Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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nempe ſinus EH, grad. </
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<
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<
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xml:space
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<
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ſinus totius 10000000. </
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<
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<
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">reliqui numeri radix quadrata accipia-
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tur, quę eſt 8660254. </
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<
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xml:space
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<
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<
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<
s
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xml:space
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">DEINDE, quoniam recta AF, fecans
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arcum BC, bifariam, fecat quoque, ex lem-
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mate definitionum, rectam BC, bifariam, at-
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que adeo & </
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<
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<
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xml:space
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arcus CF, grad. </
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<
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<
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<
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ſit, & </
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xml:space
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lus ACL, ſemirectus, atque adeo angulo
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CAL, æqualis. </
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<
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les erunt. </
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æquale ſit quadratis rectarum AL, CL, ſi-
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mul; </
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<
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xml:space
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plum quadrati ſinus CL, grad. </
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<
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<
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igitur quadrati ſinus totius erit quadratũ rectæ CL, cuius radix quadrata da-
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bit ſinum CL, 7071068. </
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<
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xml:id
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xml:space
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">fere pro arcu grad. </
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<
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">45. </
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<
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xml:space
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">Qui etiam hoc modo re-
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perietur. </
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<
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">Quoniam quadratum rectæ BC, æquale eſt quadratis rectarum AB,
<
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<
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AC; </
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<
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xml:space
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">atque adeo duplum quadrati ſinus totius AC, ſi quadratum ſinus to-
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tius duplicetur, habebitur quadratum rectæ BC, cuius quadrati radix dabit re
<
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ctam BC, partium 14142136. </
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<
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">fere, & </
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<
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<
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CL, grad. </
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<
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">RVRSVS, quia recta AD, ſecans arcum CE, bifariam, ſecat quoque
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rectam CE, bifariam in K, ex lemmate definitionum, atque adeo & </
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<
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los rectos; </
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<
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">erit CK, ſinus arcus CD, grad. </
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<
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<
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">quem ſic inueniemus. </
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<
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ex propoſ. </
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<
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nus totius, & </
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<
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<
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">(qui quidem habetur, ſi EH, ſinus grad. </
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<
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</
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<
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">ex ſinu toto AC, detrahatur, vt in coroll. </
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<
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<
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roll. </
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<
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<
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<
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<
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Nam ſi medietas ſinus totius multiplicetur in ſinum verſum CG, cognitum,
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producetur quadratum rectæ CK; </
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<
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xml:space
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tius, & </
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<
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<
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lis Ck. </
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<
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">Si igitur quadrati rectæ CK, radix eruatur, habebitur ſinus CK, par-
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tium 2588190. </
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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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>
modo inueſtigabimus. </
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<
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<
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<
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Arcus. # Sinus
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G.
<
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15 # 2588190
<
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30 # 5000000
<
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45 # 7071068
<
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60 # 8660254
<
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75 # 9659258
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90 # 10000000
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</
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le eſt quadratum rectæ EC; </
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<
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rectæ EC; </
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<
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xml:space
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">cuius quadrati radix quadrata dabit re-
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ctam EC, notam, & </
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<
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">huius medietas erit ſinus CK,
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cognitus.</
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<
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<
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<
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quoque, per propof. </
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<
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<
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CD, hoc eſt, ſinus arcus BD, grad. </
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<
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<
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">qui quidem
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deprehendetur partium 9659258. </
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<
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<
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hactenus ſinus recti arcuum continentium 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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<
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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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">HORVM autem ſinuũ beneficio ad aliorum
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inueſtigationem ita progrediemur. </
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<
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