml:id="echoid-s12460" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12461" xml:space="preserve">21. </s>
            <s xml:id="echoid-s12462" xml:space="preserve">inuenta, vt prius, ſi
              <lb/>
            addatur ſemicir culo, conficientur grad. </s>
            <s xml:id="echoid-s12463" xml:space="preserve">248. </s>
            <s xml:id="echoid-s12464" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12465" xml:space="preserve">21. </s>
            <s xml:id="echoid-s12466" xml:space="preserve">pro aſcenſione recta oblati arcus.</s>
            <s xml:id="echoid-s12467" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12468" xml:space="preserve">SI verò datus arcus comprehendat tres quadrantes, habebit eius aſcenſio recta tres ctiam qua-
              <lb/>
              <note position="left" xlink:label="note-0210-09" xlink:href="note-0210-09a" xml:space="preserve">Quando arcus
                <lb/>
              Eclipticæ com-
                <lb/>
              plectitur tres
                <lb/>
              quadrantes.</note>
              <note position="left" xlink:label="note-0210-10" xlink:href="note-0210-10a" xml:space="preserve">50</note>
            drantes, vt ex dictis patet. </s>
            <s xml:id="echoid-s12469" xml:space="preserve">Nam prior ſemicirculus habet ſemicirculum, & </s>
            <s xml:id="echoid-s12470" xml:space="preserve">reliquus quadrans qua-
              <lb/>
            drantem, & </s>
            <s xml:id="echoid-s12471" xml:space="preserve">c.</s>
            <s xml:id="echoid-s12472" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12473" xml:space="preserve">SI denique propoſitus arcus tres quadrantes ſuperauerit, auferendus erit ex toto circulo, & </s>
            <s xml:id="echoid-s12474" xml:space="preserve">reliqui
              <lb/>
              <note position="left" xlink:label="note-0210-11" xlink:href="note-0210-11a" xml:space="preserve">Quando arcus
                <lb/>
              Eclipticæ tribus
                <lb/>
              quadrantibus
                <lb/>
              maior eſt.</note>
            arcus ab ♈, inchoati aſcenſio recta inuenta, vt antea, ex toto circulo detrahenda. </s>
            <s xml:id="echoid-s12475" xml:space="preserve">Relinquetur enim re-
              <lb/>
            cta aſcenſio datiarcus, cum tota Ecliptica cum toto Aequatore aſcendat. </s>
            <s xml:id="echoid-s12476" xml:space="preserve">Vt ſidatus arcus contineat
              <lb/>
            grad. </s>
            <s xml:id="echoid-s12477" xml:space="preserve">290. </s>
            <s xml:id="echoid-s12478" xml:space="preserve">ita vt terminetur ingrad. </s>
            <s xml:id="echoid-s12479" xml:space="preserve">20. </s>
            <s xml:id="echoid-s12480" xml:space="preserve">♑, deducemus grad. </s>
            <s xml:id="echoid-s12481" xml:space="preserve">290. </s>
            <s xml:id="echoid-s12482" xml:space="preserve">ex 360. </s>
            <s xml:id="echoid-s12483" xml:space="preserve">& </s>
            <s xml:id="echoid-s12484" xml:space="preserve">reliqui arcus grad. </s>
            <s xml:id="echoid-s12485" xml:space="preserve">70.
              <lb/>
            </s>
            <s xml:id="echoid-s12486" xml:space="preserve">aſcenſionem rectam grad. </s>
            <s xml:id="echoid-s12487" xml:space="preserve">68. </s>
            <s xml:id="echoid-s12488" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12489" xml:space="preserve">21. </s>
            <s xml:id="echoid-s12490" xml:space="preserve">inuentam, vt prius, ex grad. </s>
            <s xml:id="echoid-s12491" xml:space="preserve">360. </s>
            <s xml:id="echoid-s12492" xml:space="preserve">ſubducemus, vt relinquantur
              <lb/>
            grad. </s>
            <s xml:id="echoid-s12493" xml:space="preserve">291. </s>
            <s xml:id="echoid-s12494" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12495" xml:space="preserve">39. </s>
            <s xml:id="echoid-s12496" xml:space="preserve">pro aſcenſione recta arcus propoſiti.</s>
            <s xml:id="echoid-s12497" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12498" xml:space="preserve">PERSPICVVM eſt ex his, qua ratione tabula aſcenſionum rectarum ſit conſtruenda. </s>
            <s xml:id="echoid-s12499" xml:space="preserve">Nam ſi
              <lb/>
              <note position="left" xlink:label="note-0210-12" xlink:href="note-0210-12a" xml:space="preserve">Quo pacto tabu
                <lb/>
              la aſcenſionum
                <lb/>
              rectarum con-
                <lb/>
              ſtruenda.</note>
            aſcenſiones rectę inueſtigentur omnium ar cuum Eclipticę à principio ♈, vſque ad finem ♊, babebimus
              <lb/>
            aſcenſiones rectas omnium punctorum primi quadrantis Eclipticę. </s>
            <s xml:id="echoid-s12500" xml:space="preserve">Quod ſi ſingulas ex ſemicirculo </s>
          </p>
        </div>
      </text>
    </echo>
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