Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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verſi alterius arcus. </
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<
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xml:space
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">Duotumat
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euum, quo
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rum vnus
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alterius eſt
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complemẽ
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tum, ſinus
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rectꝰ vtriuf
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libet æqua
<
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lis eſt com-
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plemento
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ſinus verſi
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alterius at
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eus.</
note
>
ipſe ſinus verſus à ſemidiametro ſuperatur, ſi eius arcus quadrante minor eſt, vel ſe-
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midiametrum ſuperat, ſi eius arcus maior eſt quadrante. </
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<
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xml:space
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">Vt _HE,_ dicimus comple-
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mentum tam ſinus verſi _AH,_ arcui _FA,_ reſpondentis, quàm ſinus verſi _CH,_ arcui
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_FC,_ reſpondentis. </
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<
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xml:space
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">Vides igitur, duorum arcuum _FA, FB,_ quorum vnus alterius
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eſt complementum, ſinum rectum _FK,_ arcus _FB,_ æqualem eſſe ipſi _HE,_ complemente
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ſinus verſi _AH,_ alterius arcus _FA:_ </
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<
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">Et ſinum rectum _FH,_ arcus _FA,_ æqualem eſſe
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ipſi _EK,_ complemento ſinus verſi _BK,_ alterius arcus _FB._ </
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<
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xml:space
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">Eadem ratione, quoniam
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arcus _FB,_ complementum eſt arcus _FC,_ vides ſinum rectum _FH,_ arcus _FC,_ æqualem
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eſſe ipſi _EK,_ complemente ſinus verſi _BK,_ alterius arcus _FB:_ </
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<
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">Et ſinum rectum _FK,_
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116-01
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arcus _FB,_ æqualem eſſe ipſi
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mentum ſi
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nus verſi
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quid.</
note
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_EH,_ complemento ſinus verſi
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_CH,_ alterius arcus _FC._ </
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<
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etiam ſinus complemẽtiarcus
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cuiuſuis æqualis eſt complemẽ
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to ſinus verſi eiuſdem arcus.
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</
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<
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">Vt _FK,_ ſinus complementi are
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cus _AF,_ vel _FC,_ æqualis eſt
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<
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xlink:label
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xml:space
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">14. primi.</
note
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ipſi _HE,_ complemento ſinus
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verſi _AH,_ vel _CH,_ arcus
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_AF,_ vel _FC._</
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circulo, vel in circulis æqua-
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">In eodem
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circulo, aut
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æqualibus,
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arcuum æ-
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qualium
<
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finus æqua
<
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les ſunt; &
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contra. At
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arcuũ in æ-
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qualium ſi
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nus inęqua
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les ſunt; &
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contra.</
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>
libus, ſinus tam recti, quàm
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verſi, aut ſinus complemento-
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rum arcuum æqualium, & </
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<
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<
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quadrante minorum, æquales
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ſunt: </
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<
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xml:space
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">Et contra, æqualium ſi-
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nuũ tam rectorum, quàm ver
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ſorum, aut ſinuum complemen
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torum, arcus quadrãte mino-
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res æquales ſunt. </
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<
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inæqualium, & </
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">quadrante minorum, ſinus inæquales ſunt, ſinus quidem tam rectus
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quàm verſus maioris maior, minoris verò minor; </
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arcus minor, & </
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quam verſorum, aut ſinuum complementorum, inæquales arcus ſunt, maioris qui-
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dem ſinus tam recti quàm verſi maior arcus, & </
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ſinus complementi arcus minor, & </
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_DG._ </
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</
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<
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<
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erunt quoque anguli _BEF, DEG,_ æquales. </
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<
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nec non & </
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_GL,_ quàm latera _EK, EL,_ inter ſe æqualia erunt, nempe ſinus recti inter ſe, & </
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nus complementorum inter ſe. </
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_EB, ED,_ reliqui erunt ſinus verſi _KB, LD,_ æquales. </
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ſinus æquales ſiue recti _FK, GL,_ ſiue verſi _KB, LD,_ ſiue ſinus complementorum _EK,_
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_EL._ </
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<
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