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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<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 536
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LIBER SEXTVS.
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Sectio denique communis Horizontis, Verticalis, & </
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<
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">Aequatoris, ſiue Hectemorii, qui omnes ſe
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mutuo ſecant in ortu, occaſuve æquinoctiali, & </
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<
s
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xml:space
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">per centrum mundi ducuntur, ſit recta E H. </
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>
<
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">His
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omnibus recte perceptis, & </
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<
s
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xml:space
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">demonſtratis, oſtendendum nunc eſt, arcum H K, in Meridiano æqua
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lem eſſe circunferentiæ hectemoriæ H k, in Hectemorio, ſeu Aequatore propriam poſitionem ha-
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bente; </
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>
<
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xml:space
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">& </
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<
s
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xml:space
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">arcum B M, in Meridiano æqualem circunferentiæ horariæ B K, in Horario; </
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<
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xml:space
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">& </
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<
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xml:space
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">arcum
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A P, in Meridiano æqualem circunferentiæ deſcenſiuæ A K, in Deſcenſiuo: </
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<
s
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lem eſſe meridianæ circunferentiæ inter Horizontem, & </
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<
s
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xml:space
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">Hectemorion; </
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<
s
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xml:space
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">arcum vero A T, in Meri-
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diano circunferentiæ Verticali A X, in Verticali inter Meridianum, & </
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<
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">Horarium; </
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<
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">arcum denique
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A S, in Meridiano circunferentiæ horizõtali H Y, in Horizonte inter Verticalem, & </
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<
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</
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<
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">Quod ita ferè cum Federico Commandino demonſtrabimus. </
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</
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<
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<
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xml:space
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">DVCTA recta E k, in plano Meridiani; </
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<
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xml:space
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">quoniam duo latera E K, K L, trianguli E K L, in
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plano Meridiani, æqualia ſunt duobus lateribus E K, K L, in plano Hectemorii, (vtraque enim
<
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<
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">Demonſtratio
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hectemoriæ cir
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cunferentiæ.</
note
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E K, à centro E, ad ſuperſiciem ſphæræ ducitur, proptereaq́ue vna alteri æqualis eſt: </
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<
s
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k L, in Meridiano congruet rectæ k L, communi ſectioni Hectemorii, & </
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<
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">ſemicirculi M k a Z d,
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ſi ſemicirculus Meridiani F H G, circa rectam F G, conuertatur, donec rectus ſit ad planum Me-
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ridiani; </
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<
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planum Meridiani; </
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<
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">recta quidem K L, quæ in
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plano Meridiani eſt, ex defin. </
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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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">altera vero, quòd communis ſectio ſit duorum plano-
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xml:space
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">19. vndec.</
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rum ad Meridianum rectorum. </
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<
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xml:space
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">Hinc enim fit, vt perpendicularis ſit ad eundem Meridianum.
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</
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<
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xml:space
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">Cum ergo vtraque k L, in ſuperficie ſphæræ terminetur, vna alteri æqualis erit) eſtq́ue baſis E L,
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communis; </
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<
s
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="
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xml:space
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">erunt anguli K, illorum triangulorum æquales. </
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<
s
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xml:space
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">Sed ille in plano Meridiani æqualis
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">20</
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eſt angulo alterno K E H, in eodem plano, propterea quòd rectæ K L, H E, parallelæ ſunt, ob an-
<
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gulos rectos k L E, H E L; </
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<
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">hic vero in Hectemorio, eandem ob cauſam, æqualis eſt angulo K E H,
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in eodem Hectemorio: </
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<
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">Rectæ enim k L, E H, parallelæ ſunt, cum ſint ſectiones factæ ab He-
<
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<
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ctemorio in planis parallelis, nempe in Horizonte, & </
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<
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lus K E H, in Meridiano æqualis erit angulo K E H, in Hectemorio, ideoq́ue arcus H K, in Me-
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ridiano arcui H K, in Hectemorio æqualis. </
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<
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">Quod erat oſtendẽdum. </
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<
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">Quod etiam breuius ita colli-
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<
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gi poteſt. </
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<
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">Quoniam tempore æquinoctij Hectemorion ab Aequatore non differt, erit arcus
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H k, (ſi Meridianus pro Aequatore ſumatur) inter Horizontem, & </
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<
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">centrum Solis, circunferentia
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hectemoria.</
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<
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</
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<
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<
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<
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">Horarius ducuntur per B D, polos Verticalis circuli, & </
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<
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<
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<
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xml:space
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">Demonſtratio
<
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horariæ circun-
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ferentiæ.</
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culi M K a Z d, qui Verticali æquidiſtat, erũt, per propoſ. </
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<
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<
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<
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">arcus Meridiani A M,
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& </
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<
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">arcus Horarij X K, cum inter parallelos circulos cõprehendantur, inter ſeæquales. </
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<
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A B, X B, quadrantes ſint, quod B, polus Verticalis quadrante abſit ab ipſo Verticali, ex coroll.
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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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">Theod. </
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<
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">erit quoque arcus reliquus B M, in Meridiano æqualis reliquæ circun-
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ferentiæ horariæ B K, in Horario. </
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<
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">Quod etiam breuius demonſtrabimus hoc modo. </
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<
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xml:space
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B, polus eſt ſemicirculi M K a Z d, erunt, per defin. </
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<
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">poli, chordę B M, B K, æquales. </
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<
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<
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cus B M, B k, æquales erunt. </
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<
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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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<
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<
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">Deſcenſiuus ducuntur per A, C, polos Horizontis
<
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<
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deſcenſiuæ cir-
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cunfeientiæ.</
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& </
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<
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">ſemicirculi P K V b e, qui Horizonti æquidiſtat, erunt, per propoſ. </
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<
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<
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<
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<
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Meridiani B P, & </
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<
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">arcus Deſcenſiui Y K, cum inter parallelos circulos includantur, æquales inter
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<
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ſe. </
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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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">reliquus arcus
<
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A P, in Meridiano æqualis reliquæ circunferentiæ deſcenſiuæ A K, in Deſcenſiuo. </
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>
<
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="
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xml:space
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">Quod faci-
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lius ita concludemus. </
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<
s
xml:id
="
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xml:space
="
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">Quoniam A, polus eſt ſemicirculi P K V b e, erunt per defin. </
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>
<
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xml:id
="
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xml:space
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">poli chordæ
<
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A P, A K, æquales. </
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<
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xml:id
="
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xml:space
="
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">Igitur & </
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>
<
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xml:id
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">arcus A P, A K, æquales erunt. </
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>
<
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xml:space
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">Quod eſt propoſitum.
<
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</
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<
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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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">28. tertij.</
note
>
</
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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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">IAM vero B F, eſſe circunferentiam meridianam, perſpicuum eſt, cum inter lineam meridia
<
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<
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xlink:label
="
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xlink:href
="
note-0551-16a
"
xml:space
="
preserve
">Demonſtratio
<
lb
/>
meridianę cir-
<
lb
/>
cunferentiæ.</
note
>
nam B D, ſiue Horizontem, & </
s
>
<
s
xml:id
="
echoid-s34542
"
xml:space
="
preserve
">Hectemorion F H G, interijciatur.</
s
>
<
s
xml:id
="
echoid-s34543
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s34544
"
xml:space
="
preserve
">RVRSVS, quia Horarius circulus B K X b D, ſecat duos circulos parallelos, nempe Hori-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0551-17
"
xlink:href
="
note-0551-17a
"
xml:space
="
preserve
">Demonſtratio
<
lb
/>
Verticalis cir-
<
lb
/>
cunferenriæ.</
note
>
zontem, & </
s
>
<
s
xml:id
="
echoid-s34545
"
xml:space
="
preserve
">ſemicirculum P K V b e, erunt ſectiones, quas in illis facit, hoc eſt, rectæ B D, K b,
<
lb
/>
inter ſe parallelæ: </
s
>
<
s
xml:id
="
echoid-s34546
"
xml:space
="
preserve
">Eſtautem, propter angulos rectos B E O, P O E, recta P e, ipſi B D, quoque pa-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0551-18
"
xlink:href
="
note-0551-18a
"
xml:space
="
preserve
">16. vndec.</
note
>
rallela. </
s
>
<
s
xml:id
="
echoid-s34547
"
xml:space
="
preserve
">Igitur & </
s
>
<
s
xml:id
="
echoid-s34548
"
xml:space
="
preserve
">rectæ K b, P e, parallelæ inter ſe erunt. </
s
>
<
s
xml:id
="
echoid-s34549
"
xml:space
="
preserve
">Item quia ſemicirculus P K V b e, ſecãs
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0551-19
"
xlink:href
="
note-0551-19a
"
xml:space
="
preserve
">50</
note
>
<
note
position
="
right
"
xlink:label
="
note-0551-20
"
xlink:href
="
note-0551-20a
"
xml:space
="
preserve
">28. primi.</
note
>
circulos parallelos, nimirum Verticalem, & </
s
>
<
s
xml:id
="
echoid-s34550
"
xml:space
="
preserve
">ſemicirculum M K a Z d, facit communes ſectiones
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0551-21
"
xlink:href
="
note-0551-21a
"
xml:space
="
preserve
">9. vndec.</
note
>
V O, K L, parallelas, parallelogrãmum erit K L O I, proptereaq́; </
s
>
<
s
xml:id
="
echoid-s34551
"
xml:space
="
preserve
">recta O I, rectę L K, æqualis, hoc
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0551-22
"
xlink:href
="
note-0551-22a
"
xml:space
="
preserve
">16. vndec.</
note
>
eſt rectæ O R, cũ OR, ſumpta ſit æqualis, ipſi K L. </
s
>
<
s
xml:id
="
echoid-s34552
"
xml:space
="
preserve
">Cum igitur duo latera I O, O E, trianguli I O E,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0551-23
"
xlink:href
="
note-0551-23a
"
xml:space
="
preserve
">34. primi.</
note
>
æqualia ſint duobus lateribus R O, O E, trianguli R O E, & </
s
>
<
s
xml:id
="
echoid-s34553
"
xml:space
="
preserve
">anguli I O E, R O E, ſub ipſis contenti
<
lb
/>
recti. </
s
>
<
s
xml:id
="
echoid-s34554
"
xml:space
="
preserve
">(Quoniã enim tam Verticalis, quam ſemicirculus P K V b e, ad Meridianum rectus eſt, erit
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s34555
"
xml:space
="
preserve
">ipſorum cõmunis ſectio V O, ad eundẽ perpendicularis, atque adeo & </
s
>
<
s
xml:id
="
echoid-s34556
"
xml:space
="
preserve
">ad rectam A C, ex defin.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s34557
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-0551-24
"
xlink:href
="
note-0551-24a
"
xml:space
="
preserve
">19. vndec.</
note
>
3. </
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>
<
s
xml:id
="
echoid-s34558
"
xml:space
="
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">lib. </
s
>
<
s
xml:id
="
echoid-s34559
"
xml:space
="
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">11. </
s
>
<
s
xml:id
="
echoid-s34560
"
xml:space
="
preserve
">Eucl. </
s
>
<
s
xml:id
="
echoid-s34561
"
xml:space
="
preserve
">Igitur angulus I O E, rectus eſt: </
s
>
<
s
xml:id
="
echoid-s34562
"
xml:space
="
preserve
">angulus autem R O E, per conſtructionem re-
<
lb
/>
ctus eſt:) </
s
>
<
s
xml:id
="
echoid-s34563
"
xml:space
="
preserve
">erit angulo I E O, angulus R E O, æqualis. </
s
>
<
s
xml:id
="
echoid-s34564
"
xml:space
="
preserve
">Quocirca & </
s
>
<
s
xml:id
="
echoid-s34565
"
xml:space
="
preserve
">arcus A T, in Meridiano ſubten
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0551-25
"
xlink:href
="
note-0551-25a
"
xml:space
="
preserve
">4. primi.</
note
>
dens angulum T E A, in centro æqualis erit circunferentiæ Verticali A X, qui angulum X E A,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0551-26
"
xlink:href
="
note-0551-26a
"
xml:space
="
preserve
">26. tertij.</
note
>
in centro ſubtendit.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s34566
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-0551-27
"
xlink:href
="
note-0551-27a
"
xml:space
="
preserve
">Demonſtratio
<
lb
/>
horizontalis cir
<
lb
/>
cunferentiæ.</
note
>
</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s34567
"
xml:space
="
preserve
">POSTREMO, quoniam circulus Deſcenſiuus A K Y Z C, ſecat duos circulos </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>
