Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ſubtendentia angulos, per conſtructionem, æqualia; </
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DF, æquales, ac propterea & </
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cuum æqualium AG, AD, erunt æquales. </
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<
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<
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autem ſinus arcus AG, ad ſinum arcus GL, ita demonſtratum eſt, eſſe ſinum
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arcus AB, vel CB, ad ſinum arcus BI, vel BK, propterea quòd puncta B, G,
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in eodem ſemicirculo ſumpta ſunt. </
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CB, ad ſinum arcus BI, vel BK, ita ſinus arcus AD, ad ſinum arcus DF, &</
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circuli ſemicirculo vtrouis
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nempe in AEC, aliud pun
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ctum L: </
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circuli AEC, arcus maxi-
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mi circuli ducatur IBK:
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circuli ABC, arcus LGM,
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maximi circuli; </
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anguli I, G, recti. </
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ſus, vt eſt ſinus arcus AB,
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ad ſinum arcus BI, ita eſſe
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ſinum arcus AL, ad ſinum
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arcus LG, &</
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los enim vtriusque circuli
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ABCD, AECF, arcus cir
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culi maximi ducatur RE;
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">eruntq́ue anguli R, E, re-
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cti, diuidenturq́ue ſemicir-
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culi ABC, AEC, bifa-
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riam in punctis R, E; </
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adeo ſinus quadrantum AR, AE, æquales erunt; </
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ſinus arcus AR, ad ſinum arcus RE, quæ ſinus arcus AE, ad ſinum arcus ER.
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ad ſinum arcus BI, vt demonſtratum eſt; </
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B, in eodem ſemicirculo) erit quoque, vt ſinus arcus AE, ad ſinum arcus ER,
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ita ſinus arcus AB, ad ſinum arcus BI: </
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AE, ad ſinum arcus ER, ita ſinus arcus AL, ad ſinum arcus LG. </
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quoque, vt ſinus arcus AB, ad ſinum arcus BI, ita ſinus arcus AL, ad ſinum
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arcus LG, &</
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eiuſdem circuli AECF, aliud punctum, nempe F, & </
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lum D, rectum, erit adhuc, vt ſinus arcus AB, ad linum arcus BI, ita ſinus ar-
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cus AF, ad ſinum arcus FD, &</
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<
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cus AB, ad ſinum arcus BI, ita eſt arcus ſinus AL, ad ſinum arcus LG: </
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autem ſinus arcus AL, ad ſinum arcus LG ita demonſtratum eſt, eſſe ſinum
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arcus AF, ad ſinum arcus FD, quòd puncta L, F, ſumantur in duobus ſemi-
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circulis eiuſdem circuli. </
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cus BI, ita ſinus arcus AF, ad ſinum arcus FD: </
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eſt propoſitio, quomodocunq; </
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AECF, ſe mutuo ſecantad angulos non rectos.</
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