Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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rint, vel alter eorũ obtuſus: </
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<
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">erit in triangulo rectangulo ABD, vt latus AB,
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ad latus AD, ita ſinus anguli recti D, ad ſinum anguli B, vt ſupra eſt demon-
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ſtratum: </
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<
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ſinus anguli C, ad ſinum anguli recti D. </
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<
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<
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">perturbata
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proportione erit, vt latus AB, ad latus AC, ita ſinus anguli C, (Habẽt enim
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duo anguli ad C, in obtuſangulo triangulo eundem ſinum, vt in tractatione
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ſinuum oſtendimus. </
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<
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xml:space
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">ad ſinum anguli B, vt in formula ſuprapoſita apparet: </
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<
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conuertendo quoq;</
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<
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xml:space
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">, vt latus AC, ad latus AB, ita ſinus anguli B, ad ſinum
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anguli C. </
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<
s
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xml:space
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">Eodem modo concludemus eſſe, vt latus AB, ad latus BC, ita ſi-
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num anguli C, ad ſinum anguli BAC: </
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<
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xml:space
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">Vel vt latus BC, ad latus AB, ita ſi-
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num anguli BAC, ad ſinum anguli C, &</
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<
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<
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ctilineo latera quæuis duo eandem proportionem habent, quam ſinus angu-
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lorum illis oppoſitorum. </
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<
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<
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ex @@ibꝰ vel
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duobusan-
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gulis notis
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cuiuſuis
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triãguli co-
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gnoſcantur
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propottio-
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nes laterũ.</
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<
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">_EX_ hac propoſ facile colligemus proportiones laterum cuiuſuis trianguli recti-
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linei, cuius omnes anguli cogniti ſint, vel duo tantum Sint entm omnes anguli in
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triangulo _ABC,_ noti. </
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<
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">Dico proportiones laterum notas eſſe. </
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<
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ſit proportio lateris _AB,_ ad latus
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313-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/313-01
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_AC,_ quæ ſinus anguli _C,_ ad ſinum
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anguli _B;_ </
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<
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_C, B,_ notorum cogniti ex tabula ſi-
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nuum; </
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<
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ad latus _AC,_ &</
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<
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<
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ponatur in primo triangulo angulus
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_C,_ grad. </
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<
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<
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<
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<
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grad. </
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<
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<
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</
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<
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<
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">93969._ </
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<
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_AB,_ ad _AC,_ eadem, quæ _86602._ </
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<
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<
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<
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ad _93969._ </
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<
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<
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">_AC,_ ad _BC,_ eadem, quæ _76604._ </
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<
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<
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do ponatur angulus _B,_ rectus, ac proinde grad. </
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<
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<
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Horum ſinus ſunt _100000. </
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<
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<
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<
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">Eritigitur _AB,_ ad _AC,_ vt _76604._ </
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_100000._ </
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<
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<
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<
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<
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<
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<
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_64278._ </
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<
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<
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<
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grad. </
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<
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<
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">_A,_ grad _26_ Horum ſinus ſunt (ſi pro ſinu anguli obtuſi accipiatur ſi-
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nus complementi ipſius vſq; </
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<
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_43837_ Quare erit _AB,_ ad _AC,_ vt _50000._ </
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<
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ad _43837._ </
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<
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<
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">IT AQVE vt facile pro@ortiones laterum habeantur, ſatis eſt, ſila-
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">Praxis.</
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teribus ſinus angulorum oppoſitorum aſcribantur: </
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ra eandem proportionem habent, quam oppoſitorum angulorum ſinus, vt
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demonſtratum eſt.</
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<
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">_QVOD_ ſi duo tantum anguli cogniti ſint, erit reliquus tertius quoq; </
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<
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<
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<
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auxilio antecedentis propoſ. </
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<
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<
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<
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