Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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quauis ad eandem partem producta; </
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<
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<
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xml:space
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">producta,
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& cũ dia-
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metro pro-
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ducta con-
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ueniens, ad
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ſegmẽtum
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exterius.</
note
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proportio totius chordæ productæ ad ſegmẽtum
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exterius, quæ ſinus arcus inter punctú, per quod
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diameter producta eſt, & </
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<
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tremum dictæ chordæ, ad ſinum arcus inter idem
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punctum diametri, & </
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<
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tremum eiuſdem chordæ.</
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</
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<
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<
s
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xml:space
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">IN circulo ABCD, chorda AD, arcus AD, ad partes D, producta con-
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ueniat cum diametro BC, ad eaſdem partes producta in puncto E; </
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<
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turq́ue AF, DG, ad diametrum BC, perpendiculares; </
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<
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arcus AC: </
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">& </
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<
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ſe AE, ad DE, ut AF, ad DG. </
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<
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AF, DG, parallelæ ſunt obangulos rectos F,
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Coroll. 4.
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ſexti.</
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G; </
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<
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xml:space
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re erit, ut AE, ad AF, ita DE, ad DG: </
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<
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xml:space
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mutando, ut AE, ad DE, ita AF, ad DG. </
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<
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xml:space
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igitur in circulo chorda cuiuſlibet arcus ad
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unam partem producatur, conueniatq́ue cum
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diametro quauis, &</
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<
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data duorũ
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arcuũ, quo
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rum quili-
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bet ſemicir
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culo minor
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ſit, vel duo-
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rum angu-
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lotum, vna
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cũ propor-
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ticne, quã
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eorũ ſinus
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habẽ@, vter-
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que cogno
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ſcitur.</
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<
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">DATO aggregato duorum arcuum, quo-
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rum ſinguli ſemicirculo ſint minores, vel duorum
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angulorum rectilineorum, ſiue minus illud ſit, ſi
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ue maius, quàm grad. </
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<
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<
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">vnà cum proportione,
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quam eorum ſinus habent: </
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<
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gillatim exhibere notum.</
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</
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<
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<
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xml:space
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">IN circulo ABCD, cuius centrum E, datum ſit primo aggregatum ar-
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<
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">Quãdo ag
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gregatũ ar-
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cuum, vel
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angulorũ
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minus eſt,
<
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quã grad.
<
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180.</
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cuum BF, FD, quorum ſinguli ſint ſemicirculo minores, uel angulorũ BEF,
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FED, & </
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<
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</
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<
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anguli BEF, ad ſinum arcus FD, uel anguli FED, eadẽ, quæ 10.</
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tet ex his utrumque arcum BF, FD, uel utrumque angulum BEF, FED,
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notum efficere. </
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<
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iunguntur, diameter FC, ſecans chordam BD, in G. </
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<
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