Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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larem ex B, in planum circuli
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, demiſſam, ita ſinus arcus AG, ad perpendi-
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cularem ex G, in planum circuli AECF, demiſſam: </
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<
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AB, AG, ſuntipſæmet perpendiculares ex B, G, in planum circuli AECF, demiſſæ
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cadentes in rectam AC, communem circulorum ſectionem, vt patet.</
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<
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rimum ad ſphæricorum triangulerum calculum conducunt. </
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<
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">Primum autem ac ſecun-
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dum ſunt duo Theoremata Ptolemæi Cyclica in primo lib. </
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<
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">Almageſti, ſed multo bre-
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uius, ac facilius demonſtrata ex ijs, quæ in hoc ſcholio oſtenſa ſunt. </
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@on videbantur, licet eorum vſus in hiſce triangulis non appareat.</
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<
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circulorum educantur, quorum vterque ſemicitculo ſit minor, & </
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<
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eorum terminis in ipſos reflectantur alij duo arcus maximorum cir-
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culorum ſe inter duos illos priores arcus interſecantes: </
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quam ſinus ſegmẽti vnius eductorum arcuum inter terminum eius,
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& </
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">arcum reflexum habet ad ſinum alterius ſegmenti eiuſdem arcus
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educti, componitur ex proportione, quam ſinus ſegmenti arcus re-
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flexi inter eundem terminum, & </
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ſinum alterius ſegmenti eiuſdem arcus reflexi, & </
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quam ſinus ſegmenti alterius eductorum arcuum inter eius termi-
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num, & </
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minores, & </
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">à terminis B, C, reflectantur adipſos duo arcus BD, CE, ſe interſe-
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cantes in F.</
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portione ſinus arcus
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, ad ſinum arcus
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D, & </
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ſinum arcus CA. </
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circuli CE, tribus perpendicularibus BG, AH, DI; </
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duo circuli AB, CE, ſe mutuo ſecant in E, & </
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">ex punctis B, A,
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in planum circuli
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, demiſſæ ſunt perpendiculares
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G, AH;
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huius. &
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permutan.
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do.</
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rectam AH: </
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E, ſe mutuo
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ſecant in
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, & </
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">ex punctis B,D, in planum circuli CE, deductæ
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ſunt perpendiculares BG, DI; </
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cus
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, ad ſinum arcus FD, ita recta BG, ad rectam DI: </
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nique quia duo circuli AC,
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, ſe interſecant in C, & </
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punctis D,
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in planum circuli
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, demiſſæ ſunt perpendi-
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culares rectæ lineæ DI, AH; </
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<
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CD, ad ſinum arcus CA, ita recta DI, ad rectam AH. </
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p@rtio autem recta BG, ad rectam AH, (poſita media linea DI.) </
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portione rectæ BG, ad rectam DI, & </
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tur & </
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, ad ſinum arcus EA, (quæ eadem eſt, quæ propor-
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tio BG, ad AH.) </
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(quæ eadem eſt, quæ proportio BG, ad DI.) </
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@inum arcus AC, (quæ eadem eſt, quæ DI, ad AH.) </
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