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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[141.] GNOMONICES LIBER SECVNDVS.
[142.] AVCTORE CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
[143.] DE HOROLOGIIS HORIZONTALIBVS. PROBLEMA 1. PROPOSITIO 1.
[144.] SCHOLIVM.
[145.] PROBLEMA 2. PROPOSITIO 2.
[146.] SCHOLIVM.
[147.] PROBLEMA 3. PROPOSITIO 3.
[148.] SCHOLIVM.
[149.] PROBLEMA. 4. PROPOSITIO 4.
[150.] SCHOLIVM.
[151.] PROBLEMA 5. PROPOSITIO 5.
[152.] SCHOLIVM.
[153.] PROBLEMA 6. PROPOSITIO 6.
[154.] SCHOLIVM.
[155.] PROBLEMA 7. PROPOSITIO 7.
[156.] SCHOLIVM.
[157.] PROBLEMA 8. PROPOSITIO 8.
[158.] COROLLARIVM.
[159.] SCHOLIVM.
[160.] PROBLEMA. 9. PROPOSITIO 9.
[161.] I. Sole exiſtente in principio ♈.
[162.] II. Sole exiſtente in principio ♎.
[163.] III. Sole exiſtente in principio ♋.
[164.] IIII. Sole exiſtente in principio ♑.
[165.] Arcus ſemidiurni in initijs ſignorum, ad latitudinem grad. 42.
[166.] VI. Mediationes cœli, & anguli terræ, eorumq́; declinationes, orientibus 12. ſignorum Zodiaci initiis, ad latitudinem grad. 42.
[167.] VII. Puncta Eclipticæ in circulo horę 6. conſtituta, eorumq́ue declinationes, orientibus 12. ſignorum Zodiaci principijs, ad latitudinem grad. 42.
[168.] VIII. Puncta Eclipticæ in circulo horę 11. exiſtentia, eorumq́; declinationes, cum principia 12. ſignorum Zodiaci oriuntur, ad latitudinem grad. 42.
[169.] SCHOLIVM.
[170.] SEQVVNTVR TABELLÆ.
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            <s xml:id="echoid-s9797" xml:space="preserve">
              <pb o="152" file="0172" n="172" rhead="GNOMONICES"/>
            rca ducta recta Q F, ſinus rectus erit eiuſdem arcus B F, (Sinus enim verſus cuiuſuis arcus terminatur
              <lb/>
            in ſinu recto eiuſdem arcus, vt conſtat ex tractatione ſinuum) & </s>
            <s xml:id="echoid-s9798" xml:space="preserve">ad meridianam lineam B H, perpendi-
              <lb/>
            cularis. </s>
            <s xml:id="echoid-s9799" xml:space="preserve">Eſt autem recta F L M, ad eandem meridianam lineam perpendicularis; </s>
            <s xml:id="echoid-s9800" xml:space="preserve">propterea quòd, ex
              <lb/>
              <note position="left" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">29. primi.</note>
              <figure xlink:label="fig-0172-01" xlink:href="fig-0172-01a" number="126">
                <image file="0172-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0172-01"/>
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              <note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0172-03" xlink:href="note-0172-03a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0172-04" xlink:href="note-0172-04a" xml:space="preserve">30</note>
            ſcholio propoſ. </s>
            <s xml:id="echoid-s9801" xml:space="preserve">27. </s>
            <s xml:id="echoid-s9802" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9803" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9804" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s9805" xml:space="preserve">parallela eſt ipſi S T, ob æquales arcus F T, M S. </s>
            <s xml:id="echoid-s9806" xml:space="preserve">Igitur recta F L M, per
              <lb/>
            punctum Q, tranſit. </s>
            <s xml:id="echoid-s9807" xml:space="preserve">Quoniam vero & </s>
            <s xml:id="echoid-s9808" xml:space="preserve">planum horologij, & </s>
            <s xml:id="echoid-s9809" xml:space="preserve">planum parallelogrammi per O P, E Q,
              <lb/>
            ductirectum eſt ad Meridianum, erit quoque communis eorum ſectio ad eundem recta in Q, ac propte-
              <lb/>
              <note position="left" xlink:label="note-0172-05" xlink:href="note-0172-05a" xml:space="preserve">19. vndec.</note>
              <note position="left" xlink:label="note-0172-06" xlink:href="note-0172-06a" xml:space="preserve">40</note>
            rea, per defin. </s>
            <s xml:id="echoid-s9810" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9811" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9812" xml:space="preserve">11. </s>
            <s xml:id="echoid-s9813" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s9814" xml:space="preserve">ad rectam B Q, in Meridiano exiſtentem perpendicularis in puncto Q. </s>
            <s xml:id="echoid-s9815" xml:space="preserve">Re-
              <lb/>
            cta igitur F Q, perpendicularis ad B Q, communis ſectio erit horologij & </s>
            <s xml:id="echoid-s9816" xml:space="preserve">parallelogrammi per O P,
              <lb/>
            E Q, ducti: </s>
            <s xml:id="echoid-s9817" xml:space="preserve">ac proinde latus eiuſdem parallelogrammi ex P, ductum in rectam Q F, cadet; </s>
            <s xml:id="echoid-s9818" xml:space="preserve">quandoqui-
              <lb/>
            dem recta F Q, & </s>
            <s xml:id="echoid-s9819" xml:space="preserve">latus dictum in plano illius parallelogrammi exiſtunt. </s>
            <s xml:id="echoid-s9820" xml:space="preserve">Et quoniam E P, E Q,
              <lb/>
            rectis A Z, A H, parallelæ ſunt oſtenſę, erit angulus P E Q, angulo Z A H, ęqualis: </s>
            <s xml:id="echoid-s9821" xml:space="preserve">Eſt autem angu-
              <lb/>
              <note position="left" xlink:label="note-0172-07" xlink:href="note-0172-07a" xml:space="preserve">10. vndec.</note>
            lus Z A H, rectus: </s>
            <s xml:id="echoid-s9822" xml:space="preserve">oſtendimus enim ſupra Z Y, perpendicularẽ eſſe ad axem. </s>
            <s xml:id="echoid-s9823" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s9824" xml:space="preserve">angulus P E Q,
              <lb/>
            rectus eſt. </s>
            <s xml:id="echoid-s9825" xml:space="preserve">At recta F Q, perpendicularis oſtenſa ad Meridianum, perpendicularis quoque eſt, per defin.
              <lb/>
            </s>
            <s xml:id="echoid-s9826" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9827" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9828" xml:space="preserve">11. </s>
            <s xml:id="echoid-s9829" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s9830" xml:space="preserve">ad rectam E Q, in Meridiano exiſtentem. </s>
            <s xml:id="echoid-s9831" xml:space="preserve">Igitur rectę Q F, E P, in eodem plano paral-
              <lb/>
            lelogrammi per O P, E Q, ducti exiſtentes, cum ad rectam E Q, ſint perpendiculares, parallelę inter
              <lb/>
              <note position="left" xlink:label="note-0172-08" xlink:href="note-0172-08a" xml:space="preserve">28. primi.</note>
            ſe erunt. </s>
            <s xml:id="echoid-s9832" xml:space="preserve">Parallelogrammum ergo erit quadrilaterum, cuius latera ſunt E Q, E P, latus cylindri du-
              <lb/>
              <note position="left" xlink:label="note-0172-09" xlink:href="note-0172-09a" xml:space="preserve">50</note>
            ctum ex P, & </s>
            <s xml:id="echoid-s9833" xml:space="preserve">portio rectę Q F, inter Q, & </s>
            <s xml:id="echoid-s9834" xml:space="preserve">dictũ latus ex P, ductum. </s>
            <s xml:id="echoid-s9835" xml:space="preserve">Eſt enim & </s>
            <s xml:id="echoid-s9836" xml:space="preserve">latus ex P, ductum
              <lb/>
            rectę E Q, parallelum, quòd illud latus, & </s>
            <s xml:id="echoid-s9837" xml:space="preserve">recta E Q, ſi producantur, coniungant rectasęquales in ba-
              <lb/>
              <note position="left" xlink:label="note-0172-10" xlink:href="note-0172-10a" xml:space="preserve">33. primi.</note>
            ſibus cylindri ęqualibus, nempe rectam E P, & </s>
            <s xml:id="echoid-s9838" xml:space="preserve">aliam rectam d b, in oppoſita baſi ei reſpondentem, quę
              <lb/>
            videlicet ſinus rectus eſt arcus b e, quatuor horarum, quemadmodum & </s>
            <s xml:id="echoid-s9839" xml:space="preserve">E P, ſinus rectus eſt arcus B P,
              <lb/>
            quatuor horarum; </s>
            <s xml:id="echoid-s9840" xml:space="preserve">quę quidem rectæ ęquidiſtantes ſunt, cum ſint ſectiones baſium ęquidictantium factę
              <lb/>
              <note position="left" xlink:label="note-0172-11" xlink:href="note-0172-11a" xml:space="preserve">16. vndec.</note>
            à parallelogrammo per O P, E Q, ducto. </s>
            <s xml:id="echoid-s9841" xml:space="preserve">Quapropter recta E P, ęqualis erit oppoſito lateri prædicti
              <lb/>
              <note position="left" xlink:label="note-0172-12" xlink:href="note-0172-12a" xml:space="preserve">34. primi.</note>
            parallelogrammi, hoc eſt, ſegmento rectę Q F, inter Q, & </s>
            <s xml:id="echoid-s9842" xml:space="preserve">latus cylindri ex P, ductum. </s>
            <s xml:id="echoid-s9843" xml:space="preserve">Eſt autem E P,
              <lb/>
            ſinus rectus arcus B P, quatuor horarum ęqualis ſinui recto K μ, (qui ex K, ducitur perpendicularis ad
              <lb/>
            B H) arcus C K, quatuor quoque horarum, quòd circuli θ Y B Z, C R X, æquales ſint, ex conſtructione.
              <lb/>
            </s>
            <s xml:id="echoid-s9844" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s9845" xml:space="preserve">portio rectæ Q F, intercepta inter Q, & </s>
            <s xml:id="echoid-s9846" xml:space="preserve">latus cylindri ex P, ductum ęqualis erit ſinui recto
              <lb/>
            K μ. </s>
            <s xml:id="echoid-s9847" xml:space="preserve">Cum ergo Q L, ipſi K μ, ſit ęqualis, ob parallelogrammum L μ, tranſibit omnino latus cylindri ex
              <lb/>
              <note position="left" xlink:label="note-0172-13" xlink:href="note-0172-13a" xml:space="preserve">34. primi.</note>
            </s>
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