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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tum. </
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<
s
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xml:space
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">In inferiori verò habetur idem Meridianus inſularum fortunatarum, ſi longitudo loci ſup-
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putetur à puncto B, verſus D, vſque ad H. </
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<
s
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"
xml:space
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">Nam ſi horologium inferius propriam habeat poſi-
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tionem, ita vt linea horizontalis ſuperiorem occupet locum, & </
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<
s
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"
xml:space
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">punctum A, in feriorem, atq; </
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<
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xml:space
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">pun
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ctum C, ortum reſpiciat, & </
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>
<
s
xml:id
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"
xml:space
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">D, occaſum, ſecabit Meridianus loci planum horologij ſupra Hori-
<
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zontem in puncto B, infra verò Horizontem in puncto A, Quare à B, verſus D, ſunt partes oc-
<
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cidentales, & </
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>
<
s
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="
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xml:space
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">orientales verſus C, &</
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>
<
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xml:space
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">c.</
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>
<
s
xml:id
="
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xml:space
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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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">SED præſtat Meridianos circulos in horologio inferiori deſcribere ex circulis Meridianis ſu-
<
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<
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xlink:label
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xlink:href
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xml:space
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">Quo modo In
<
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ferius horolo
<
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gium Meridia-
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norum ex Supe
<
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riori ori
<
unsure
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um ha
<
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beat.</
note
>
perioris horologij, vt oſtenſum eſt in ſcholio propoſ. </
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>
<
s
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xml:space
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">14. </
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<
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<
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xml:space
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">in verticali horologio fa-
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ctum eſt in ſcholio propoſ. </
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>
<
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xml:space
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">28. </
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<
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xml:space
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">huius libri, omnia enim, quæ ibi dicta ſunt, huc transferri poſ-
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ſunt, intelligendo tamen ſemper pro auſtrali horologio ſuperius æquinoctiale, & </
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>
<
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xml:id
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xml:space
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">pro boreali in-
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<
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">10</
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ferius. </
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<
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xml:space
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">Exemplum habes in figura propoſita. </
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<
s
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xml:space
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">Vbi vides Meridianum 105. </
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<
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xml:space
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">vltra centrum E, pro-
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ductum in ſuperiori horologio habere grad. </
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<
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">285. </
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<
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xml:space
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">qui illi opponitur, at vltra lineam horizontalem
<
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productum, iterum aſſumere grad 105. </
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>
<
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xml:id
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xml:space
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">in inferiori horologio, & </
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>
<
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xml:id
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xml:space
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">ſic de cæteris. </
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>
<
s
xml:id
="
echoid-s19118
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xml:space
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">Meridianos ergo,
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id eſt, circulos longitudinũ, in eodem horologio æquinoctiali deſcripſimus. </
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>
<
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xml:space
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">Quod faciendũ erat.</
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<
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</
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</
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<
head
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xml:space
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">PROBLEMA 55. PROPOSITIO 55.</
head
>
<
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<
s
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xml:space
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">PARALLELOS ciuitatum, ſiue circulos latitudinum, in eodem
<
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æquinoctiali horologio depingere.</
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<
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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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">PRO parallelis per initia ſignorum Zodiaci ductis accipiantur paralleli per vertices ciuitatũ
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<
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xml:space
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">Deſcriptio pa-
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rallelorum ciui
<
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tatum, latitudi-
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numve, in eodẽ
<
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horologio æqui
<
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noctiali.</
note
>
intra tropicos exiſtentium tranſeuntes, & </
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>
<
s
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="
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xml:space
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">alia omnia fiant, quæ de parallelis ſignorum Zodiaci de-
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ſcribendis propoſ. </
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<
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<
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">huius lib. </
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<
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">præcepimus; </
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<
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xml:space
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">factumq́ue erit, quod proponitur. </
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>
<
s
xml:id
="
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xml:space
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">Igitur parallelos
<
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cíuitatum, ſiue circulos latitudinum, &</
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>
<
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xml:space
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">c. </
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<
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xml:space
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">Quod faciendum erat.</
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>
<
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</
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</
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<
head
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xml:space
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">PROBLEMA 56. PROPOSITIO 56.</
head
>
<
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<
s
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xml:space
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">DOMOS cœleſtes in codem horologio æquinoctiali de-
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ſcribere.</
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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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">SECETVR circulus A C B D, principio facto à linea meridiana, in 12. </
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>
<
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xml:space
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">partes æquales, vel
<
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<
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xlink:label
="
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xlink:href
="
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xml:space
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">Cœleſtium do-
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morum in eo-
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dẽ æquinoctiali
<
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horologio de-
<
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ſcriptio ſecun-
<
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dum
<
unsure
/>
loan. Re-
<
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giom.</
note
>
in plures, ſi ſingularum domorum partes etiam defideremus. </
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>
<
s
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xml:space
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">Nos illum diuiſimus in 12. </
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>
<
s
xml:id
="
echoid-s19138
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xml:space
="
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">vt inte-
<
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græ domus duntaxat deſcribantur. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Per puncta autem diuiſionum, & </
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>
<
s
xml:id
="
echoid-s19140
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xml:space
="
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">centrum E, ducantnr rectæ
<
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lineæ occultæ. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Deinde per punctum m, vbi meridiana linea horizontalem interſecat, dictis lineis
<
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agantur lineæ parallelæ, deſcriptæq́ue erunt domus cœleſtes in vtroque horologio ſecundum do-
<
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ctrinam Ioan, Regiom. </
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<
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xml:space
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">Quoniam enim circuli domorum cœleſtium ſecundum Ioan. </
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<
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xml:space
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">Regiom.
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</
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<
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<
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xlink:label
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xml:space
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">Demonſtratio
<
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deſcriptionis
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domorum cœle
<
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ſtium ſecundũ
<
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10. Regiom.</
note
>
diuidunt Aequatorem in partes æquales, initio facto à Meridiano, qui vnus eſt ex dictis circulis,
<
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tranſeuntq́ue per centrum mundi, ſiue Æquatoris, tranſibunt neceſſario per communes ſectiones
<
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<
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Aequatoris, & </
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<
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xml:space
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">circulorum horariorum à meridie, vel media nocte, cum hi quoque per centrum
<
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mundi incedentes ſecent Aequatorem in partes æquales, principio facto à Meridiano; </
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>
<
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xml:id
="
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xml:space
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">ita vt com-
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munes ſectiones circulorum domorum cœleſtium & </
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>
<
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xml:id
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xml:space
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">Aequatoris à communibus ſectionibus cir-
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culorum horariorum & </
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<
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xml:space
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">Aequatoris non diſcrepent. </
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>
<
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xml:space
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">Sed communes ſectiones plani horologij,
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& </
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>
<
s
xml:id
="
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xml:space
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">circulorum domorum cœleſtium parallelæ ſunt communibus ſectionibus Aequatoris, & </
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>
<
s
xml:id
="
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xml:space
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">eo-
<
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<
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xlink:label
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xml:space
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">16. vndec.</
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>
rundem circulorum; </
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>
<
s
xml:id
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xml:space
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">his autem parallelæ quoque ſunt (cum ſint oſtenſæ eædem, quæ ſectiones
<
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<
note
position
="
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xlink:label
="
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xlink:href
="
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xml:space
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">16. vndec.</
note
>
communes Aequatoris, & </
s
>
<
s
xml:id
="
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xml:space
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">horariorum circulorum) communes ſectiones plani horologij, & </
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>
<
s
xml:id
="
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xml:space
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">cir-
<
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culorum horarum à meridie, vel media nocte. </
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>
<
s
xml:id
="
echoid-s19155
"
xml:space
="
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">Igitur communes ſectiones plani horologii, & </
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>
<
s
xml:id
="
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xml:space
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<
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circulorum domorum cœleſtium parallelæ quoque erunt communibus ſectionibus eiuſdem pla-
<
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<
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position
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xlink:label
="
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xml:space
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ni horologii, & </
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>
<
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xml:id
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">horariorum circulorum. </
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>
<
s
xml:id
="
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xml:space
="
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">Cum ergo rectæ per centrum E, ductæ, diuidentesq́ue
<
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<
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="
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xlink:label
="
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="
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xml:space
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">50</
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>
circulum A C B D, in 12. </
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>
<
s
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="
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xml:space
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">partes æquales, vel etiam in plures, vel pauciores, ſint communes ſectio-
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nes plani horologii, & </
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>
<
s
xml:id
="
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xml:space
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">circulorum horariorum, vt propoſ. </
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<
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="
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">49. </
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>
<
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">huius lib. </
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>
<
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">demonſtrauimus; </
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>
<
s
xml:id
="
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xml:space
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">erunt
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his rectis parallelæ, communes ſectiones plani horologii, & </
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>
<
s
xml:id
="
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xml:space
="
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">circulorum domorum cœleſtium.
<
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</
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quocirca cum communes ſectiones hæ tranſeant omnes per punctum m, vt conſtat ex propoſ. </
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>
<
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="
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<
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18. </
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>
<
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xml:id
="
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">ſuperioris lib. </
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>
<
s
xml:id
="
echoid-s19169
"
xml:space
="
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">propterea quòd cõmunis ſectio omnium circulorum cœleſtium domorum, hoc
<
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/>
eſt, axis Verticalis circuli, ſeu cõmunis ſectio Meridiani, & </
s
>
<
s
xml:id
="
echoid-s19170
"
xml:space
="
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">Horizontis, plano horologii occurrit
<
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in eodem puncto m, vt patet ex figura propoſ. </
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>
<
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xml:id
="
echoid-s19171
"
xml:space
="
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">50. </
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>
<
s
xml:id
="
echoid-s19172
"
xml:space
="
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">huius lib. </
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>
<
s
xml:id
="
echoid-s19173
"
xml:space
="
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">in qua communis iſta ſectio eſt recta
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/>
l m, ſi triangulum E l m, intelligatur rectum ad planum horologii, hoc eſt, in plano Meridiani; </
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>
<
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="
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xml:space
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<
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xlink:href
="
note-0298-13a
"
xml:space
="
preserve
">Quibus horis à
<
lb
/>
mer vel med.
<
lb
/>
noc initia do-
<
lb
/>
morum cœle-
<
lb
/>
ſtium parallela
<
lb
/>
ſint.</
note
>
erunt rectæ per m, ductæ rectis per E, emiſſis parallelæ, communes ſectiones plani horologii, & </
s
>
<
s
xml:id
="
echoid-s19175
"
xml:space
="
preserve
">
<
lb
/>
circulorum cœleſtium domorum. </
s
>
<
s
xml:id
="
echoid-s19176
"
xml:space
="
preserve
">Quod eſt propoſitum. </
s
>
<
s
xml:id
="
echoid-s19177
"
xml:space
="
preserve
">Manifeſtum autem eſt, initia domo-
<
lb
/>
rum cœleſtium parallela eſſe lineis horarum à meridiana linea diſtantibus duabus, quatuor, & </
s
>
<
s
xml:id
="
echoid-s19178
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>