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-s29986" xml:space="preserve">
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            punctis, à quibus ad diametros educantur perpendiculares λ 3, μ 4, ξ 7, π 8, ρ 9, @ 10, φ 11, ψ ω.
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            </s>
            <s xml:id="echoid-s29987" xml:space="preserve">Dico circulum inclinatum ſecare parallelos in punctis 3, 4, 7, 8, 9, 10, 11, ω. </s>
            <s xml:id="echoid-s29988" xml:space="preserve">Cum enim, poſito ſemi-
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            circulo ♋, F R G, in propria poſitione, nimirum ad Meridianum recto, perpendicularis ex 3, in planum
              <lb/>
            Meridiani demiſſa cadat in
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              <figure xlink:label="fig-0470-01" xlink:href="fig-0470-01a" number="309">
                <image file="0470-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0470-01"/>
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            F G, communem ſectionem
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              <note position="left" xlink:label="note-0470-01" xlink:href="note-0470-01a" xml:space="preserve">38. vndec.</note>
            ipſius, ac Meridiani, ſit{q́ue}
              <lb/>
            propterea ad rectam F G,
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            ex defin. </s>
            <s xml:id="echoid-s29989" xml:space="preserve">3. </s>
            <s xml:id="echoid-s29990" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s29991" xml:space="preserve">11. </s>
            <s xml:id="echoid-s29992" xml:space="preserve">Eucl.
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            </s>
            <s xml:id="echoid-s29993" xml:space="preserve">perpendicularis, cadet ne-
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            ceſſario ea perpendicularis
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              <note position="left" xlink:label="note-0470-02" xlink:href="note-0470-02a" xml:space="preserve">10</note>
            in punctum λ, ne ex pun-
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            cto 3, duæ perpendiculares
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            dicantur duci ad rectã F G,
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            quod fieri non poteſt, vt ad
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            propoſ. </s>
            <s xml:id="echoid-s29994" xml:space="preserve">16. </s>
            <s xml:id="echoid-s29995" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s29996" xml:space="preserve">1. </s>
            <s xml:id="echoid-s29997" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s29998" xml:space="preserve">de-
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            monſtratum eſt à nobis ex
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            Proclo. </s>
            <s xml:id="echoid-s29999" xml:space="preserve">Quare recta 3 λ,
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            ad planum Meridiani recta
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            eſt, ac propterea, cum ex
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            propoſ. </s>
            <s xml:id="echoid-s30000" xml:space="preserve">24. </s>
            <s xml:id="echoid-s30001" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s30002" xml:space="preserve">1. </s>
            <s xml:id="echoid-s30003" xml:space="preserve">perpen-
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              <note position="left" xlink:label="note-0470-03" xlink:href="note-0470-03a" xml:space="preserve">20</note>
            diculares à circunferentia
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            circuli inclinati in planum
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            Meridiani demiſſæ cadant
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            quoque in Ellipſim, ſecabit
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            circunferentia circuli incli-
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            nati parallelum ♋, F R G,
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            in puncto 3, ex quo videli-
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            cet perpendicularis in pla-
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            num Meridiani deducta ca-
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            dit in λ; </s>
            <s xml:id="echoid-s30004" xml:space="preserve">& </s>
            <s xml:id="echoid-s30005" xml:space="preserve">ſic de reliquis.
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            </s>
            <s xml:id="echoid-s30006" xml:space="preserve">Abſcindet ergo circulus inclinatus ex parallelo ♋, arcũ F 3; </s>
            <s xml:id="echoid-s30007" xml:space="preserve">ex parallelo ♑, arcũ G 4; </s>
            <s xml:id="echoid-s30008" xml:space="preserve">ex ♉, & </s>
            <s xml:id="echoid-s30009" xml:space="preserve">♍, ar
              <lb/>
              <note position="left" xlink:label="note-0470-04" xlink:href="note-0470-04a" xml:space="preserve">30</note>
            cũ K 7; </s>
            <s xml:id="echoid-s30010" xml:space="preserve">ex ♏, & </s>
            <s xml:id="echoid-s30011" xml:space="preserve">♓, arcum L 8; </s>
            <s xml:id="echoid-s30012" xml:space="preserve">ex ♈, & </s>
            <s xml:id="echoid-s30013" xml:space="preserve">♎, arcum A 9, vel C 10; </s>
            <s xml:id="echoid-s30014" xml:space="preserve">ex ♊, & </s>
            <s xml:id="echoid-s30015" xml:space="preserve">♌, arcum I ω; </s>
            <s xml:id="echoid-s30016" xml:space="preserve">ex ♐ & </s>
            <s xml:id="echoid-s30017" xml:space="preserve">
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            ♒, arcum H 11: </s>
            <s xml:id="echoid-s30018" xml:space="preserve">qui arcus ſcilicet inter Meridianũ, & </s>
            <s xml:id="echoid-s30019" xml:space="preserve">circulum inclinatum interijciuntur. </s>
            <s xml:id="echoid-s30020" xml:space="preserve">Vnde ſi tro
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            picus ♋, F R G, & </s>
            <s xml:id="echoid-s30021" xml:space="preserve">reliqui paralleli in horas diſtribuantur, initio facto ſiue à Meridiano, nempe à pun-
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            cto F, vel G, & </s>
            <s xml:id="echoid-s30022" xml:space="preserve">c. </s>
            <s xml:id="echoid-s30023" xml:space="preserve">more Aſtronomorũ, ſiue ab Horizonte, vt à puncto R, vel S, & </s>
            <s xml:id="echoid-s30024" xml:space="preserve">c. </s>
            <s xml:id="echoid-s30025" xml:space="preserve">more Babyloniorũ,
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            Italorumve, liquido conſtabit, quænã hora, aut horæ particula in punctũ 3. </s>
            <s xml:id="echoid-s30026" xml:space="preserve">vel 7. </s>
            <s xml:id="echoid-s30027" xml:space="preserve">vel 9. </s>
            <s xml:id="echoid-s30028" xml:space="preserve">& </s>
            <s xml:id="echoid-s30029" xml:space="preserve">c. </s>
            <s xml:id="echoid-s30030" xml:space="preserve">cadat.</s>
            <s xml:id="echoid-s30031" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s30032" xml:space="preserve">CAETERVM vt cognoſcamus, an punctum 3. </s>
            <s xml:id="echoid-s30033" xml:space="preserve">vel 7. </s>
            <s xml:id="echoid-s30034" xml:space="preserve">vel 9, & </s>
            <s xml:id="echoid-s30035" xml:space="preserve">c. </s>
            <s xml:id="echoid-s30036" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s30037" xml:space="preserve">hora, vbi
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            parallelus à circulo inclinato ſecatur, ſit ex parte Orientali, Occidentalive, diligenter inſpiciendus erit
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            ſitus, ac poſitio circuli inclinati. </s>
            <s xml:id="echoid-s30038" xml:space="preserve">Hoc enim cognito, facile illud intelligemus, vt paulo infra in ſolutione
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            eiuſdem huius problematis per doctrinam ſinuum docebimus.</s>
            <s xml:id="echoid-s30039" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s30040" xml:space="preserve">QVOD ſi quando Ellipſis diametrum paralleli duobus in locis ſecet citra pumctum, in quo eadem
              <lb/>
              <note position="left" xlink:label="note-0470-05" xlink:href="note-0470-05a" xml:space="preserve">Quando circu-
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              lus inclinatus
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              duobus in locis
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              ſecet patallelũ
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              Solis propoſi-
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              tum.</note>
              <note position="left" xlink:label="note-0470-06" xlink:href="note-0470-06a" xml:space="preserve">40</note>
            diameter ab Horizontis diametro diuiditur, abſcindentur duo arcus ex parallelo, vnus quidem ad par-
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            tes Orientis, alter verò ad partes Occidentis. </s>
            <s xml:id="echoid-s30041" xml:space="preserve">Et ſi circuli ſuperior facies ad occaſum ſpectet, erit
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            punctum vicinius Meridiano orientale, remotius autem occidentale. </s>
            <s xml:id="echoid-s30042" xml:space="preserve">Contra verò ſi ad ortum ſpectet, vt
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            ex ſequentibus magis perſpicuum fiet. </s>
            <s xml:id="echoid-s30043" xml:space="preserve">Hoc autem plerunque accidit in planis per verticem tranſeunti-
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            bus, & </s>
            <s xml:id="echoid-s30044" xml:space="preserve">exiguam declinationem habentibus à Verticali circulo, & </s>
            <s xml:id="echoid-s30045" xml:space="preserve">in alijs nonnullis, vt ex ſphæra ma-
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            teriali intelligi poteſt.</s>
            <s xml:id="echoid-s30046" xml:space="preserve"/>
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            <s xml:id="echoid-s30047" xml:space="preserve">IN circulis ad Meridianũ rectis, qualis eſt Verticalis propriè dictus, & </s>
            <s xml:id="echoid-s30048" xml:space="preserve">omnes circuli, quibus horo
              <lb/>
              <note position="left" xlink:label="note-0470-07" xlink:href="note-0470-07a" xml:space="preserve">Quando circu
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              lus ad Meridia
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              num rectus eſt,
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              qua ratione in
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              quiratur, quæ
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              horæ ſupra v-
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              tramuis faciem
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              contineantur</note>
            logia ad Horizontẽ inclinata æquidiſtãt, res propoſita nullius est negotii ex Analẽmate. </s>
            <s xml:id="echoid-s30049" xml:space="preserve">Nam ſi ex pun
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            cto, vbi cõmunis ſectio circuli propoſiti, & </s>
            <s xml:id="echoid-s30050" xml:space="preserve">Meridiani diametrũ paralleli cuiuslibet interſecat, ad diame
              <lb/>
            trũ paralleli ducatur perpendicularis, ſecabitur circũferentia paralleli in puncto, in quo à dicto circulo
              <lb/>
              <note position="left" xlink:label="note-0470-08" xlink:href="note-0470-08a" xml:space="preserve">50</note>
            ſecatur tam ante meridiẽ, quam poſt meridiem. </s>
            <s xml:id="echoid-s30051" xml:space="preserve">Exemplum habes in proxima figura in Verticali circulo,
              <lb/>
            cuius diameter eſt 12 13, vbi perpendiculares V Z, X α, E D, Y β, indicant puncta, in quibus paralleli
              <lb/>
            à Verticali circulo ſecantur; </s>
            <s xml:id="echoid-s30052" xml:space="preserve">quia vt demonſtratum eſt, illæ perpendiculares communes ſectiones ſunt
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            Verticalis circuli, & </s>
            <s xml:id="echoid-s30053" xml:space="preserve">par allelorum. </s>
            <s xml:id="echoid-s30054" xml:space="preserve">Eadem{q́ue} ratio eſt, ſi diameter γ δ, ponatur communis ſectio Me-
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            ridiani, & </s>
            <s xml:id="echoid-s30055" xml:space="preserve">alicuius circuli maximi, cuihorologium ad Horizontem inclinatum æquidiſtat, ita vt altitu
              <lb/>
            do poli ſupra ipſum ſit arcus δ D. </s>
            <s xml:id="echoid-s30056" xml:space="preserve">Perpendiculares enim ex punctis, vbi γ δ, parallelorum diametros
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            ſecat, ad eaſdem diametros eductæ communes ſectiones erunt parallelorum, & </s>
            <s xml:id="echoid-s30057" xml:space="preserve">dicti circuli maximi;
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            </s>
            <s xml:id="echoid-s30058" xml:space="preserve">quod demonſtrabitur, vt de Verticali circulo, & </s>
            <s xml:id="echoid-s30059" xml:space="preserve">Horizonte dictum eſt.</s>
            <s xml:id="echoid-s30060" xml:space="preserve"/>
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            <s xml:id="echoid-s30061" xml:space="preserve">EX his facile intelligi poteſt, qua hora Sol illuminare incipiat faciem ſuperiorem, inferioremve cir-
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            culi inclinati, & </s>
            <s xml:id="echoid-s30062" xml:space="preserve">ad quas horas ſupputandæ ſint altitudines Solis. </s>
            <s xml:id="echoid-s30063" xml:space="preserve">Quando enim circuli facies </s>
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