Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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<
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">SED iam circuli ABCD, AECF, ſecent ſe mutuo ad angulos rectos in
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punctis A, C; </
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<
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<
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<
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">ſemicirculo ABC, bifariam in H, vt ſint quadrantes AH, CH, ſumantur
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duo puncta vtcunque B, G. </
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<
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ſinum arcus AB, ad ſinum arcus, qui per B, ductus
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rectos angulos facit cum circulo AECF, vt eſt
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ſinus arcus AG, ad ſinum arcus, qui per G, ductus
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cum circulo AECF, rectos facit angulos. </
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<
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niam enim circulus ABC, cum rectus ad circulum
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AEC, ponatur, tranſit per polos circuli AEC,
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Coroll. 16.
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1. Theod.</
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erit H, polus circuli AEC. </
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diculares ad circulum AEC, per puncta B, G, du-
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cti neceſſario per H, tranſibunt; </
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<
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">atque adeò arcus
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illi erunt BA, GA: </
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">Perſpicuum autem eſt, vt eſt
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ſinus arcus AB, ad ſinum arcus BA, ita eſſe ſinum
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arcus AG, ad ſinum arcus GA, cum vtrobique
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ſit proportro æqualitatis, ſeu identitatis: </
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<
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nim idem ſinus arcus AB, & </
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">arcus BA, necnon
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idem ſinus arcus AG, & </
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<
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">QVOD ſi alterum punctorum ſit H, polus circuli AEC, erit quicun-
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que arcus ex H, ductus, qualis eſt HE, perpendicularis, ad AEC, atque adeò
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quadrans. </
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<
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">Rurſus igitur manifeſtum eſt, ita eſſe ſinum arcus AB, ad ſinum ar-
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xml:space
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">Coroll. 16.
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1. Theod.</
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cus BA, vt eſt ſinus arcus AH, ad ſinum arcus HE, vel HA; </
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<
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">cum vtrobique
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quoque ſit æ qualitatis proportio, &</
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<
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">c. </
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">Si duo ergo circuli maximi in ſphæra
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ſe mutuo ſecent, &</
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">PERSPICVVM eſt ex demonſtratis: </
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<
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">Si duo circuli ſe mutuo ſecent, & </
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<
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">in vno
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eorum ex duobus punctis vtcunq; </
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<
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">aſſumptis ducantur ad alterius circuli planum duæ
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lineæ rectæ perpendiculares; </
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<
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">ita eſſe ſinum rectum arcus intercepti inter vnum illo-
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rum punctorum, & </
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<
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">alterutram circulorum ſectionem, ad perpendicularem ex illo
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puncto in planum alterius circuli demiſſam, vt eſt ſinus rectus arcus inter alterum
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punctum, & </
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<
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">alterutram ſectionem circulorum interiecti, ad perpendicularem ab hoc
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altero puncto in planum alterius circuli demiſſam. </
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<
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">Nam in priori figura buius pro-
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poſ. </
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<
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">oſtenſum eſt, ita eſſe ſinum arcus
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, vel
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, ad BP, ſinum rectum arcus BI,
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vt eſt ſinus arcus AG, vel CG, ad GQ, ſinum rectum arcus GL. </
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<
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">Cum ergo ſinus BP,
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GQ, ſint perpendiculares ex punctis B, G, in planum circuli
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, demiſſæ, pa-
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tet propoſitum. </
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<
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">Quòd ſi vnum punctorum acceptum ſit B, ex vna parte ſectionis A,
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& </
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<
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, in eodem circulo;
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</
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<
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">erit nibilominus ita ſinus arcus AB, ad perpendicularem BP, ex B, demiſſam in pla-
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num alterius circuli AECF, vt ſinus arcus AD, ad perpendicularem, quæ ex D, in
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planum alterius circuli AECF, demitteretur: </
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<
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">propterea quod oſtenſum eſt, ita eſſe
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ſinum arcus AB, ad ſinum arcus BI, vt @ſt ſinus arcus AD, ad ſinum arcus DF; </
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<
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">qui
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quidem ſinus arcuum BI, DF, ſunt perpendiculares ex punctis B, D, in planum
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circuli AECF, cadentes, vt ex demonſtratis in hac propoſ. </
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<
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<
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">Idem
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perſpicitur in figura poſteriori; </
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<
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