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 figures

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            <s xml:id="echoid-s42897" xml:space="preserve">
              <pb o="652" file="0668" n="668" rhead="GNOMONICES"/>
            uenirentur, vt perſpicuum eſt, ſi res paulo diligentius conſideretur.</s>
            <s xml:id="echoid-s42898" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Inuentio decli-
            <lb/>
          nationum om-
            <lb/>
          nium punctor
            <unsure/>
          ũ
            <lb/>
          Eclip@icæ in A-
            <lb/>
          nalẽmate, una
            <lb/>
          c
            <unsure/>
          um demonſtra
            <lb/>
          tione.</note>
          <p>
            <s xml:id="echoid-s42899" xml:space="preserve">CVM hæc demonſtrarem, venit mihi in mentem, eadem fere ratione demonſtrari poſſe con
              <lb/>
            ſtructionem Analemmatis lib. </s>
            <s xml:id="echoid-s42900" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42901" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s42902" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42903" xml:space="preserve">traditam, ac multò quidem facilius, quàm ibi. </s>
            <s xml:id="echoid-s42904" xml:space="preserve">Sit
              <lb/>
            enim Meridianus Analemmatis A B C D, circa centrum E, in quo diameter Horizontis B D; </s>
            <s xml:id="echoid-s42905" xml:space="preserve">Ver-
              <lb/>
            ticalis A C; </s>
            <s xml:id="echoid-s42906" xml:space="preserve">Aequatoris H I; </s>
            <s xml:id="echoid-s42907" xml:space="preserve">axis mundi F G; </s>
            <s xml:id="echoid-s42908" xml:space="preserve">diametri parallelorum ſemper apparentium, ſem-
              <lb/>
            perq́ue latentium maximorum D k, B L. </s>
            <s xml:id="echoid-s42909" xml:space="preserve">Supputata maxima declinatione à puncto H, ad vtraſq;
              <lb/>
            </s>
            <s xml:id="echoid-s42910" xml:space="preserve">partes, vſque ad M, & </s>
            <s xml:id="echoid-s42911" xml:space="preserve">N, iungatur recta M N, quæ in O, bifariam, & </s>
            <s xml:id="echoid-s42912" xml:space="preserve">ad angulos rectos ſecabitur,
              <lb/>
              <figure xlink:label="fig-0668-01" xlink:href="fig-0668-01a" number="429">
                <image file="0668-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0668-01"/>
              </figure>
            vt propoſ. </s>
            <s xml:id="echoid-s42913" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42914" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42915" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42916" xml:space="preserve">oſtenſum eſt. </s>
            <s xml:id="echoid-s42917" xml:space="preserve">Deſcripto quo-
              <lb/>
            que ex O, circa M N, circulo M P N Q, eoq́;
              <lb/>
            </s>
            <s xml:id="echoid-s42918" xml:space="preserve">diuiſo in 12. </s>
            <s xml:id="echoid-s42919" xml:space="preserve">partes æquales, ducãtur per quæ-
              <lb/>
              <note position="left" xlink:label="note-0668-02" xlink:href="note-0668-02a" xml:space="preserve">10</note>
            libet bina puncta à P Q, æqualiter diſtantia li-
              <lb/>
            neę rectæ Y S λ, X R μ, Z T ξ, α V π, quæ ex
              <lb/>
            ſcholio propoſ. </s>
            <s xml:id="echoid-s42920" xml:space="preserve">27. </s>
            <s xml:id="echoid-s42921" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42922" xml:space="preserve">3. </s>
            <s xml:id="echoid-s42923" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s42924" xml:space="preserve">æquidiſtabunt
              <lb/>
            rectæ Q P I. </s>
            <s xml:id="echoid-s42925" xml:space="preserve">Ducentur autem magis exquiſite
              <lb/>
            huiuſmodi parallelæ, ſi à puncto I, ſupputetur
              <lb/>
            quoque vtrinque maxima Solis declinatio vſ-
              <lb/>
            quead θ, & </s>
            <s xml:id="echoid-s42926" xml:space="preserve">ρ, iunctaq́ue recta θ ρ, ſemicircu-
              <lb/>
            lus ex puncto 8, deſcribatur, qui in ſex æquales
              <lb/>
            partes ſecetur, &</s>
            <s xml:id="echoid-s42927" xml:space="preserve">c. </s>
            <s xml:id="echoid-s42928" xml:space="preserve">vt propoſ. </s>
            <s xml:id="echoid-s42929" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42930" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42931" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42932" xml:space="preserve">monui-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s42933" xml:space="preserve">Poſtremo iungantur rectę M θ, N ρ, quæ
              <lb/>
              <note position="left" xlink:label="note-0668-03" xlink:href="note-0668-03a" xml:space="preserve">20</note>
            ex eodem ſcholio ipſi H I, æquidiſtabunt. </s>
            <s xml:id="echoid-s42934" xml:space="preserve">Dico
              <lb/>
            haſce rectas diametros eſſe parallelorum, nem-
              <lb/>
            pe communes eorum cum Meridiano ſectio-
              <lb/>
            nes, ita vt arcus H γ, H ß, H δ, H ε, metiantur
              <lb/>
            declinationes aliorum parallelorum, qui per ſi-
              <lb/>
            gnorum initia ducũtur, quemadmodum H M,
              <lb/>
            H N, maximas declinationes Solis metiuntur:
              <lb/>
            </s>
            <s xml:id="echoid-s42935" xml:space="preserve">hoc ordine, vt arcus H γ, H ß, metiantur declinationes illorum punctorũ Eclipticę, quæ à prin-
              <lb/>
            cipio ♋, verſus ♈, vel ♎, tot gradibus abſunt, quot gradibus puncta X, Y, R, S, à puncto M, di-
              <lb/>
            ſtant; </s>
            <s xml:id="echoid-s42936" xml:space="preserve">arcus autem H δ, H ε
              <unsure/>
            , illorum punctorum Eclipticæ declinationes metiantur, quæ tantum
              <lb/>
              <note position="left" xlink:label="note-0668-04" xlink:href="note-0668-04a" xml:space="preserve">30</note>
            à principio ♑, verſus ♈, vel ♎, diſtant, quanto ſpatio puncta Z, α, T, V, in ſuo circulo à puncto
              <lb/>
            N, abſunt. </s>
            <s xml:id="echoid-s42937" xml:space="preserve">Quod ita demonſtrabitur. </s>
            <s xml:id="echoid-s42938" xml:space="preserve">Ducta recta M ρ, quæ diameter erit Eclipticæ, poſito princi
              <lb/>
            pio ♋, in M, & </s>
            <s xml:id="echoid-s42939" xml:space="preserve">principio ♑, in ρ; </s>
            <s xml:id="echoid-s42940" xml:space="preserve">ſecetq́ue M ρ, rectã X R μ, verbi gratia, in p, & </s>
            <s xml:id="echoid-s42941" xml:space="preserve">ex p, ad M ρ, per-
              <lb/>
            pendicularis ducatur p b, intelligaturq́; </s>
            <s xml:id="echoid-s42942" xml:space="preserve">ſemicirculus M b ρ, inſtar Eclipticæ cõuerti circa M ρ, do
              <lb/>
            nec rectus ſit ad Meridianum A B C D. </s>
            <s xml:id="echoid-s42943" xml:space="preserve">Eſt enim in eo ſitu planum Eclipticæ rectum ad Meri-
              <lb/>
            dianum, ex propoſ. </s>
            <s xml:id="echoid-s42944" xml:space="preserve">15. </s>
            <s xml:id="echoid-s42945" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42946" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42947" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s42948" xml:space="preserve">cum Meridianus per eius polos ducatur. </s>
            <s xml:id="echoid-s42949" xml:space="preserve">Concipiatur quo-
              <lb/>
            que per b, punctum Eclipticæ duci circulus Aequatori æquidiſtans, & </s>
            <s xml:id="echoid-s42950" xml:space="preserve">ad Meridianum rectus. </s>
            <s xml:id="echoid-s42951" xml:space="preserve">Et
              <lb/>
            quoniam tam Ecliptica, quàm hic parallelus rectus eſt ad Meridianum, erit quoque communis
              <lb/>
            eorum ſectio per punctum b, tranſiens ad Meridianum recta: </s>
            <s xml:id="echoid-s42952" xml:space="preserve">Eſt autem b p, ad Meridianum per-
              <lb/>
              <note position="left" xlink:label="note-0668-05" xlink:href="note-0668-05a" xml:space="preserve">19. vndec.</note>
            pendicularis, ex defin. </s>
            <s xml:id="echoid-s42953" xml:space="preserve">4. </s>
            <s xml:id="echoid-s42954" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42955" xml:space="preserve">11. </s>
            <s xml:id="echoid-s42956" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s42957" xml:space="preserve">Igitur b p, communis ſectio erit Eclipticę, & </s>
            <s xml:id="echoid-s42958" xml:space="preserve">paralleli per
              <lb/>
              <note position="left" xlink:label="note-0668-06" xlink:href="note-0668-06a" xml:space="preserve">40</note>
            b, ducti; </s>
            <s xml:id="echoid-s42959" xml:space="preserve">atque adeo dictus parallelus Meridianum ſecabit in p. </s>
            <s xml:id="echoid-s42960" xml:space="preserve">Cum ergo Meridianus in Aequa-
              <lb/>
            tore, & </s>
            <s xml:id="echoid-s42961" xml:space="preserve">dicto parallelo faciat communes ſectiones parallelas, erit recta X R μ, per p, ducta paralle
              <lb/>
              <note position="left" xlink:label="note-0668-07" xlink:href="note-0668-07a" xml:space="preserve">16. vndec.</note>
            la diametro Aequatoris H I, communis ſectio dicti paralleli, & </s>
            <s xml:id="echoid-s42962" xml:space="preserve">Meridiani, hoc eſt, diameter ip-
              <lb/>
            ſius paralleli. </s>
            <s xml:id="echoid-s42963" xml:space="preserve">Quocirca arcus H γ, declinatio erit eiuſdem paralleli, ſeu puncti Eclipticæ b: </s>
            <s xml:id="echoid-s42964" xml:space="preserve">Eſt
              <lb/>
            autem arcus Eclipticę M b, ſimilis arcui M X, in circulo M P N Q, ex lemmate propoſ. </s>
            <s xml:id="echoid-s42965" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42966" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42967" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s42968" xml:space="preserve">propterea quòd ita ſe habet M E, ſinus totus Eclipticæ ad M O, ſinum totum circuli M P N Q,
              <lb/>
              <note position="left" xlink:label="note-0668-08" xlink:href="note-0668-08a" xml:space="preserve">4. ſex@@</note>
            vt M p, ſinus verſus arcus M b, ad M φ, ſinum verſum arcus M X. </s>
            <s xml:id="echoid-s42969" xml:space="preserve">Igitur recta X R μ, ducta dia-
              <lb/>
            metro Aequatoris parallela per punctum X, dat in Meridiano arcũ H γ, declinationis puncti Ecli
              <lb/>
            pticę b, quod totidẽ gradibus à puncto M, diſtat, quot gradibus punctũ X, ab eodẽ puncto M, di-
              <lb/>
            ſtat in circulo M P N Q. </s>
            <s xml:id="echoid-s42970" xml:space="preserve">Eademq́; </s>
            <s xml:id="echoid-s42971" xml:space="preserve">eſt ratio de alijs. </s>
            <s xml:id="echoid-s42972" xml:space="preserve">quod demonſtrandum erat. </s>
            <s xml:id="echoid-s42973" xml:space="preserve">Ex hac demõſtra-
              <lb/>
              <note position="left" xlink:label="note-0668-09" xlink:href="note-0668-09a" xml:space="preserve">50</note>
            tione liquido cõſtat, ſi circulus A B C D, ſecetur in 12. </s>
            <s xml:id="echoid-s42974" xml:space="preserve">partes æquales, hoc eſt, in partes ſimiles
              <lb/>
            partibus circuli M P N Q, initio facto à puncto M, & </s>
            <s xml:id="echoid-s42975" xml:space="preserve">quælibet bina puncta æqualiter remota ab
              <lb/>
            M, rectis lineis iungantur a 7, b 6, d 5, e 4, 23, quæ perpendiculares ſunt ad M ρ, in punctis l,
              <lb/>
            p, E, q, u, (quod demonſtrabitur, vt propoſ. </s>
            <s xml:id="echoid-s42976" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42977" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42978" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42979" xml:space="preserve">oſtenſum eſt, rectam
              <unsure/>
            M N, ſectam eſſe ad rectos
              <lb/>
            angulos) rectas per hæc puncta ductas rectæ H I, parallelas, quales ſunt ß λ, γ μ, δ ξ, ε π, auferre
              <unsure/>
              <lb/>
            quoque ex Meridiano arcus declinationum. </s>
            <s xml:id="echoid-s42980" xml:space="preserve">Id quod & </s>
            <s xml:id="echoid-s42981" xml:space="preserve">in ſcholio propoſ. </s>
            <s xml:id="echoid-s42982" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42983" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42984" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42985" xml:space="preserve">tradidimus.
              <lb/>
            </s>
            <s xml:id="echoid-s42986" xml:space="preserve">Hoc enim
              <unsure/>
            demonſtrauimus de puncto b, quod tot gradibus abeſt ab M, in circulo A B C D, quot
              <lb/>
            gradibus punctum X, diſtat in circulo M P N Q, ab M, eademq́ue ratio eſt de cęteris.</s>
            <s xml:id="echoid-s42987" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s42988" xml:space="preserve">ANTEQVAM huic operi extremam manum apponerem, ſedulo in eam curam incumbe-
              <lb/>
            bam, vt praxim illam ſcholij propoſ. </s>
            <s xml:id="echoid-s42989" xml:space="preserve">33. </s>
            <s xml:id="echoid-s42990" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42991" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42992" xml:space="preserve">qua Andreas Schonerus breuiſſime ac facilime
              <lb/>
            radios arcuum diurnorum inquirit, ratione aliqua Geometrica corroborarem: </s>
            <s xml:id="echoid-s42993" xml:space="preserve">quam cum </s>
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