Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ra DE, EI, lateribus KE, EI, æqualia ſint, & </
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<
s
xml:id
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<
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xml:id
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echoid-s9692
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xml:space
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">angulus DEI,
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angulo KEI, æqualis erit. </
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<
s
xml:id
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echoid-s9693
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xml:space
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">Quia ergo arcus BFD, datus eſt grad. </
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<
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">130. </
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<
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xml:space
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<
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tur reliquus DK, de ſemicirculo grad. </
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<
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<
s
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">eius ſemiſsis, id eſt, angulus DEI,
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grad. </
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<
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">25. </
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<
s
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xml:space
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">Rurſus quia finus arcus BF, ad ſinum arcus FD, ponitur, ut 10. </
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<
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5. </
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<
s
xml:id
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xml:space
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">eſtq́ue idem ſinus arcus KF, qui arcus BF, vt in defin. </
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<
s
xml:id
="
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xml:space
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">ſinuum oſtenſum eſt:
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</
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<
s
xml:id
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xml:space
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">erit quoque ſinus arcus KF, ad ſinum arcus DF, vt 10.</
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<
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<
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ſinus arcus KF, ad ſinum arcus DF, ita KL, ad DL; </
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<
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xml:space
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">erit etiam KL, ad DL, vt
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<
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xml:space
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10.</
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<
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<
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xml:space
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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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">eius
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ſemiſsis ID, 2 {1/2}. </
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<
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xml:space
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">At quoniam, vt ad initium tangentium & </
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<
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xml:space
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">ſecantiũ diximus,
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poſito ſinu toto EI, recta ID, tangens eſt anguli DEI, hoc eſt, grad. </
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>
<
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xml:id
="
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xml:space
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">25. </
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<
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xml:id
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bitur ID, ex tabula tangẽtium, partium 46631. </
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>
<
s
xml:id
="
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xml:space
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">Dicemus ergo per auream re
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gulam. </
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<
s
xml:id
="
echoid-s9720
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xml:space
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">Si ID, ſemiſsis differentiæ inter terminos proportionis datæ, nempe
<
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2 {1/2}. </
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>
<
s
xml:id
="
echoid-s9721
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xml:space
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">dat ID, tangentem ſemiſsis differentiæ inter aggregatum datum, & </
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<
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circulum, partium 46631. </
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<
s
xml:id
="
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xml:space
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">quid dabit IL, compoſita ex ſemiſſe differentiæ in-
<
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ter terminos datæ proportionis, & </
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<
s
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">conſequente eiuſdem proportionis, nimi-
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rum 7 {1/2}? </
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<
s
xml:id
="
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xml:space
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">reperiemusq́ue IL, partium 139893. </
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<
s
xml:id
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">qualium ID, eſt 46631. </
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<
s
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">vel
<
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EI, 100000. </
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<
s
xml:id
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xml:space
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">vt hic vides.</
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<
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ID. # ID. # IL. # # IL.
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2 {1/2}. # 46631. # 7 {1/2}? # ſit # 139893.
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</
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<
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<
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xml:space
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">Cum ergo IL, ſit tangens anguli IEL, poſito ſinu toto EI, vt in tractatione
<
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tangentium ac ſecantium tradidimus; </
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<
s
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xml:space
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">dabitur, ex tangentium tabula, angulus
<
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IEF, grad. </
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<
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">54. </
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<
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">Min. </
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<
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">26. </
s
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<
s
xml:id
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xml:space
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">Ablato ergo angulo DEI, grad.</
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<
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echoid-s9736
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<
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">nimirum ſemiſſe
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differentiæ inter datum aggregatum, & </
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<
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FED, ac propterea & </
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<
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">arcus FD, minor, grad.</
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<
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<
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">Min. </
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<
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<
s
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">qui ſubtractus ex da-
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to aggregato grad. </
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<
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<
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<
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<
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">arcum BF,
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maiorem, grad.</
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<
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">100. </
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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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<
s
xml:id
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xml:space
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">IGITVR ſi fiat, vt ſemiſſis differentiæ inter terminos proportio-
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<
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xlink:label
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">Praxis.</
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nis datæ ad tangentem ſemiſſis diff rentiæ inter aggregatum datum, & </
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<
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ſemicirculum, ita aggregatum ex ſemiſſe differentiæ inter terminos datæ
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proportionis, & </
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<
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xml:id
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xml:space
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">conſequente eiuſdem proportionis, ad aliud, inuenietur
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tangens anguli, à quo ſi dematur ſemiſſis differentiæ inter datum aggrega-
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tum, & </
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<
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">ſemicir culum, reliquus erit angulus, ſeu arcus minor quæſitus: </
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<
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detractus ex aggregato dato, relinquet maiorẽ angulum, ſine arcũ quęſitũ.</
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</
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<
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<
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">ALITER adhuc per ſolos ſinus ſine tangentibus. </
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<
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">Ijsdem poſitis, quo-
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<
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que tangẽ-
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tibus.</
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niam vt in ſinubus declarauimus, poſito ſinu toto EB, recta BH, eſt ſinus an-
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guli BEH, nempe ſemiſsis aggregati angulorum, vel arcuũ dati, nempe 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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xml:id
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xml:space
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">HE, ſinus anguli EBH, grad. </
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<
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xml:id
="
echoid-s9764
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xml:space
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">25. </
s
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<
s
xml:id
="
echoid-s9765
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xml:space
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">vtpote complementi anguli BEH; </
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<
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<
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dabitur ex tabula ſinuum, BH, partium 90631. </
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<
s
xml:id
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">at HE, partiũ 42262. </
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<
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ſi dicamus. </
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<
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">Si BH, ſemiſsis aggregati terminorum proportionis datæ, nempe
<
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7 {1/2}.</
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<
s
xml:id
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xml:space
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">dat BH, ſinum ſemiſsis aggregati angulorum, vel arcuum, partiũ 90631. </
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<
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quid dabit HG, differentia inter ſemiſſem aggregati terminorum proportio-
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nis datæ, & </
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<
s
xml:id
="
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xml:space
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">alterutrum terminorum, nimirum 2 {1/2}? </
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<
s
xml:id
="
echoid-s9773
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xml:space
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">reperiemus HG, partium
<
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30210. </
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>
<
s
xml:id
="
echoid-s9774
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xml:space
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">qualium ſinus totus EB, eſt 100000. </
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<
s
xml:id
="
echoid-s9775
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xml:space
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">vel EH, 42262. </
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<
s
xml:id
="
echoid-s9776
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xml:space
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">vt hic patet.</
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<
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BH. # BH. # HG. # # HG.
<
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7 {1/2}. # 90631. # 2 {1/2}? # ſit # 30210.
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</
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<
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<
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xml:id
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xml:space
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">Quia vero quadrata rectarum HE, HG, nempe 1786076644. </
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>
<
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="
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xml:space
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">912644100.
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</
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<
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xml:id
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<
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xlink:label
="
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">47. primi.</
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