Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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">_EXPONATVR_ circulus _ABCD,_ cuius centrum _E,_ per quod ducantur duæ
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diametri _AC, BD,_ ſeſe ad rectos angulos ſecantes & </
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<
s
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">totum circulum in quatuor
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quadrantes equales diuidentes, vtpote qui angulis rectis æqualibus in centro ſub
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<
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xlink:label
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note-114-01
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note
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tenduntur: </
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">& </
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<
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_FG, FI,_ ſecantes diametros in _H,_ & </
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xlink:label
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xml:space
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">Exẽpla deſi
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nitionum.</
note
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arcus _FA;_ </
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<
s
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xml:space
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">quia quadrans _AB,_ arcum _FA,_ ſuperat arcu _FB._ </
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_FA,_ complementum nominatur arcus _FB._ </
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<
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xml:space
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arcus _AI;_ </
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<
s
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xml:space
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">quiaarcu _BI,_ ſuperatur quadrans _AB,_ ab arcu _AI._</
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<
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114
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/114-01
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<
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">_RECTA_ deinde _FG,_
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chorda dicitur arcus _FAG;_
<
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</
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<
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xml:space
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">& </
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<
s
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xml:space
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">recta _FI,_ chorda arcus
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_FBI._ </
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<
s
xml:id
="
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xml:space
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">Et quia diameter _AC,_
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lb
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ſecãs arcũ _FAG,_ bifariã ſecat
<
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quoq; </
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<
s
xml:id
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xml:space
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">rectã _FG,_ bifariã, vt ex
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coroll, 1. </
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<
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<
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Euil. </
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<
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">cõſtat, (quod tamen in
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lẽmate ſequẽti breuius oſtẽde
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mus.) </
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<
s
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xml:space
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">erit recta _FH,_ ſinus re-
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ctus arcus _FA,_ iuxtapriorẽ de
<
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fin. </
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<
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<
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">quia eſt dimi-
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diũ chordæ _FG,_ ſubtendentis
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arcũ _FAG,_ duplum arcus _FA,_
<
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cuius _FH,_ dicitur ſinus. </
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<
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">Itaq; </
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<
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<
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ſi quemlibet arcũ, eiusq́; </
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<
s
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dam bifariã ſecemus, dimidiũ
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chordæ dicetur ſinus rectus
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dimidiati arcus. </
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<
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eſt, vt Sinus recti à plerisque
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xlink:label
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">Sinus recti
<
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curdicãtur
<
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ſemiſſes re-
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ctarum in
<
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circulo ſub
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tenſarum.</
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>
dicantur Semiſſes rectarum
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in circulo ſubtenſarum. </
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<
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_FA,_ ſecundum poſteriorem defin. </
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<
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">quoniam perpendicularis eſt, ducta ab _F,_
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extremo dicti arcus ad diametrum _AC,_ ab altero extremo _A,_ eiuſdem arcus ductam;
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</
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<
s
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">propterea quod recta _EA,_ ſecans rectã _FG,_ bifariam, ſecat eandẽ ad angulos rectos.</
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<
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<
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_AC,_ inter _A,_ extremum dicti arcus, & </
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<
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autem verſus Inc Sinus, quia verſomodo collocatur, ſi cum ſinu recto conferatur.
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ſus cur di-
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catur ſagit
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ta.</
note
>
Hunc nonnulli dicunt ſagittam, quoniam inſtar ſagittæ eſt in arcu _FAG,_ à chorda
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_FG,_ excuſſæ.</
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<
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<
s
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xml:space
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">quia eſt ſinus rectus arcus
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<
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cõplemẽti
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alicuius ar
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cus quid.</
note
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FB, qui complementum eſt arcus FA.</
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<
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">_RECTA_ autem _KB,_ eſt ſinus verſus complementi arcus _FA,_ hoc eſt, ſinus ber-
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ſus arcus _FB,_ qui complementum eſt arcus _FA._</
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<
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</
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<
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primꝰ ac ſe
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cundus: Itẽ
<
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ſinus pri-
<
lb
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mus & ſinꝰ
<
lb
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ſecundus
<
lb
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apud quos
<
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dam quid.</
note
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<
s
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">_NONNVLLI_ porro Aſtronomi Sinum, quem nos rectum diximus, appellant
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Sinum rectum primum; </
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<
s
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xml:space
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">Sinum vero, quem Sinum complementi diximus, bocant Sinum
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rectum ſecundum. </
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<
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<
s
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ctam bero _FK,_ ſinum rectum ſecundum eiuſdem arcus. </
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<
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rectum ſimpliciter appellent ſinum primum, verſum autem dicantſinum ſecundum.</
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