Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ximus, atque adeò idem non ſit, qui EF; </
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<
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ſupra, (nihil enim intereſt, quocunque cadat.) </
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<
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">fiat nihilominus angulus
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">10. huius.</
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FDH, angulo A, æqualis: </
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<
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">eritq̀ue rurſus arcus DH, arcui DE, hoc eſt, ar-
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<
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xlink:label
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">28. tertij.</
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cui AB, æqualis; </
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<
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xml:space
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">eo quòd rectæ ſubtendentes DE, DH, æquales ſint, ex de-
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fin. </
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<
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AB, AC, lateribus DH, DF, æqualia ſint, angulosq̀ue contineant æquales;
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</
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<
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<
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xml:space
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">Quoniam verò circulus maximus DF, per
<
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<
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D, polum circuli EHF, tranſiens eum bifariam ſecat; </
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<
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<
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circulo minor; </
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">(quia arcus à puncto F, per E, vſque ad illud punctum, in quo,
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ſi protractus eſſet vltra E, ſecaretur ab arcu FD, ad partes D, producto, eſt
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ſemicirculus: </
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<
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">quandoquidem circulus arcus EHF, bifariam ſecatur a circulo
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arcus FD, vt dictum eſt.) </
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<
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">atque adeo recta FE, maior, quàm recta FH, in eo-
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">25. tertij.</
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dem circulo: </
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<
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">quia illa propin quior eſt centro circuli EHF, hoc eſt, diame-
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tro, quàm hæc. </
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<
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les; </
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<
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<
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">2. huius.</
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ior arcu HF: </
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<
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">Oſtenſus autem eſt arcus HF, æqualis arcui BC. </
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<
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erit quoque arcus EF, arcu BC. </
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<
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</
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<
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<
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">SINT deinde triangula propoſita non Iſoſcelia, ſed latus AB, maius
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ſit latere AC, ac proinde & </
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<
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<
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">Producto ergo arcu
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DF, ad partes F, abſciſſoq́ue arcu DG, æquali ipſi DE, qui minor eſt ſe-
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micirculo, deſcribatur ex polo D, per pun
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cta E, G, arcus circuli EHG, ſiue maxi-
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ximus is ſit, ſiue non maximus. </
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<
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ſus angulus FDH, angulo A, æqualis;
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</
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">20. huius.</
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eritq́ue arcus DH, arcui DE, hoc eſt, ar-
<
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<
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xlink:label
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">28. tertij.</
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cui AB, æqualis; </
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<
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">eò quòd rectæ ſubtenſæ
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DH, DE, æquales ſint, ex defin. </
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<
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">poli. </
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<
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cto igitur per puncta H, F, arcu circuli
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maximi HF, erit, vt prius, arcus BC, ar-
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cui HF, æqualis. </
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<
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maximus DG, per D, polum circuli EG,
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<
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ducitur, eſtq́ue punctum F, intra periphe-
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riam circuli EG, (nempe inter circulum, & </
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<
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">& </
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<
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</
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<
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">erit arcus FE, maior arcu FH, cum ille propin quior ſit arcui FD, per po-
<
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<
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xlink:label
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lum D, tranſeunti, & </
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<
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<
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<
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rea quòd non ſe interſecant, niſi in puncto F: </
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<
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arcui BC, æqualis. </
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<
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">Maior ergo erit quoque arcus EF, arcu BC. </
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<
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propoſitum.</
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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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A. </
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<
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lo A, erit vel æqualis, vel minor. </
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<
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dicatur eſſe, erit arcus EF, æqualis arcui
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<
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B C. </
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<
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<
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EF, maior arcu BC. </
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<
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">Si verò minor dicatur
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eſſe angulus D, angulo A, erit, vt iam oſten
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ſum eſt, arcus BC, maior arcu EF. </
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<
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etiam abſurdum eſt, cum EF, maior </
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