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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nationes, & </
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<
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">latitudines ortiuas, liquido conſtat, differentias inter aſcenſiones rectas, & </
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<
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xml:space
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">obliquas om-
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nium punctorum prioris quadrantis Eclipticæ ad quamuis poli altitudinem compertas, æquales eſſe diffe-
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rentijs aſcenſionum omnium punctorum trium poſteriorum quadrantum Eclipticæ in eadem altitudine
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poli. </
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<
s
xml:id
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xml:space
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">Quocirca ſatis erit, ſi inquir antur differentiæ aſcenſionum conuenientes punctis prioris quadrantis
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Eclipticæ à principio ♈, vſque ad principium ♋.</
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</
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<
s
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xml:space
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">EX his porrò differentijs aſcenſionum prioris quadrantis Eclipticæ, ita tabulam aſcenſionum obli-
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xlink:label
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xlink:href
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xml:space
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">Quo pacto ta-
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bula aſcenſio-
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num obliqua-
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rum ex differẽ-
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tiis aſcenſio na-
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libus compona
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tu
<
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r
<
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.</
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quarum omnium punctorum Eclipticæ ad datam altitudinem poli, pro qua differentiæ perueſtigatæ ſunt,
<
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componemus. </
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<
s
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xml:space
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">Quoniam in medietate Eclipticæ ab ♈, vſque ad ♎, perpetuo differentia aſcenſionum
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detrahenda eſt ab aſcenſione recta, vt obliqua aſcenſio cognita fiat, propterea quòd hæc medietas borea-
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lis eſt, ac proinde circulus maximus ex polo mundi, per punctum quodlibet illius ductus Aquatorem in-
<
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<
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fra Horizontem ſecat, vt ex priori duarum proximarum figurarum patet, efficitur, vt differentiæ aſcen-
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ſionum omnium punctorum prioris ſemicirculi ablata ex aſcenſionibus rectis eorundem punctorum re-
<
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linquant illorum aſcenſiones obliquas. </
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<
s
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xml:space
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">Rurſus quia in altero Eclipticæ ſemicirculo à ♎, vſq; </
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<
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">ad ♈, diffe
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rentia aſcenſionum ſemper adijcienda est ad aſcenſionem rectam, vt aſcenſio obliqua cognoſcatur, propte-
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rea quòd hic ſemicir culus auſtralis eſt, atque adeò circulus maximus ex polo mundi per quoduis punctum
<
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illius ductus Aequatorem ſupra Horizontem ſecat, vt conſtat ex posteriori figura proxima, perſpicuum
<
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eſt, differentias aſcenſionum omnium punctorum poſterioris huius ſemicirculi additas rectis aſcenſioni-
<
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bus eorundem punctorum conficere illorum aſcenſiones obliquas. </
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<
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<
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grad. </
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<
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<
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">♉, quam inuenimus ad latitudinem grad. </
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<
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<
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xml:space
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">eſſe grad. </
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<
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<
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">Min. </
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<
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">7. </
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<
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xml:id
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xml:space
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">æqualis eſt differentię aſcen-
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ſionum grad. </
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<
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">1. </
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<
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<
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">grad. </
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<
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<
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<
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">grad. </
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<
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<
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<
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xml:space
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">Hæc enim quatuor puncta eandem habent declinatio-
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nem. </
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<
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<
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<
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">♉, hoc eſt, ex grad. </
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<
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<
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<
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<
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erit aſcenſio obliqua grad. </
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<
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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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">Item ſi eandem differentiam ſubducamus ex
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recta aſcenſione grad. </
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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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<
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<
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<
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<
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<
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">pro aſcenſione
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obliqua grad. </
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<
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xml:id
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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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">Rurſus ſi eandem differentiam addamus aſcenſioni rectę grad. </
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<
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xml:id
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xml:space
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<
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xml:id
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xml:space
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">♏, quæ continet
<
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grad. </
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<
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">236. </
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<
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xml:id
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">Min. </
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<
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">46. </
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<
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">conficiemus grad. </
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<
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">255. </
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<
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">Min. </
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<
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="
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xml:space
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">53. </
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>
<
s
xml:id
="
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xml:space
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">pro aſcenſione obliqua grad. </
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<
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xml:id
="
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xml:space
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">29. </
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<
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">♏. </
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<
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">Ad extremum
<
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ſi apponamus differentiam eandem ad aſcenſionem rectam grad. </
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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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">14. </
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<
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xml:id
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xml:space
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tur, conflabitur arcus grad. </
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<
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<
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">Min. </
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<
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">21. </
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<
s
xml:id
="
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xml:space
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">pro obliqua aſcenſione grad. </
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>
<
s
xml:id
="
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xml:space
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">1. </
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>
<
s
xml:id
="
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xml:space
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">♒. </
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<
s
xml:id
="
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"
xml:space
="
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">Eadem{q́ue} de cæteris eſt ha-
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benda ratio. </
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>
<
s
xml:id
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xml:space
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">Hæc pauca libuit hocloco deguſtare ex aſcenſionibus rectis, & </
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<
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">obliquis; </
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<
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">plura enim alio
<
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in loco de eiſdem diſputauimus.</
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<
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<
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<
head
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xml:space
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">PROBLEMA. 10. PROPOSITIO 10.</
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<
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<
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">HOROLOGIVM Italicum Horizontale conſtituere. </
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<
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lineas horarum ab occaſu Solis in plano Horizonti æquidiſtanti 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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="
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">SECETVR circulus ex E, deſcriptus propoſ. </
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>
<
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">1. </
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>
<
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="
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">huius lib. </
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>
<
s
xml:id
="
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xml:space
="
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">in duas portiones, vt in ſcholio pro-
<
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<
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xlink:label
="
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xlink:href
="
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">I
<
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/>
talici horolo-
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gii horizontalis
<
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<
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compoſitio.</
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>
poſ. </
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>
<
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xml:id
="
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">1. </
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<
s
xml:id
="
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xml:space
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">præcedentis libri tradidimus, quarum a N b, ſimilis ſit arcui diurno tropici ♋, & </
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>
<
s
xml:id
="
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">a M b, ar-
<
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cui nocturno eiuſdem tropici. </
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<
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="
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xml:space
="
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">Diuiſo autem circulo eodem ex E, deſcripto in partes 24. </
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>
<
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="
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xml:space
="
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">æquales,
<
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<
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="
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xlink:label
="
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="
note-0212-06a
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">40</
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>
initio facto à pũcto b, quod occidentale eſt in communi ſectione Horizontis, & </
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>
<
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="
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xml:space
="
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">paralleli a b, (vt
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lb
/>
conſtat, ſi dictus circulus ex E, deſcriptus in propria poſitione concipiatur collocatus eſſe) tranſi-
<
lb
/>
bunt per hæc puncta diuiſionum, & </
s
>
<
s
xml:id
="
echoid-s12705
"
xml:space
="
preserve
">per centrum E, ſi circulus in propria poſitione exiſtat, circuli
<
lb
/>
maximi per polos Mundi, & </
s
>
<
s
xml:id
="
echoid-s12706
"
xml:space
="
preserve
">per horas ab occaſu in tropico ♋, ducti, inſtar horariorum circulo-
<
lb
/>
rum à meridie, vel media nocte. </
s
>
<
s
xml:id
="
echoid-s12707
"
xml:space
="
preserve
">Quoniam enim circuli maximi per polos mundi ducti diui-
<
lb
/>
dunt tropicum ♋, & </
s
>
<
s
xml:id
="
echoid-s12708
"
xml:space
="
preserve
">Aequatorem, per propoſ. </
s
>
<
s
xml:id
="
echoid-s12709
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s12710
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s12711
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s12712
"
xml:space
="
preserve
">Theod. </
s
>
<
s
xml:id
="
echoid-s12713
"
xml:space
="
preserve
">in arcus ſimiles; </
s
>
<
s
xml:id
="
echoid-s12714
"
xml:space
="
preserve
">erit arcus Ae-
<
lb
/>
quatoris interceptus inter Meridianum, & </
s
>
<
s
xml:id
="
echoid-s12715
"
xml:space
="
preserve
">circulum maximum per horam 24. </
s
>
<
s
xml:id
="
echoid-s12716
"
xml:space
="
preserve
">ab occaſu in tropi-
<
lb
/>
co ♋, hoc eſt, per punctum, vbi tropicus ♋, Horizontem ſecat, ductum, ſimilis arcui tropici ♋,
<
lb
/>
inter eoſdem circulos poſito, hoc eſt, arcui ſemidiurno tropici ♋. </
s
>
<
s
xml:id
="
echoid-s12717
"
xml:space
="
preserve
">Quoniam vero communes ſe-
<
lb
/>
ctiones, quas dicti circuli maximi cum Æquatore faciunt, per centrum Æquatoris E, ductæ ſe-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0212-07
"
xlink:href
="
note-0212-07a
"
xml:space
="
preserve
">50</
note
>
cant quoque, per ea, quæ ad finem cap. </
s
>
<
s
xml:id
="
echoid-s12718
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s12719
"
xml:space
="
preserve
">ſphæræ à nobis demonſtrata ſunt, Æquatorem, & </
s
>
<
s
xml:id
="
echoid-s12720
"
xml:space
="
preserve
">circu-
<
lb
/>
lum M a N b, ex E, centro Aequatoris, in eiuſdemq́ue plano deſcriptum, in arcus ſimiles; </
s
>
<
s
xml:id
="
echoid-s12721
"
xml:space
="
preserve
">erit
<
lb
/>
quoque arcus circuli M a N b, inter dictas ſectiones communes poſitus, ſimilis arcui ſemidiurno
<
lb
/>
tropici ♋. </
s
>
<
s
xml:id
="
echoid-s12722
"
xml:space
="
preserve
">Cum ergo M N, ſit ſectio facta in Aequatore à Meridiano, atque adeo Meridianus per
<
lb
/>
punctum N, ducatur, arcusq́; </
s
>
<
s
xml:id
="
echoid-s12723
"
xml:space
="
preserve
">N b, ſimilis ſit arcui ſemidiurno tropici ♋, (Quoniam enim totus
<
lb
/>
arcus b N a, ſimilis eſt, per conſtructionem, toti arcui diurno tropici ♋, erit quoque b N, dimidia-
<
lb
/>
tus arcus ipſius b N a, ſemidiurno arcui tropici ♋, ſimilis) atque adeo & </
s
>
<
s
xml:id
="
echoid-s12724
"
xml:space
="
preserve
">arcui Aequatoris inter
<
lb
/>
prædictas ſectiones interiecto, tranſibit neceſſario circulus alter maximus per horam 24. </
s
>
<
s
xml:id
="
echoid-s12725
"
xml:space
="
preserve
">ab occa-
<
lb
/>
ſu in tropico ♋, ductus, per punctum b. </
s
>
<
s
xml:id
="
echoid-s12726
"
xml:space
="
preserve
">Si enim per aliud punctum tranſiret, non auferrent dictæ
<
lb
/>
ſectiones ex Aequatore arcum ſimilem arcui b N, ſed illi, qui inter rectam E N, & </
s
>
<
s
xml:id
="
echoid-s12727
"
xml:space
="
preserve
">aliud illud pun-
<
lb
/>
ctum interijceretur. </
s
>
<
s
xml:id
="
echoid-s12728
"
xml:space
="
preserve
">Quod eſt abſurdum. </
s
>
<
s
xml:id
="
echoid-s12729
"
xml:space
="
preserve
">Oſtendimus enim arcum ex Aequatore ablatum </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>