Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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arcus
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, compoſita ex proportione ſinus arcus
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, ad ſinum arcus DE, & </
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proportione ſinus totius quadrantis AD, ad ſinum arcus
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. </
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<
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ſit complementum arcus
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.) </
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<
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">vt ſinus arcus CF, ad ſinum arcus
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, ita ſinus to-
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<
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tus ad tangentem arcus
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: </
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<
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">Item, (cum DE, ſit cowplementum arcus EF.) </
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<
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nus arcus DE, ad ſinum arcus EF, ita ſinus totus ad tangentem arcus
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; </
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">& </
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<
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uertendo, vt ſinus arcus
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, ad ſinum arcus
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, ita tangens arcus
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, ad ſinum
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totum. </
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, compoſita erit ex
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proportione tangentis arcus
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, ad ſinũ totum, & </
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<
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drantis
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D, ad ſinum arcus
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. </
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<
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">Cum ergo proportio tangentis arcus
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, ad ſi-
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num arcus
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, componatur quoque ex proportione tangentis arcus
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, ad ſinum
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totum, & </
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<
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; </
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<
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">quòd ſinus totus ſit me-
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dius inter illam tangentem, & </
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<
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, ita tangens arcus
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, ad ſinum arcus
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. </
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ſe mutuo ſecent, & </
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">à duobus punctis in vno aſſumptis ad alterum cir-
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culum duo arcus perpendiculares ducantur: </
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punctum ſectionis, & </
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">alterutrum punctorum ſumptorum ad ſecan-
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tem complementi arcus per reliquum punctum aſſumptum ducti, ita
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ſinus arcus inter punctum ſectionis, & </
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<
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ptum ad ſecantem complementi arcus per alterum illud punctum aſ-
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ſumptum ducti.</
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<
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">IN proxima figura ſecent ſeſe duo maximi circuli AD, AE, in A, ad angulosno@
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rectos, & </
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ducanturq́;</
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">Erunt BF, DF, quadrantes, ac propterea CF,
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,
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complementa arcuum
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,
<
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. </
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arcus
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, ad ſecantem arcus CF, vt eſt ſinus ar-
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cus AC, ad ſecantem arcus
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419-01
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puncto D, duo arcus educuntur
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, DF, à quo-
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rum terminis
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, F, duo alij ad ipſos reflectuntur
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<
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, ſe interſecantes in C; </
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<
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nus arcus
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, ad ſinum arcus
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, compoſita ex
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5. huius
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ſcholij.</
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proportione ſinus arcus
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, ad ſinum totum qua-
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drantis DF, & </
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<
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">ex proportione ſinus totius qua-
<
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<
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drantis
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, ad ſinum arcus
<
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. </
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<
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ſinus arcus
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, ad ſinum totum quadrantis DF,
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ita ſinus totus ad ſecantem arcus
<
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; </
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<
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quòd ſinus totus medio loco proportionalis eſt in-
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<
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ter ſinum rectum arcus
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, & </
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<
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<
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, qui complementum eſt arcus
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:
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</
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<
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ademq́; </
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<
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">ratione ita eſt ſecans arcus CF, ad ſinum totum, vt ſinus totus quadrantis
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<
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, ad ſinum arcus
<
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; </
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<
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">quòd ſinus totus medio quoque loco ſit proportionalis inter
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ſecantem arcus CF, qui complementum eſt arcus
<
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, & </
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<
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. </
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Igitur proportio ſinus arcus
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, ad ſinum arcus
<
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, componetur quoque ex pro-
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portione ſecantis arcus CF, ad ſinum totum, & </
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<
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