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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LIBER SECVNDVS.
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<
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style
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<
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xml:space
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ęqu
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i
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noctialis in
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utrouis horolo-
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gi
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o Meridi
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ano
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inter lineã ho-
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ræ 6. & b@nas ho
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ras u@rinque à
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linea ho@æ 6.
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æquali @empo-
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ris @patio re
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m
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o
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tas, ſ
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untæqua-
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lia.</
note
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<
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<
s
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xml:space
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">IN quocunq; </
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>
<
s
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xml:space
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">horologio Meridiano binæ lineæ quæunq; </
s
>
<
s
xml:id
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echoid-s16214
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xml:space
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">horariæ hinc inde à linea horæ ſextæ D E,
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æquali ſpatio temporis remotæ auferunt ex linea æquinoctiali A C, lineas inter ipſas, & </
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>
<
s
xml:id
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xml:space
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">lineã horæ ſex-
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tæ interiectas æquales, ita vt in linea æquinoctiali ſpatia horaria ante ſextam horam æqualia ſint hora-
<
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rijs ſpatijs poſt ſextam horam, ſingula ſingulis. </
s
>
<
s
xml:id
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xml:space
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">Vt lineæ A M, A N, in occident ali horologio, quarum
<
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quælibet quatuor horas complectitur, æquales ſunt. </
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>
<
s
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xml:space
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">Cũ enim anguli M E A, N E A, in centro E, æqua-
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libus arcubus ſubtenſi æquales ſint, & </
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<
s
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xml:space
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">anguli ad A, recti, latus{q́ue} A E, commune; </
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<
s
xml:id
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xml:space
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">erunt quoque rectæ
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A M, A N, æquales, ſimiliter & </
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<
s
xml:id
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xml:space
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">E M, E N. </
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>
<
s
xml:id
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"
xml:space
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">Eademq́, de cæteris ratio eſt habenda. </
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<
s
xml:id
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xml:space
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">Ex quo fit, ſatis eſſe
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<
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xlink:label
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note-0257-02
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xlink:href
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xml:space
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">27. tertij.</
note
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<
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xlink:label
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note-0257-03
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xlink:href
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xml:space
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">26. primi.</
note
>
ad deſcriptionem horologij Meridiani, ſi per centrum E, & </
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<
s
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xml:space
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">puncta diuiſionum vnius quadrantis, nem-
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<
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xlink:label
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">10</
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<
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xlink:label
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xml:space
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">Saus e@tad de-
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ſcriptionẽ horo
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logii Meridia-
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ni, ſi vnus dun-
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taxat quadrans
<
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circuli ex E, de-
<
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ſcripu in 6. par
<
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tes æquales di
<
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-
<
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ſtribuatur.</
note
>
pe H I, rectæ ducantur ſecantes æquinoctialem lineam in punctis S, N, Q, & </
s
>
<
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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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">Nam ſi hæc puncta ex
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A, in alteram partem eiuſdem lineæ æquinoctialis beneficio circini trans ferantur, habebuntur omnia pũ
<
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cta, per quæ ducendæ ſunt lineæ horariæ.</
s
>
<
s
xml:id
="
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xml:space
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"/>
</
p
>
<
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<
s
xml:id
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xml:space
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">IAM vero ſi horologium in plano, quod Meridiano æquidiſtet, collocetur, it a vt A B, recta Hori-
<
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zonti ſit æquidiſtans, & </
s
>
<
s
xml:id
="
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xml:space
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">punctum A, Boream, punctum vero B, Auſtrum reſpiciat, adeo vt angulus com-
<
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plementi altitudinis poli B A C, qui ſupra a lineam horizontalem A B, exiſtit, in auſtrum vergat in vtro-
<
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<
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position
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xlink:label
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xlink:href
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xml:space
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">Quon odovtrũ
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que horologiũ
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Meridianu
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@@
<
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collecandum,
<
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vnà cum ſtylo,
<
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vt horas demon
<
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ſtret.</
note
>
que horologio, qui vero infra eandem lineam horizontalem huic oppoſitus eſt, in Boream, indicabuntur ho
<
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ræ à gnomone A E, ad angulos rectos inſiſtente plano horologij in puncto A, ita vt ſtylus ipſe communis
<
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ſectio ſit Horizontis, & </
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>
<
s
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">Aequatoris, ſeu circuli horæſextæ, Verticaliſue. </
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>
<
s
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xml:space
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">Hæc enim cõmunis ſectio per-
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<
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">20</
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pendicularis eſt ad planum horologij in puncto A, per quod dictorum circulorum plana ad planum ho-
<
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rologii recta exiſtentia tranſeunt. </
s
>
<
s
xml:id
="
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xml:space
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">Quòd ſi ex duobus punctis quibuslibet rectæ D E, vt ex D, & </
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>
<
s
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">E, eri-
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<
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">19. vndec.</
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>
gantur ad planum horologij duæ perpendiculares E O,
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0257-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0257-01
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D P, gnomoni aſſumpto A E, æquales, ipſis{q́ue} ſuperpo-
<
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natur recta O P, fungetur hæc munere axis, cum per cen
<
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trum mundi tranſeat; </
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>
<
s
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="
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xml:space
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">per punctum nimirum, quod eſt
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vertex styli ex A, erecti, æquidiſtet{q́ue} lineæ horæ 6. </
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>
<
s
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">vt
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ratio poſtulat. </
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>
<
s
xml:id
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xml:space
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">Nam linea horæ ſextæ, & </
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<
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xml:space
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">axis mundi
<
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<
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ſunt æquidiſtantes, communes videlicet ſectiones Meri-
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diani circuli, & </
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>
<
s
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">plani horology factæ à circulo horæ 6.
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</
s
>
<
s
xml:id
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xml:space
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">Huius igitur axis O P, vmbra proiecta in lineas hora-
<
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<
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xlink:label
="
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xlink:href
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">30</
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rias à meridie, vel media nocte, indicabit quoque horas à meridie, vel media nocte, quemadmodum de ho
<
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rologio horizontali, Verticali{q́ue} diximus.</
s
>
<
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</
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<
note
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xml:space
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">Cui ſegmento
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æquinoctialis li
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neæ in vtroque
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horologio Me-
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ridiano ſtylus
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æqualis ſit.</
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>
<
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<
s
xml:id
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xml:space
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">GNOMON autem aſſumptus A E, perpetuo æqualis est parti æquinoctialis lineæ, quæ inter A,
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& </
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>
<
s
xml:id
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xml:space
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">horam tertiam vel nonam interijcitur, id eſt, rectæ A Q, vel A R, in occidentali horologio. </
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>
<
s
xml:id
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xml:space
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">Quo-
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niam enim totus quadrans G H, diuiſus eſt in 6. </
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>
<
s
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xml:space
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">æquales horas, diuidet circulus horæ nonæ tribus horis
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diſtans à recta E H, horæſextæ, vel à recta E G, horæ 12. </
s
>
<
s
xml:id
="
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xml:space
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">eundem quadrantem bifariam; </
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>
<
s
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">ac proinde an-
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gulus A E R, angulo G E R, æqualis erit. </
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>
<
s
xml:id
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xml:space
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">Cum ergo totus A E G, rectus ſit, erit vterq; </
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<
s
xml:id
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xml:space
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">angulorũ G E R,
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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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">27. tertij.</
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>
A E R, ſemirectus. </
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>
<
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xml:space
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">Quare cum angulus E A R, rectus ſit, erit & </
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>
<
s
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xml:space
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">reliquus angulus E R A, ſemirectus;
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</
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>
<
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xml:space
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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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">32. primi.</
note
>
<
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xlink:label
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xlink:href
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xml:space
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">O@entale horo
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logium, ſi ita
<
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inuertatur, vt
<
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ſuperiota in in
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feriora, & quæ
<
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in hoc ſi@u dex-
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rra ſunt, fiant ſi
<
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niſtra, & cõtra,
<
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exhibet horolo
<
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gium occiden-
<
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tale. Eodemq́;
<
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modo occiden-
<
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tale dabi
<
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orien
<
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tale.</
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ac propterea exiſtentibus angulis E R A, A E R, æqualibus, æquales quoque erunt rectæ A E, A R; </
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>
<
s
xml:id
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xml:space
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">Ea-
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dem{q́ue} ratio eſt de A E, A Q, & </
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>
<
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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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<
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<
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<
s
xml:id
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xml:space
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">SATIS autem eſt, ſi ſolum horologiũ ad ortum ſpectans deſcribatur. </
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>
<
s
xml:id
="
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xml:space
="
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">Hoc enim ſi ita inuertatur,
<
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vt ſuperiora in inferiora, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">dextra in ſiniſtra mutentur, vt in ſcholio propoſ. </
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>
<
s
xml:id
="
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xml:space
="
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">14. </
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>
<
s
xml:id
="
echoid-s16258
"
xml:space
="
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">huius libri docuimus,
<
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præbebit nobis alterum horologium, quod ad occaſum ſpectat. </
s
>
<
s
xml:id
="
echoid-s16259
"
xml:space
="
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">Quod hac etiam ratione faciemus perſpi-
<
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cuum. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quoniam in triangulo A E C, in orientali horologio, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">in triangulo A E S, in occidentali, anguli
<
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ad A, æquales ſunt, nempe recti, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">anguli quoque ad E, æquales, ob æquales arcus inter H, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">rectas
<
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/>
E C, E S, poſitos, quibus inſistunt, necnon & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">latera A E, A E, dictis angulis adiacentia ſunt æqualia,
<
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cum vtrumq; </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſit longitudo ſtyli; </
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>
<
s
xml:id
="
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"
xml:space
="
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">erunt quoque latera A C, A S, æqualia. </
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>
<
s
xml:id
="
echoid-s16267
"
xml:space
="
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">Quoniam vero, ſi horologium
<
lb
/>
orientale occidentali ſuperponatur, ita vt punctum A, puncto A, & </
s
>
<
s
xml:id
="
echoid-s16268
"
xml:space
="
preserve
">linea horizontalis A B, lineæ hori
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0257-16
"
xlink:href
="
note-0257-16a
"
xml:space
="
preserve
">27. tertij.</
note
>
zontali A B, congruat, & </
s
>
<
s
xml:id
="
echoid-s16269
"
xml:space
="
preserve
">pars ſuperior Orientalis horologij cadat infra horizontalem lineam, & </
s
>
<
s
xml:id
="
echoid-s16270
"
xml:space
="
preserve
">infe
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0257-17
"
xlink:href
="
note-0257-17a
"
xml:space
="
preserve
">26. primi.</
note
>
rior ſupra: </
s
>
<
s
xml:id
="
echoid-s16271
"
xml:space
="
preserve
">Item in co ſitu pars dextra mutetur in ſiniſtram, & </
s
>
<
s
xml:id
="
echoid-s16272
"
xml:space
="
preserve
">contra, æquinoctialis linea A C, Orien
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0257-18
"
xlink:href
="
note-0257-18a
"
xml:space
="
preserve
">50</
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>
talis horologij lineæ æquinoctiali A S, horologij occidentalis congruit, propter æqualitatem angulorum,
<
lb
/>
quos vtraq; </
s
>
<
s
xml:id
="
echoid-s16273
"
xml:space
="
preserve
">linea æquinoctialis cum horizontali facit verſus eaſdem partes in hoc ſitu, quem orienta-
<
lb
/>
le horologium habet eo modo inuerſum, vt diximus; </
s
>
<
s
xml:id
="
echoid-s16274
"
xml:space
="
preserve
">cadet quoque punctum C, in punctum S, propter
<
lb
/>
æquales lineas A C, A S. </
s
>
<
s
xml:id
="
echoid-s16275
"
xml:space
="
preserve
">Quare & </
s
>
<
s
xml:id
="
echoid-s16276
"
xml:space
="
preserve
">linea primæ horæ orientalis horologii per punctum C, ducta lineæ
<
lb
/>
primæ horæ occidentalis horologii per punctum S, ductæ congruet, cum vtraq; </
s
>
<
s
xml:id
="
echoid-s16277
"
xml:space
="
preserve
">cum æquinoctiali linea an
<
lb
/>
gulum rectum conſtituat, vt ſupra ostendimus. </
s
>
<
s
xml:id
="
echoid-s16278
"
xml:space
="
preserve
">Eodem modo reliquas lineas horarias horologii orienta-
<
lb
/>
lis reliquis lineis horariis occidentalis horologii demonſtrabimus congruere. </
s
>
<
s
xml:id
="
echoid-s16279
"
xml:space
="
preserve
">Quocirca orientale horolo-
<
lb
/>
gium inuerſum, vt dictum eſt, exhibebit horologium occidentale, cum illud hac ratione eundem ſitum,
<
lb
/>
quem hoc, ſortiatur, ei{q́ue} æquale ſit omni ex parte, vt oſtendimus.</
s
>
<
s
xml:id
="
echoid-s16280
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s16281
"
xml:space
="
preserve
">SED horæ, quæ in orientali horologio numer antur à media nocte, ſunt poſt illam inuerſionem compu
<
lb
/>
tandæ à meridie, cum iam factum ſit occidentale.</
s
>
<
s
xml:id
="
echoid-s16282
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>