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 contents

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[31.] PROBLEMA 2. PROPOSITIO 8.
Page: 46 (26)
[32.] SCHOLIVM.
Page: 49 (29)
[33.] LEMMA.
Page: 49 (29)
[34.] LEMMA PRIMVM.
Page: 51 (31)
[35.] LEMMA II.
Page: 51 (31)
[36.] LEMMA PRIMVM.
Page: 53 (33)
[37.] LEMMA II.
Page: 53 (33)
[38.] THEOREMA 7. PROPOSITIO 9.
Page: 57 (37)
[39.] SCHOLIVM.
Page: 58 (38)
[40.] THEOREMA 8. PROPOSITIQ 10.
Page: 59 (39)
[41.] COROLLARIVM.
Page: 60 (40)
[42.] SCHOLIVM.
Page: 60 (40)
[43.] THEOREMA 9. PROPOSITIO 11.
Page: 62 (42)
[44.] SCHOLIVM.
Page: 63 (43)
[45.] COROLLARIVM PRIMVM.
Page: 63 (43)
[46.] COROLLARIVM II.
Page: 63 (43)
[47.] THEOREMA 10. PROPOSITIO 12.
Page: 63 (43)
[48.] COROLLARIVM.
Page: 64 (44)
[49.] THEOREMA 11. PROPOSITIO 13.
Page: 64 (44)
[50.] THEOREMA 12. PROPOSITIO 14.
Page: 65 (45)
[51.] SCHOLIVM.
Page: 66 (46)
[52.] THEOREMA 13. PROPOSITIO 15.
Page: 66 (46)
[53.] LEMMA.
Page: 69 (49)
[54.] COROLLARIVM.
Page: 69 (49)
[55.] THEOREMA 14. PROPOSITIO 16.
Page: 69 (49)
[56.] COROLLARIVM.
Page: 70 (50)
[57.] THEOREMA 15. PROPOSITIO 17.
Page: 70 (50)
[58.] LEMMA.
Page: 72 (52)
[59.] SCHOLIVM.
Page: 72 (52)
[60.] THEOREMA 16. PROPOSITIO 18.
Page: 72 (52)
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            <s xml:id="echoid-s1318" xml:space="preserve">
              <pb o="18" file="0038" n="38" rhead="GNOMONICES"/>
            in priori arcu occidere, more hor arum ab ortu, paulo post horam decimamquintam, oriri verò paulo ante
              <lb/>
            horam nonam more hor arum ab occaſu, &</s>
            <s xml:id="echoid-s1319" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1320" xml:space="preserve">Horæ externæ in arcu diurno ♋ d M e, & </s>
            <s xml:id="echoid-s1321" xml:space="preserve">nocturno d θ e,
              <lb/>
            pertinent ad horas Italicas, & </s>
            <s xml:id="echoid-s1322" xml:space="preserve">internæ ad Babylonicas. </s>
            <s xml:id="echoid-s1323" xml:space="preserve">Contra verò in arcu diurno ♑ d θ e, & </s>
            <s xml:id="echoid-s1324" xml:space="preserve">no-
              <lb/>
            cturno d M e, externæ horæ ad horas Babylonicas, & </s>
            <s xml:id="echoid-s1325" xml:space="preserve">internæ ad Italicas ſpectant. </s>
            <s xml:id="echoid-s1326" xml:space="preserve">Semper tamen pun-
              <lb/>
            ctume, ſumitur pro ortu Solis, ſi de horis ab ortu loquamur, & </s>
            <s xml:id="echoid-s1327" xml:space="preserve">punctum d, pro occaſu. </s>
            <s xml:id="echoid-s1328" xml:space="preserve">E contrario au-
              <lb/>
            tem, ſi de horis ab occaſu ſermo habeatur, punctum e, ſumendum eſt pro occaſu Solis, & </s>
            <s xml:id="echoid-s1329" xml:space="preserve">d, pro ortu, vt
              <lb/>
            numeri horarum demonſtrant.</s>
            <s xml:id="echoid-s1330" xml:space="preserve"/>
          </p>
          <figure number="16">
            <image file="0038-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0038-01"/>
          </figure>
          <note position="left" xml:space="preserve">10</note>
          <note position="left" xml:space="preserve">20</note>
          <note position="left" xml:space="preserve">30</note>
          <p style="it">
            <s xml:id="echoid-s1331" xml:space="preserve">IDEM videre licet in horis astronomicis, ſi circuli diuiſio incipiat à puncto M, Meridiei, ut manife-
              <lb/>
            ſtum est in alio circulo minori A B C D, circa centrum E, deſcripto, qui per rectam B D, diuiſus eſt ad
              <lb/>
            ſimilitudinem circuli M d θ e, ita vt ſit inſtar paralleli ♋, vel ♑, deſcripti ex minore aliquo Ana-
              <lb/>
            lemmate. </s>
            <s xml:id="echoid-s1332" xml:space="preserve">Itaque cernis etiam hic arcum diurnum ♋, B A D, complecti horas quindecim, & </s>
            <s xml:id="echoid-s1333" xml:space="preserve">eo am-
              <lb/>
            plius, nocturnum verò B C D, paulo minus, quàm horas 9. </s>
            <s xml:id="echoid-s1334" xml:space="preserve">Item in priori Solem oriri in D, paulo ante
              <lb/>
            horam 4 {1/2} post mediam noctem, & </s>
            <s xml:id="echoid-s1335" xml:space="preserve">occidere in B, paulo poſt horam 7 {1/2} poſt meridiem, &</s>
            <s xml:id="echoid-s1336" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1337" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1338" xml:space="preserve">HAEC omnia experiri licebit in omnibus alijs parallelis Solis, & </s>
            <s xml:id="echoid-s1339" xml:space="preserve">in quocunque climate, ſi pro alti-
              <lb/>
            tudine poli in dato climate Analemma conſtituatur.</s>
            <s xml:id="echoid-s1340" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quo modo da-
            <lb/>
          tus citculus di-
            <lb/>
          uidatur in duas
            <lb/>
          portiones, qua-
            <lb/>
          rum vna ſimi-
            <lb/>
          lis ſit arcui diur
            <lb/>
          no, & nocturno
            <lb/>
          aliera, Sole in
            <lb/>
          qu@cunque gra
            <lb/>
          du Ecliptiçæ
            <lb/>
          exiſtente.</note>
          <p>
            <s xml:id="echoid-s1341" xml:space="preserve">SED doceamus, quanam arte circulus ille minor A B C D, vel quiuis alius, etiam maior, beneficio
              <lb/>
            Analemmatis diuidendus ſit in duas portiones, quarum vna ſimilis ſit arcui diurno, & </s>
            <s xml:id="echoid-s1342" xml:space="preserve">altera nocturno,
              <lb/>
              <note position="left" xlink:label="note-0038-05" xlink:href="note-0038-05a" xml:space="preserve">40</note>
            Sole exiſtente in principio ♋ vel in quouis alio gradu Eclipticæ. </s>
            <s xml:id="echoid-s1343" xml:space="preserve">Egregium enim vſum hæc res habebit
              <lb/>
            in deſcribendis horis ab ortn, vel occaſu Solis, vt ex ijs, quæ ſcquuntur, liquido conſtabit. </s>
            <s xml:id="echoid-s1344" xml:space="preserve">Sit ergo exem
              <lb/>
            pli gratia, circulus A B C D, diuidendus in ar cum diurnum, & </s>
            <s xml:id="echoid-s1345" xml:space="preserve">nocturnum ♋ quemadmodum circu-
              <lb/>
            lus M d θ e, diuiſus eſt. </s>
            <s xml:id="echoid-s1346" xml:space="preserve">Ducta diametro vtcunque A C, ducatur ex A, recta A G, faciens cum A C,
              <lb/>
            quemeunque angulum, ex qua abſcindatur A G, æqualis diametro paralleli ♋ M θ, in Analemmate,
              <lb/>
            & </s>
            <s xml:id="echoid-s1347" xml:space="preserve">rurſus recta A H, æqualis portioni M a, eiuſdem diametri. </s>
            <s xml:id="echoid-s1348" xml:space="preserve">Coniuncta deinde recta G C, agatur ei per
              <lb/>
            H, parallela H F, ſecans diametrum A C, in F, & </s>
            <s xml:id="echoid-s1349" xml:space="preserve">per F, ad A C, excitetur perpendicularis B D. </s>
            <s xml:id="echoid-s1350" xml:space="preserve">Di-
              <lb/>
            co arcum B A D, ſimilem eſſe arcui diurno ♋ & </s>
            <s xml:id="echoid-s1351" xml:space="preserve">arcum B C D nocturno, hoc eſt, arcum B A D, arcui
              <lb/>
            d M e, in maiori circulo, & </s>
            <s xml:id="echoid-s1352" xml:space="preserve">arcum B C D, arcui d θ e, ſimilem eſſe. </s>
            <s xml:id="echoid-s1353" xml:space="preserve">Quoniam enim eſt, vt A H, ad H G,
              <lb/>
            hoc eſt M a, ad a θ, ita A F, ad F C, erit componendo, vt M θ, ad a θ, ita A C, ad F C, & </s>
            <s xml:id="echoid-s1354" xml:space="preserve">permutan-
              <lb/>
              <note position="left" xlink:label="note-0038-06" xlink:href="note-0038-06a" xml:space="preserve">2. ſexti.</note>
              <note position="left" xlink:label="note-0038-07" xlink:href="note-0038-07a" xml:space="preserve">50</note>
            do vt M θ, ad A C, ita a θ, ad F C. </s>
            <s xml:id="echoid-s1355" xml:space="preserve">Vt autem M θ, ad A C, diameter ad diametrum, ita eſt M b, ſemi-
              <lb/>
              <note position="left" xlink:label="note-0038-08" xlink:href="note-0038-08a" xml:space="preserve">15. quinti.</note>
            diameter ad ſemidiametrum A E. </s>
            <s xml:id="echoid-s1356" xml:space="preserve">Igitur erit quoque, vt M b, ſemidiameter ad ſemidiametrum A E, ita
              <lb/>
            a θ, ſinus verſus arcus nocturni ♋ d θ e, ad F C, ſinum verſum arcus B C D. </s>
            <s xml:id="echoid-s1357" xml:space="preserve">Per lemma ergo ſupe-
              <lb/>
            rius, arcus nocturnus ♋ d θ e, & </s>
            <s xml:id="echoid-s1358" xml:space="preserve">B C D, ſimiles ſunt; </s>
            <s xml:id="echoid-s1359" xml:space="preserve">ac proinde arcus B C D, tot horas ſui circuli cõ-
              <lb/>
            prehendet, quot in arcu d θ e, continentur. </s>
            <s xml:id="echoid-s1360" xml:space="preserve">Quamobrem & </s>
            <s xml:id="echoid-s1361" xml:space="preserve">reliquus B AD, reliquo arcui diurno d M e,
              <lb/>
            ſimilis erit. </s>
            <s xml:id="echoid-s1362" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s1363" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1364" xml:space="preserve">IAM verò latitudo ortiua, vel occidua ex Analemmate ita inuenietur. </s>
            <s xml:id="echoid-s1365" xml:space="preserve">Ex puncto a, vbi paralle-
              <lb/>
              <note position="left" xlink:label="note-0038-09" xlink:href="note-0038-09a" xml:space="preserve">Inuentio latitu
                <lb/>
              dinis ortiuæ &
                <lb/>
              occiduæ ex A-
                <lb/>
              nalemmate.</note>
            lus Horizontem ſecat, ducatur ad Horizontis diametrum B D, perpendicularis a d. </s>
            <s xml:id="echoid-s1366" xml:space="preserve">Dico arcum d A,
              <lb/>
            eſſe latitudinem ortiuam, vel occiduam. </s>
            <s xml:id="echoid-s1367" xml:space="preserve">Quoniam enim, vt paulo ante demonſtrauimus, communis ſe-
              <lb/>
            ctio paralleli, & </s>
            <s xml:id="echoid-s1368" xml:space="preserve">Horizontis recta eſt ad planum Meridiani, at que adeo, ex definitione 3. </s>
            <s xml:id="echoid-s1369" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1370" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1371" xml:space="preserve">Eucli-
              <lb/>
            dis, perpendicularis ad rectam B D, in plano Meridiani exiſtentem; </s>
            <s xml:id="echoid-s1372" xml:space="preserve">fit vt ſi circulus </s>
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