Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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tra A, & </
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<
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xml:space
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">cum circuli maximi ſe mu-
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tuo bifariam ſecent. </
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<
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xml:space
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BC, ſemicirculo minor eſt. </
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<
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xml:space
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">Eodem modo,
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productis arcubus AB, AC, oſtendemus ar
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cum AC, ſemicirculo eſſe minorem. </
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<
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xml:space
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uenient autem arcus BA, BC, producti vl-
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tra puncta A, & </
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<
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">C, propterea quòd ſphæ-
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ricos angulos faciunt cũ arcu AC, ſuntq̀;
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</
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<
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">omnes tres arcus portiones circulorum ma
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ximorum, qui ſe mutuo ſecant in punctis
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A,B, C, non autem tangunt. </
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<
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fit, vt vterque arcus BA, BC, productus arcum AC, productum ſecet in pun-
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ctis A, C, vt ex defin. </
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<
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omniergo triangulo ſphærico, &</
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<
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quo ſunt maiora, quomodocunque aſſumpta.</
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<
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maiora eſſe latere BC. </
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">Si enim triangulum eſt æquilaterum, manifeſtum eſt
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duo ſimul dupla eſſe reliqui, atque adeo maiora. </
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AC, æquale ſit lateri BC, vel maius,
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vel etiã vtrumq; </
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<
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quoque eſt, duo latera AB, AC, ma-
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iora eſſe reliquo BC. </
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<
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que latus AB, AC, aſſumptum late-
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re tertio BC, minus ſit, demonſtrabi-
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mus, latera AB, AC, ſimul maiora eſ-
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ſe latere BC, hac ratione. </
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circulus arcus tertij BC. </
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polo B, nempe ex altero extremo ma
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ioris lateris BC, ad interuallũ vtriuſ-
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uis arcuum minorum, nimirum ad in-
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teruallũ arcus BA, in ſuperficie ſphæ
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ræ circulus deſcribatun AD, ſecans ar
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cum BC, qui maior ponitur arcu BA,
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in D, puncto inter B, & </
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<
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circulus BC, tranſit quoque per reliquum polum circuli AD; </
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lus E, qui per ſemicirculũ remotus erit à polo B; </
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Cum ergo arcus BC, ſemicirculo minor ſit, exiſtet polus E, vltra punctum C:
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Eſt autem punctum D, inter B, & </
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puncta D, E, cadet. </
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AD, eſt, & </
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<
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circulorum CB, CA, ſemicirculo minores (quòd latera ſint trianguli ſphæ-
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rici ABC.) </
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<
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nor arcu CA. </
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<
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<
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