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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GNOMONICES
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<
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<
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<
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paralleli illius arcus ab Aequatore inquirere.</
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</
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<
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<
s
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xml:space
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">DIVIDATVR circulus quicunque A B C D, cuius centrũ P, & </
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<
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xml:space
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<
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talleli, cuius
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arcus di@@nus
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contineat quot-
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cunque quis @@@
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ras propoſu@ri@
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quo artificio in
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ueniatur per
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Analemma.</
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B D, ſe mutuo ad angulos rectos ſecantes, in horas vigintiquatuor æquales vnà cum ſemihoris,
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92
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0126-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0126-01
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& </
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<
s
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">quadrantibus, ſi placuerit, initio
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facto à quouis punctorum A, B, C, D.
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</
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<
s
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xml:space
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">Numerato autẽ à puncto B, hinc in-
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de arcu ſemidiurno B E, B F, vel à D,
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hinc inde arcu ſeminocturno D E,
<
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D F, vt totus arcus E B F, ſit verbi gra-
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tia arcus diurnus horarum 14. </
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<
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E D F, arcus nocturnus horarum 10.
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</
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<
s
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xml:space
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">datus, ducatur recta E F, ſecans B D,
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in G, quæ ipſi A C, ob æquales arcus
<
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A E, C F, parallela erit, per ea, quæ ad
<
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propoſ. </
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<
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<
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<
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">3. </
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<
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">Euclidis, demonſtra
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uimus; </
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<
s
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xml:space
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">atque adeo ad B D, perpendi-
<
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<
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cularis. </
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<
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xml:space
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">Conſtituatur iam angulus
<
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<
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xlink:label
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xml:space
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">29. primi.</
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P G k, æqualis angulo altitudinis Ae-
<
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quatoris, ſeu complementi altítudi-
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nis poli; </
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<
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">ſecetq́; </
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<
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xml:space
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">recta G k, rectã A C,
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in k, puncto, ex quo recta ducatur
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K B. </
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>
<
s
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="
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xml:space
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">Dico P B k, æqualem eſſe angu-
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lo declinationis paralleli illius, cuius
<
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arcus diurnus tot horas cõplectitur,
<
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quot ſunt in arcu E B F, nempe 14. </
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>
<
s
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xml:space
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">Ducta enim recta K D, deſcribatur circulus B O M N, ex cen-
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tro K, interualloq́; </
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<
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xml:space
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">k B, vel K D. </
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<
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xml:space
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">Sunt enim rectæ K B, K D, inter ſe æquales. </
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<
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xml:space
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">Nam cum latera
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<
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B P, P K, lateribus D P, P K, in triangulis B P K, D P K, ęqualia ſint, angulosq́; </
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<
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">contineant æqua-
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les, vtpote rectos, ęquales erunt rectæ K B, K D. </
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<
s
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xml:space
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">Deinde per K, ipſi B D, parallela agatur diame-
<
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<
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ter L M. </
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<
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">Extendatur quoque recta G K, hinc inde. </
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<
s
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xml:space
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">Quoniam igitur P G K, ex conſtructione, an-
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gulus eſt complementi altitudinis poli, erit P
<
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G, angulus altitudinis poli. </
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<
s
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">Quare arcus I N, alti-
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tudinem poli ſupra Horizontem metietur, atque adeo ſi circulus N L O M, ponatur eſſe Meridia
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nus, erit recta HI, communis ſectio Meridiani, & </
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<
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<
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<
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nis ſectio Meridiani, & </
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<
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">Acquatoris; </
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<
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xml:space
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">B D, communis ſectio Meridiani, & </
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<
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">paralleli A B C D, cuius
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arcus diurnus E B F, datus. </
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<
s
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xml:space
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">Eſt enim E F, communis ſectio Horizontis, & </
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<
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ita planum fiet. </
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<
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xml:space
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">Quoniam tam Horizon per HI, ductus, quàm parallelus A B C D, ad Meridianũ
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N L O M, rectus eſt, ſi hi circuli propriã cõcipiantur habere poſitionẽ in ſphæra, erit quoque com
<
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<
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munis eorũ ſectio, quæ quidẽ in G, cadit, vbi ſe interſecãt Horizon & </
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<
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">dictus parallelus, ad Meridia
<
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<
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num recta, atque adeo per defin. </
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<
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<
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<
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<
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<
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xml:space
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">perpendicularis ad rectam B D, in Meridiano exi-
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ftentem. </
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<
s
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xml:space
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">Cum ergo E F, per G, ducta, ſit oſtenſa perpendicularis ad B D, erit E F, communis ſectio
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Horizontis & </
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<
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<
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xml:space
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">Eſt ergo B L, in Meridiano N L O M, arcus declinationis paral-
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leli A B C D, ab Aequatore, atque adeo B K L, angulus eiuſdem declinationis, cui quidem æqua-
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lis eſt angulus P B K, alternus, quod eſt propoſitum.</
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<
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</
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<
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<
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<
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tinet horas 13. </
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<
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<
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ctitur, &</
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<
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<
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nus continet pauciores hotas, quàm 12. </
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<
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<
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<
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xml:space
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">Nam in eadem figura, ſi à puncto D,
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<
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vtrinque numeretur exempli gratia arcus ſemidiurnus D E, D F, horarum 5. </
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<
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">& </
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<
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xml:space
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prius, erit HI, communis ſectio Horizontis, & </
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<
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">Meridiani, arcusq́; </
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<
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">H O, numerabit altitudinẽ po-
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li ſupra Horizontem, & </
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<
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xml:space
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<
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<
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ſic de reliquis.</
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<
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</
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<
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<
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xml:space
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">IDEM parallelus auſtralis, cuius arcus diurnus datus eſt, nempe horarũ 10. </
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<
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tione. </
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<
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xml:space
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">Numeretur à puncto B, in vtramque partẽ arcus ſemidiurnus, nimirũ hor. </
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<
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<
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plo. </
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<
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xml:space
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">Deinde per extremitates horum arcuum ſemidiurnorum ducatur recta linea ſecans rectam
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B D, in puncto, per quod ſi agatur ipſi H I, parallela, conſtituens nimirum cum B D, angulum cõ-
<
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plementi altitudinis poli angulo B G H, æqualem, ſecabitur recta A P, in puncto, ad quod ducta
<
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recta ex B, continebit cum recta B D, angulum declinationis quæſitum, qui omnino æqualis erit
<
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angulo P D K, vel P B K. </
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<
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<
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