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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in priori arcu occidere, more hor arum ab ortu, paulo post horam decimamquintam, oriri verò paulo ante
<
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horam nonam more hor arum ab occaſu, &</
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<
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xml:space
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<
s
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xml:space
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">Horæ externæ in arcu diurno ♋ d M e, & </
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<
s
xml:id
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xml:space
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">nocturno d θ e,
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pertinent ad horas Italicas, & </
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<
s
xml:id
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xml:space
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">internæ ad Babylonicas. </
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<
s
xml:id
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echoid-s1323
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xml:space
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">Contra verò in arcu diurno ♑ d θ e, & </
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<
s
xml:id
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echoid-s1324
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xml:space
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">no-
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cturno d M e, externæ horæ ad horas Babylonicas, & </
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<
s
xml:id
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echoid-s1325
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xml:space
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">internæ ad Italicas ſpectant. </
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<
s
xml:id
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echoid-s1326
"
xml:space
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preserve
">Semper tamen pun-
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ctume, ſumitur pro ortu Solis, ſi de horis ab ortu loquamur, & </
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>
<
s
xml:id
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echoid-s1327
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xml:space
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">punctum d, pro occaſu. </
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<
s
xml:id
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echoid-s1328
"
xml:space
="
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">E contrario au-
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tem, ſi de horis ab occaſu ſermo habeatur, punctum e, ſumendum eſt pro occaſu Solis, & </
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<
s
xml:id
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echoid-s1329
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xml:space
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">d, pro ortu, vt
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numeri horarum demonſtrant.</
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<
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<
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<
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<
s
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xml:space
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">IDEM videre licet in horis astronomicis, ſi circuli diuiſio incipiat à puncto M, Meridiei, ut manife-
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ſtum est in alio circulo minori A B C D, circa centrum E, deſcripto, qui per rectam B D, diuiſus eſt ad
<
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ſimilitudinem circuli M d θ e, ita vt ſit inſtar paralleli ♋, vel ♑, deſcripti ex minore aliquo Ana-
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lemmate. </
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>
<
s
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xml:space
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">Itaque cernis etiam hic arcum diurnum ♋, B A D, complecti horas quindecim, & </
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<
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xml:space
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">eo am-
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plius, nocturnum verò B C D, paulo minus, quàm horas 9. </
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<
s
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xml:space
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preserve
">Item in priori Solem oriri in D, paulo ante
<
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horam 4 {1/2} post mediam noctem, & </
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>
<
s
xml:id
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echoid-s1335
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">occidere in B, paulo poſt horam 7 {1/2} poſt meridiem, &</
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<
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xml:space
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">c.</
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<
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</
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<
s
xml:id
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xml:space
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">HAEC omnia experiri licebit in omnibus alijs parallelis Solis, & </
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<
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xml:space
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">in quocunque climate, ſi pro alti-
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tudine poli in dato climate Analemma conſtituatur.</
s
>
<
s
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="
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</
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<
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xml:space
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">Quo modo da-
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tus citculus di-
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uidatur in duas
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portiones, qua-
<
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/>
rum vna ſimi-
<
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lis ſit arcui diur
<
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no, & nocturno
<
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aliera, Sole in
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qu@cunque gra
<
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du Ecliptiçæ
<
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exiſtente.</
note
>
<
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<
s
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="
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xml:space
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">SED doceamus, quanam arte circulus ille minor A B C D, vel quiuis alius, etiam maior, beneficio
<
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Analemmatis diuidendus ſit in duas portiones, quarum vna ſimilis ſit arcui diurno, & </
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<
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xml:space
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">altera nocturno,
<
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<
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">40</
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Sole exiſtente in principio ♋ vel in quouis alio gradu Eclipticæ. </
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>
<
s
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xml:space
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">Egregium enim vſum hæc res habebit
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in deſcribendis horis ab ortn, vel occaſu Solis, vt ex ijs, quæ ſcquuntur, liquido conſtabit. </
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>
<
s
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="
echoid-s1344
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xml:space
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">Sit ergo exem
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pli gratia, circulus A B C D, diuidendus in ar cum diurnum, & </
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<
s
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">nocturnum ♋ quemadmodum circu-
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lus M d θ e, diuiſus eſt. </
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<
s
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xml:space
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">Ducta diametro vtcunque A C, ducatur ex A, recta A G, faciens cum A C,
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quemeunque angulum, ex qua abſcindatur A G, æqualis diametro paralleli ♋ M θ, in Analemmate,
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& </
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<
s
xml:id
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xml:space
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">rurſus recta A H, æqualis portioni M a, eiuſdem diametri. </
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<
s
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xml:space
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">Coniuncta deinde recta G C, agatur ei per
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H, parallela H F, ſecans diametrum A C, in F, & </
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>
<
s
xml:id
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xml:space
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">per F, ad A C, excitetur perpendicularis B D. </
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<
s
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echoid-s1350
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xml:space
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">Di-
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co arcum B A D, ſimilem eſſe arcui diurno ♋ & </
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>
<
s
xml:id
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xml:space
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">arcum B C D nocturno, hoc eſt, arcum B A D, arcui
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d M e, in maiori circulo, & </
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>
<
s
xml:id
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echoid-s1352
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xml:space
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">arcum B C D, arcui d θ e, ſimilem eſſe. </
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<
s
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xml:space
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">Quoniam enim eſt, vt A H, ad H G,
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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, & </
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<
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xml:space
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">permutan-
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<
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xml:space
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">2. ſexti.</
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do vt M θ, ad A C, ita a θ, ad F C. </
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<
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xml:space
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">Vt autem M θ, ad A C, diameter ad diametrum, ita eſt M b, ſemi-
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<
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xlink:label
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xml:space
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">15. quinti.</
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diameter ad ſemidiametrum A E. </
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<
s
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xml:space
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">Igitur erit quoque, vt M b, ſemidiameter ad ſemidiametrum A E, ita
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a θ, ſinus verſus arcus nocturni ♋ d θ e, ad F C, ſinum verſum arcus B C D. </
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<
s
xml:id
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xml:space
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">Per lemma ergo ſupe-
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rius, arcus nocturnus ♋ d θ e, & </
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<
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xml:space
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<
s
xml:id
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xml:space
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">ac proinde arcus B C D, tot horas ſui circuli cõ-
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prehendet, quot in arcu d θ e, continentur. </
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<
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xml:id
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xml:space
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">Quamobrem & </
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<
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">reliquus B AD, reliquo arcui diurno d M e,
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ſimilis erit. </
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<
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xml:id
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">quod eſt propoſitum.</
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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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">IAM verò latitudo ortiua, vel occidua ex Analemmate ita inuenietur. </
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<
s
xml:id
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xml:space
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">Ex puncto a, vbi paralle-
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<
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xlink:label
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xml:space
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">Inuentio latitu
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dinis ortiuæ &
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occiduæ ex A-
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nalemmate.</
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lus Horizontem ſecat, ducatur ad Horizontis diametrum B D, perpendicularis a d. </
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<
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">Dico arcum d A,
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eſſe latitudinem ortiuam, vel occiduam. </
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<
s
xml:id
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xml:space
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">Quoniam enim, vt paulo ante demonſtrauimus, communis ſe-
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ctio paralleli, & </
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<
s
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">Horizontis recta eſt ad planum Meridiani, at que adeo, ex definitione 3. </
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<
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<
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<
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dis, perpendicularis ad rectam B D, in plano Meridiani exiſtentem; </
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<
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