Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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Ioan. de Sacro Boſco.
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<
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<
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in ſphęra non maximi ſe inuicem ſecantes, ſe mutuo biſariam
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non ſecant. </
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">Nam ſi mutuo ſe bifariam ſecarent, eſſent ipſi per propoſ. </
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<
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xml:space
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">Theodoſij, circuli maximi, quod eſt contra hypotheſim. </
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rum diuidi aliquando bifariam, ſed cum hoc accidit, alter tunc nequaquam bi
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fariam ſecabitur, niſi ambo circuli ſint maximi.</
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<
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<
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cir culos ſphęræ non maximos ſolum ij ſunt æquales inter ſe, qui
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æqualiter a centro ſphærę remouentur. </
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<
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">Et contra circuli non maximi inter ſe
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ęquales ęqualiter recedunt à centro ſphęræ. </
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doſio lib. </
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<
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<
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circulus maximus in ſphęra tranſiens per polos alterius circuli
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ſiue maximi, ſiue non maximi, diuidit eum bifariam, & </
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contra circulus in ſp hæra diuidens alium circulum bifariam, & </
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ctos eſt, circulus maximus, inceditq́; </
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eſt demonſtratum.</
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<
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circulus maximus in ſphęra, per cuius polos tranſit alius circulus
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in ſphęra maximus, tranſit uiciſſi@@ per polos illius. </
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nobis theoremate 1. </
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<
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in ſphęra maximus, qui aliquem circulum non maximum
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tangit, tanget quoque alium non maximum illi ęqualem, & </
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quidem oſtendit Theodoſius lib. </
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<
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in ſphęra maximus ſecãs circulos non maximos non per po
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los eorum, hoc eſt, oblique, ſecat illos in partes inæquales, ita tamen, ut ęqua-
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lium, ac parallelorum circulorum ſegmenta alterna inter ſe ſint ęqualia. </
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perſpicuum eſt ex 19. </
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<
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tres circuli in ſphęra maximi ſe mutuo ſecant ad angulos
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rectos, erunt duo poli cuiuslibet illorum præciſe in communibus ſectionibus
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circunfer entiarum aliorum duorum. </
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<
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in ſphæra, ita ut duo poli cuiuſuis illorum reperiantur in communibus ſectio-
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nibus aliorum duorum, ſecabunt ſe mutuo ad angulos rectos. </
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<
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que facile deduci poteſt ex Theodoſio, ſeu proprietatibus adductis, uidelicet
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ex 5. </
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<
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quoque utriuſque habes in ſphæra materiali. </
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Æquatuor, Meridianus, & </
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ctos ſecent, quod tum demum fiet, cum uterque mundi polus præciſe in Ho-
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rizonte iacebit, ficut accidit in ſphęra recta) uidebis polos Æquatoris eſſe in
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communibus ſectiouibus Meridiani, atque Horizontis; </
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communibus ſectionibus Aequatoris Horizontisq́ue; </
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tis in communibus ſectionibus Aequatoris, ac Meridiani, &</
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