Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ducto auferatur numerus procreatus ex multiplicatione duarum chordarum datarum in-
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ter ſe; </
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<
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">reliquus autem numerus per diametrum diuidatur, relinquetur chorda, ex qua ſi per
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propoſ. </
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<
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<
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erit hæc inuenta ſubtendens arcum compoſitum ex duobus arcubus duarum chordarum
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datarum. </
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<
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<
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<
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<
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xml:space
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<
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cto ex da-
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ta chorda
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reperiatur
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chorda ſe-
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miſſis arcus
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datæ chor-
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dæ.</
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<
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">EX data chorda cuiuſuis arcus chordã ſemiſ-
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ſis illius arcus inuenire.</
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<
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<
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<
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">IN circulo ABC, cuius centrum E, data ſit chorda BC, arcus BDC, cu-
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ius ſemiſsis ſit arcus BD, eiusq́; </
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<
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">chorda BD, quam inuenire oporteat. </
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<
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diametro DG, ſecabitea, per lemma in definitionibus poſitum, rectam BC,
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bifariam, ac proinde ad angulos rectos. </
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<
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duo triangula ABC, EFC, æquiangula, cum angulus EFC, oſtenſus ſitre-
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ctus, & </
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">rectus in ſemicirculo, at angulus C, commu
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nis. </
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">& </
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<
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xml:space
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">4. ſexti.</
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144
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="
193-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/193-01
"/>
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permutando, vt CF, ad CB, ita FE, ad BA. </
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<
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ergo CF, dimidium ſit ipſius CB, vt oſtendimus,
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erit & </
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AB, data ſit ex data BC, data quoq; </
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<
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dempta ex ſemidiametro ED, nota, data erit quoq;
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</
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<
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<
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">Quoniam vero in triangulo GBD, an-
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gulus B, rectus eſt, à quo demiſſa eſt BF, ad baſim
<
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<
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GD, perpendicularis; </
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<
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tionalis inter GD, & </
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<
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ſub GD, FD, notis quadrato rectæ DB, æquale.
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</
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<
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Notum ergo erit quadratum rectæ DB; </
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<
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ctam DB, notam exhibebit. </
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nota facta eſt, erunt quadrata rectarum FD, FB, nota: </
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<
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<
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quadrato rectæ BD; </
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rum rectam BD, efficiet notam. </
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<
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<
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<
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BDC, cuius ſemiſsis ſit arcus DC, ciusq́; </
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<
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</
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<
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<
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Diuiſa quoq; </
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<
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145
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193-02
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DF. </
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lia ſunt duobus lateribus EA, AD, anguloſq;
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</
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<
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<
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DC; </
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<
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<
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BD, recta rectæ DC, æqualis. </
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<
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eidem DC, æqualis erit. </
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<
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EF, FD, duobus lateribus CF, FD, æqualia ſint,
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baſisq́; </
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<
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<
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<
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æquales, ideoq́; </
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<
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erit quoq; </
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<
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linquetur EC; </
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