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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lis ſumantur paralleli arcuum diurnorum, &</
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<
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<
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xml:space
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<
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<
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ſcripſimus. </
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<
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xml:space
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<
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</
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</
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<
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style
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<
s
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xml:space
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">HIC etiam, vt in ſcholio propoſ. </
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<
s
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xml:space
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">3. </
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<
s
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"
xml:space
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">huius libri monuimus, per arcus diurnos duci poterunt lineæ il-
<
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<
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position
="
left
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xlink:label
="
note-0360-01
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xlink:href
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note-0360-01a
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xml:space
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">Quo artificio
<
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per
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unsure
/>
arcus diur-
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nos illę horæ
<
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deſcribantur,
<
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quæ uix æqui-
<
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noctialẽ lineã
<
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ſecant.</
note
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larum horarum, quę vix æquinoctialem lineam interſecant, quales ſunt in noſtro exemplo 8. </
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<
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<
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xml:space
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<
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">tam à
<
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meridie, quàm à media nocte. </
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<
s
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xml:space
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">Cum enim, die continente horas 16. </
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<
s
xml:id
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xml:space
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">Sol occidat hora 8. </
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<
s
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xml:space
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">à meridie, tran-
<
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ſibit hora 8. </
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>
<
s
xml:id
="
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"
xml:space
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">à meridie per illud punctum lineæ horizont alis, vbi ab arcu circuli ad interuallum rectę in
<
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/>
figura radiorum, quæ horę 8. </
s
>
<
s
xml:id
="
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"
xml:space
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">à meridie reſpondet, inter ceptæ inter C, & </
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>
<
s
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="
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xml:space
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">radium horarum 16. </
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<
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xml:space
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ſecatur. </
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<
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xml:space
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">Hæc autem hora vltra centrum C, producta dabit horam 8. </
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<
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">à media nocte. </
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<
s
xml:id
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xml:space
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">Similiter quoniam,
<
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cum dies continet horas 18. </
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<
s
xml:id
="
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xml:space
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">Sol occidit hora 9. </
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<
s
xml:id
="
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xml:space
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">à meridie, ducenda erit hora 9. </
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>
<
s
xml:id
="
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xml:space
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">à meridie per punctum
<
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/>
in linea horizontali, in quo ab arcu circuli ad interuallum rectæ in figura radiorum, quæ horæ 9. </
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>
<
s
xml:id
="
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xml:space
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">à meri-
<
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diereſpondet, interiectæ inter C, & </
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<
s
xml:id
="
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xml:space
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">radiũ horarum 18. </
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>
<
s
xml:id
="
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xml:space
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">deſcripti diuiditur. </
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>
<
s
xml:id
="
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xml:space
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">Atque hæc hora producta vl-
<
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tra centrum C, dabit horam 9. </
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<
s
xml:id
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xml:space
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">à media nocte. </
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>
<
s
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="
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xml:space
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">In horologio autem ſpectante ad ortum, idem faciendum
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erit de horis 4. </
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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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">c.</
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<
s
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xml:space
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</
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<
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<
s
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xml:space
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">SED commodius ea puncta in linea horizontali inueniemus per arcus illos diurnos priori modo, nem
<
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pe ex Analemmate, deſcriptos: </
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>
<
s
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xml:space
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">quia horæ illæ, quæ vix æquinoctialem lineam ſecant, duci nequeunt in fi-
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gura radiorum, niſi praxi Andreæ Schoneri vti velimus.</
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<
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<
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">PROBLEMA 16. PROPOSITIO 16.</
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<
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">CIRCVLOS Verticales in eodem horologio, quod ab Horizon-
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te declinat, delineare.</
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<
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</
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<
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<
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">DVCTA per K, locum ſtyli, & </
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<
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">punctum D, vbi linea horæ 6. </
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">horizontalis, & </
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<
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xml:space
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">æquinoctia-
<
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<
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xml:space
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">Vertica liũ cir-
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culorum in eo-
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dem horologio
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declinante ab
<
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Horizonte de-
<
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lineatio.</
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>
lis ſe interſecant, linea recta ſecante meridianam lineam in B, erigatur ex K, ad B D, perpendicu
<
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laris K A, ſtylo I K, æqualis; </
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>
<
s
xml:id
="
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xml:space
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">iunctaq́ue recta D A, abſcindatur ei æqualis D E. </
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>
<
s
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xml:space
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">Centro deinde E,
<
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<
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deſcribatur ad quodcunque interuallum circulus, qui in grad. </
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<
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<
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præcedentibus dictum eſt, ſecetur, initio facto à recta D E. </
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<
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xml:space
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">Si enim per centrum E, & </
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<
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puncta egrediantur rectæ, ſecabitur ab his linea horizontalis in punctis, per quæ ex puncto B,
<
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emiſſæ rectæ dabunt Verticales circulos, id eſt, communes eorum, & </
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<
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nes, ita vt B D, ſit communis ſectio plani horologij, & </
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<
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<
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tione conſirmabimus.</
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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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">CONCIPIATVR animo triangulum A D K, moueri circa D K, donec rectum ſit ad pla
<
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<
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xml:space
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">Demonſtra tio
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præcedentis cõ
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@ructionis.</
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num horologij, ac proinde punctum A, cum vertice ſtyli, ſeu centro mundi coniungatur, & </
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<
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ſum triangulum cum plano Verticalis circuli proprie dicti, quod & </
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<
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">hic Verticalis ad planum ho-
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rologij rectus ſit, tranſeatq́ue per A K, ſtylum, necnon per punctum D. </
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<
s
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xml:space
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<
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lus maximus, cui horologium æquidiſtat, per polos Verticalis propriè dicti ductus ad Vertica-
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lem, per propoſ. </
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<
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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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">rectus eſt, erit viciſſim Verticalis ad illum circulũ rectus, atque
<
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adeo & </
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<
s
xml:id
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xml:space
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">ad planum horologij, quod ei circulo æquidiſtat. </
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<
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xml:id
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xml:space
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">Cum ergo omnia plana per axẽ A K, du-
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cta ad idem planum horologij recta ſint, tranſibit Verticalis per ſtylum A K, quandoquidem per
<
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<
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verticem ipſius ducitur. </
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<
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xml:space
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">Quia vero Sole exiſtente in puncto, vbi mutuo ſe interſecant Aequator,
<
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Horizon, circulus horæ 6. </
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<
s
xml:id
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xml:space
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">nec non Verticalis proprie dictus, vmbra ſtyli cadit in D, punctum
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horæ 6. </
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<
s
xml:id
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xml:space
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">in æquinoctiali linea, vt ſupra diximus, fit vt per D, tranſeat communis quoque ſectio
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Verticalis, & </
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<
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xml:id
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<
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<
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<
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<
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">vmbra ſtyli tunc cadat in cõmunem hanc
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ſectionem. </
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<
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xml:id
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xml:space
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">Igitur B D, communis ſectio erit plani horologii, & </
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<
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<
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xml:id
="
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xml:space
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">Recta
<
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autem A D, communis erit ſectio trianguli A D K, & </
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>
<
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xml:id
="
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xml:space
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">Horizontis per verticem ſtyli A, & </
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>
<
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">pun-
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<
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">50</
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ctum D, ducti. </
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>
<
s
xml:id
="
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xml:space
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">Si igitur intelligamus circulum ex E, deſcriptum circa lineam horizontalem
<
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moueri, donec punctum E, cum vertice ſtyli A, & </
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>
<
s
xml:id
="
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xml:space
="
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">recta E D, cum recta A D, coniungatur, ob
<
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æqualitatem rectarum E D, A D, erit quoque E D, vel A D, communis ſectio Verticalis proprie
<
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/>
dicti, atque Horizontis; </
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>
<
s
xml:id
="
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xml:space
="
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">immo ipſe circulus ex E, deſcriptus in plano Horizontis erit collocatus,
<
lb
/>
eiusq́ue centrum idem erit, quod centrum mundi. </
s
>
<
s
xml:id
="
echoid-s23039
"
xml:space
="
preserve
">Rectæ igitur aliæ per centrum E, emiſſæ di-
<
lb
/>
uidentes circulum ex E, deſcriptum, ac proinde & </
s
>
<
s
xml:id
="
echoid-s23040
"
xml:space
="
preserve
">Horizontem ex eodem centro A, quod tunc
<
lb
/>
idem eſt, quod E, & </
s
>
<
s
xml:id
="
echoid-s23041
"
xml:space
="
preserve
">in eodem plano deſcriptum, in partes æquales, communes ſectiones erunt
<
lb
/>
Horizontis & </
s
>
<
s
xml:id
="
echoid-s23042
"
xml:space
="
preserve
">reliquorum Verticalium circulorum. </
s
>
<
s
xml:id
="
echoid-s23043
"
xml:space
="
preserve
">Quare Verticales circuli occurrent plano
<
lb
/>
horologii in punctis, in quibus horizontalis linea à rectis illis ex centro E, emiſſis diuiditur.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s23044
"
xml:space
="
preserve
">Quoniam verò omnes etiam ſe mutuo interſecant per propoſ. </
s
>
<
s
xml:id
="
echoid-s23045
"
xml:space
="
preserve
">18. </
s
>
<
s
xml:id
="
echoid-s23046
"
xml:space
="
preserve
">primi libri, in puncto B, in
<
lb
/>
quod eorum communis ſectio, nempe axis Horizontis cadit, ita vt B, ſit Zenith, ſeu vertex </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>