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-div659" type="section" level="1" n="170">
          <p style="it">
            <s xml:id="echoid-s12608" xml:space="preserve">
              <pb o="192" file="0212" n="212" rhead="GNOMONICES"/>
            nationes, & </s>
            <s xml:id="echoid-s12609" xml:space="preserve">latitudines ortiuas, liquido conſtat, differentias inter aſcenſiones rectas, & </s>
            <s xml:id="echoid-s12610" xml:space="preserve">obliquas om-
              <lb/>
            nium punctorum prioris quadrantis Eclipticæ ad quamuis poli altitudinem compertas, æquales eſſe diffe-
              <lb/>
            rentijs aſcenſionum omnium punctorum trium poſteriorum quadrantum Eclipticæ in eadem altitudine
              <lb/>
            poli. </s>
            <s xml:id="echoid-s12611" xml:space="preserve">Quocirca ſatis erit, ſi inquir antur differentiæ aſcenſionum conuenientes punctis prioris quadrantis
              <lb/>
            Eclipticæ à principio ♈, vſque ad principium ♋.</s>
            <s xml:id="echoid-s12612" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12613" xml:space="preserve">EX his porrò differentijs aſcenſionum prioris quadrantis Eclipticæ, ita tabulam aſcenſionum obli-
              <lb/>
              <note position="left" xlink:label="note-0212-01" xlink:href="note-0212-01a" xml:space="preserve">Quo pacto ta-
                <lb/>
              bula aſcenſio-
                <lb/>
              num obliqua-
                <lb/>
              rum ex differẽ-
                <lb/>
              tiis aſcenſio na-
                <lb/>
              libus compona
                <lb/>
              tu
                <unsure/>
              r
                <unsure/>
              .</note>
            quarum omnium punctorum Eclipticæ ad datam altitudinem poli, pro qua differentiæ perueſtigatæ ſunt,
              <lb/>
            componemus. </s>
            <s xml:id="echoid-s12614" xml:space="preserve">Quoniam in medietate Eclipticæ ab ♈, vſque ad ♎, perpetuo differentia aſcenſionum
              <lb/>
            detrahenda eſt ab aſcenſione recta, vt obliqua aſcenſio cognita fiat, propterea quòd hæc medietas borea-
              <lb/>
            lis eſt, ac proinde circulus maximus ex polo mundi, per punctum quodlibet illius ductus Aquatorem in-
              <lb/>
              <note position="left" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">10</note>
            fra Horizontem ſecat, vt ex priori duarum proximarum figurarum patet, efficitur, vt differentiæ aſcen-
              <lb/>
            ſionum omnium punctorum prioris ſemicirculi ablata ex aſcenſionibus rectis eorundem punctorum re-
              <lb/>
            linquant illorum aſcenſiones obliquas. </s>
            <s xml:id="echoid-s12615" xml:space="preserve">Rurſus quia in altero Eclipticæ ſemicirculo à ♎, vſq; </s>
            <s xml:id="echoid-s12616" xml:space="preserve">ad ♈, diffe
              <lb/>
            rentia aſcenſionum ſemper adijcienda est ad aſcenſionem rectam, vt aſcenſio obliqua cognoſcatur, propte-
              <lb/>
            rea quòd hic ſemicir culus auſtralis eſt, atque adeò circulus maximus ex polo mundi per quoduis punctum
              <lb/>
            illius ductus Aequatorem ſupra Horizontem ſecat, vt conſtat ex posteriori figura proxima, perſpicuum
              <lb/>
            eſt, differentias aſcenſionum omnium punctorum poſterioris huius ſemicirculi additas rectis aſcenſioni-
              <lb/>
            bus eorundem punctorum conficere illorum aſcenſiones obliquas. </s>
            <s xml:id="echoid-s12617" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s12618" xml:space="preserve">Differentia aſcenſionum
              <lb/>
            grad. </s>
            <s xml:id="echoid-s12619" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12620" xml:space="preserve">♉, quam inuenimus ad latitudinem grad. </s>
            <s xml:id="echoid-s12621" xml:space="preserve">42. </s>
            <s xml:id="echoid-s12622" xml:space="preserve">eſſe grad. </s>
            <s xml:id="echoid-s12623" xml:space="preserve">19. </s>
            <s xml:id="echoid-s12624" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12625" xml:space="preserve">7. </s>
            <s xml:id="echoid-s12626" xml:space="preserve">æqualis eſt differentię aſcen-
              <lb/>
            ſionum grad. </s>
            <s xml:id="echoid-s12627" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12628" xml:space="preserve">♌, & </s>
            <s xml:id="echoid-s12629" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s12630" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12631" xml:space="preserve">♏, & </s>
            <s xml:id="echoid-s12632" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s12633" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12634" xml:space="preserve">♒. </s>
            <s xml:id="echoid-s12635" xml:space="preserve">Hæc enim quatuor puncta eandem habent declinatio-
              <lb/>
              <note position="left" xlink:label="note-0212-03" xlink:href="note-0212-03a" xml:space="preserve">20</note>
            nem. </s>
            <s xml:id="echoid-s12636" xml:space="preserve">Siigitur eam detrabamus ex aſcenſione recta grad. </s>
            <s xml:id="echoid-s12637" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12638" xml:space="preserve">♉, hoc eſt, ex grad. </s>
            <s xml:id="echoid-s12639" xml:space="preserve">56. </s>
            <s xml:id="echoid-s12640" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12641" xml:space="preserve">46. </s>
            <s xml:id="echoid-s12642" xml:space="preserve">reliqua
              <lb/>
            erit aſcenſio obliqua grad. </s>
            <s xml:id="echoid-s12643" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12644" xml:space="preserve">♉, nempe grad. </s>
            <s xml:id="echoid-s12645" xml:space="preserve">37. </s>
            <s xml:id="echoid-s12646" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12647" xml:space="preserve">39. </s>
            <s xml:id="echoid-s12648" xml:space="preserve">Item ſi eandem differentiam ſubducamus ex
              <lb/>
            recta aſcenſione grad. </s>
            <s xml:id="echoid-s12649" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12650" xml:space="preserve">♌, nempe ex grad. </s>
            <s xml:id="echoid-s12651" xml:space="preserve">123. </s>
            <s xml:id="echoid-s12652" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12653" xml:space="preserve">14. </s>
            <s xml:id="echoid-s12654" xml:space="preserve">remanebunt grad. </s>
            <s xml:id="echoid-s12655" xml:space="preserve">104. </s>
            <s xml:id="echoid-s12656" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12657" xml:space="preserve">7. </s>
            <s xml:id="echoid-s12658" xml:space="preserve">pro aſcenſione
              <lb/>
            obliqua grad. </s>
            <s xml:id="echoid-s12659" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12660" xml:space="preserve">♌. </s>
            <s xml:id="echoid-s12661" xml:space="preserve">Rurſus ſi eandem differentiam addamus aſcenſioni rectę grad. </s>
            <s xml:id="echoid-s12662" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12663" xml:space="preserve">♏, quæ continet
              <lb/>
            grad. </s>
            <s xml:id="echoid-s12664" xml:space="preserve">236. </s>
            <s xml:id="echoid-s12665" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12666" xml:space="preserve">46. </s>
            <s xml:id="echoid-s12667" xml:space="preserve">conficiemus grad. </s>
            <s xml:id="echoid-s12668" xml:space="preserve">255. </s>
            <s xml:id="echoid-s12669" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12670" xml:space="preserve">53. </s>
            <s xml:id="echoid-s12671" xml:space="preserve">pro aſcenſione obliqua grad. </s>
            <s xml:id="echoid-s12672" xml:space="preserve">29. </s>
            <s xml:id="echoid-s12673" xml:space="preserve">♏. </s>
            <s xml:id="echoid-s12674" xml:space="preserve">Ad extremum
              <lb/>
            ſi apponamus differentiam eandem ad aſcenſionem rectam grad. </s>
            <s xml:id="echoid-s12675" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12676" xml:space="preserve">♒, quæ grad. </s>
            <s xml:id="echoid-s12677" xml:space="preserve">303. </s>
            <s xml:id="echoid-s12678" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12679" xml:space="preserve">14. </s>
            <s xml:id="echoid-s12680" xml:space="preserve">complecti-
              <lb/>
            tur, conflabitur arcus grad. </s>
            <s xml:id="echoid-s12681" xml:space="preserve">322. </s>
            <s xml:id="echoid-s12682" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12683" xml:space="preserve">21. </s>
            <s xml:id="echoid-s12684" xml:space="preserve">pro obliqua aſcenſione grad. </s>
            <s xml:id="echoid-s12685" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12686" xml:space="preserve">♒. </s>
            <s xml:id="echoid-s12687" xml:space="preserve">Eadem{q́ue} de cæteris eſt ha-
              <lb/>
            benda ratio. </s>
            <s xml:id="echoid-s12688" xml:space="preserve">Hæc pauca libuit hocloco deguſtare ex aſcenſionibus rectis, & </s>
            <s xml:id="echoid-s12689" xml:space="preserve">obliquis; </s>
            <s xml:id="echoid-s12690" xml:space="preserve">plura enim alio
              <lb/>
            in loco de eiſdem diſputauimus.</s>
            <s xml:id="echoid-s12691" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
        </div>
        <div xml:id="echoid-div674" type="section" level="1" n="171">
          <head xml:id="echoid-head174" xml:space="preserve">PROBLEMA. 10. PROPOSITIO 10.</head>
          <p>
            <s xml:id="echoid-s12692" xml:space="preserve">HOROLOGIVM Italicum Horizontale conſtituere. </s>
            <s xml:id="echoid-s12693" xml:space="preserve">Hoc eſt
              <lb/>
            lineas horarum ab occaſu Solis in plano Horizonti æquidiſtanti de-
              <lb/>
            ſcribere.</s>
            <s xml:id="echoid-s12694" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12695" xml:space="preserve">SECETVR circulus ex E, deſcriptus propoſ. </s>
            <s xml:id="echoid-s12696" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12697" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s12698" xml:space="preserve">in duas portiones, vt in ſcholio pro-
              <lb/>
              <note position="left" xlink:label="note-0212-05" xlink:href="note-0212-05a" xml:space="preserve">I
                <unsure/>
              talici horolo-
                <lb/>
              gii horizontalis
                <unsure/>
                <lb/>
              compoſitio.</note>
            poſ. </s>
            <s xml:id="echoid-s12699" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12700" xml:space="preserve">præcedentis libri tradidimus, quarum a N b, ſimilis ſit arcui diurno tropici ♋, & </s>
            <s xml:id="echoid-s12701" xml:space="preserve">a M b, ar-
              <lb/>
            cui nocturno eiuſdem tropici. </s>
            <s xml:id="echoid-s12702" xml:space="preserve">Diuiſo autem circulo eodem ex E, deſcripto in partes 24. </s>
            <s xml:id="echoid-s12703" xml:space="preserve">æquales,
              <lb/>
              <note position="left" xlink:label="note-0212-06" xlink:href="note-0212-06a" xml:space="preserve">40</note>
            initio facto à pũcto b, quod occidentale eſt in communi ſectione Horizontis, & </s>
            <s xml:id="echoid-s12704" xml:space="preserve">paralleli a b, (vt
              <lb/>
            conſtat, ſi dictus circulus ex E, deſcriptus in propria poſitione concipiatur collocatus eſſe) tranſi-
              <lb/>
            bunt per hæc puncta diuiſionum, & </s>
            <s xml:id="echoid-s12705" xml:space="preserve">per centrum E, ſi circulus in propria poſitione exiſtat, circuli
              <lb/>
            maximi per polos Mundi, & </s>
            <s xml:id="echoid-s12706" xml:space="preserve">per horas ab occaſu in tropico ♋, ducti, inſtar horariorum circulo-
              <lb/>
            rum à meridie, vel media nocte. </s>
            <s xml:id="echoid-s12707" xml:space="preserve">Quoniam enim circuli maximi per polos mundi ducti diui-
              <lb/>
            dunt tropicum ♋, & </s>
            <s xml:id="echoid-s12708" xml:space="preserve">Aequatorem, per propoſ. </s>
            <s xml:id="echoid-s12709" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12710" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12711" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12712" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s12713" xml:space="preserve">in arcus ſimiles; </s>
            <s xml:id="echoid-s12714" xml:space="preserve">erit arcus Ae-
              <lb/>
            quatoris interceptus inter Meridianum, & </s>
            <s xml:id="echoid-s12715" xml:space="preserve">circulum maximum per horam 24. </s>
            <s xml:id="echoid-s12716" xml:space="preserve">ab occaſu in tropi-
              <lb/>
            co ♋, hoc eſt, per punctum, vbi tropicus ♋, Horizontem ſecat, ductum, ſimilis arcui tropici ♋,
              <lb/>
            inter eoſdem circulos poſito, hoc eſt, arcui ſemidiurno tropici ♋. </s>
            <s xml:id="echoid-s12717" xml:space="preserve">Quoniam vero communes ſe-
              <lb/>
            ctiones, quas dicti circuli maximi cum Æquatore faciunt, per centrum Æquatoris E, ductæ ſe-
              <lb/>
              <note position="left" xlink:label="note-0212-07" xlink:href="note-0212-07a" xml:space="preserve">50</note>
            cant quoque, per ea, quæ ad finem cap. </s>
            <s xml:id="echoid-s12718" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12719" xml:space="preserve">ſphæræ à nobis demonſtrata ſunt, Æquatorem, & </s>
            <s xml:id="echoid-s12720" xml:space="preserve">circu-
              <lb/>
            lum M a N b, ex E, centro Aequatoris, in eiuſdemq́ue plano deſcriptum, in arcus ſimiles; </s>
            <s xml:id="echoid-s12721" xml:space="preserve">erit
              <lb/>
            quoque arcus circuli M a N b, inter dictas ſectiones communes poſitus, ſimilis arcui ſemidiurno
              <lb/>
            tropici ♋. </s>
            <s xml:id="echoid-s12722" xml:space="preserve">Cum ergo M N, ſit ſectio facta in Aequatore à Meridiano, atque adeo Meridianus per
              <lb/>
            punctum N, ducatur, arcusq́; </s>
            <s xml:id="echoid-s12723" xml:space="preserve">N b, ſimilis ſit arcui ſemidiurno tropici ♋, (Quoniam enim totus
              <lb/>
            arcus b N a, ſimilis eſt, per conſtructionem, toti arcui diurno tropici ♋, erit quoque b N, dimidia-
              <lb/>
            tus arcus ipſius b N a, ſemidiurno arcui tropici ♋, ſimilis) atque adeo & </s>
            <s xml:id="echoid-s12724" xml:space="preserve">arcui Aequatoris inter
              <lb/>
            prædictas ſectiones interiecto, tranſibit neceſſario circulus alter maximus per horam 24. </s>
            <s xml:id="echoid-s12725" xml:space="preserve">ab occa-
              <lb/>
            ſu in tropico ♋, ductus, per punctum b. </s>
            <s xml:id="echoid-s12726" xml:space="preserve">Si enim per aliud punctum tranſiret, non auferrent dictæ
              <lb/>
            ſectiones ex Aequatore arcum ſimilem arcui b N, ſed illi, qui inter rectam E N, & </s>
            <s xml:id="echoid-s12727" xml:space="preserve">aliud illud pun-
              <lb/>
            ctum interijceretur. </s>
            <s xml:id="echoid-s12728" xml:space="preserve">Quod eſt abſurdum. </s>
            <s xml:id="echoid-s12729" xml:space="preserve">Oſtendimus enim arcum ex Aequatore ablatum </s>
          </p>
        </div>
      </text>
    </echo>
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