Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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a F. </
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">Cum ergo ſit, vt Da, ad aF, ita b V, ad VF, erit quoque b V, maior,
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quàm VF, hoc eſt, GH, maior, quàm HI; </
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<
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ſinuũ recto
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rũ à princi
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pio quadrã
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tis vſq; ad
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eius finem
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ſenſim de-
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creſcunt:a-
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deo vi ſinꝰ
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minorú ar
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cuũ maio-
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res habeát
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differétias,
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q̇
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ſinꝰ arcuũ
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maiorũ; dũ
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modo arcꝰ
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habeát dif-
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ferentias ę
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quales.</
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incipientes habeant æquales differentias, exceſſusve; </
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<
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re maiores differentias, quàm ſinus arcuum maiorum; </
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<
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">adeo vt differentiæ ſinuum à prin-
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cipio quadrantis ad finem vſque ſemper decreſcant. </
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">a cci piatur arcus FX, arcubus DE, EF, æ qualis, ducaturq́ue recta XY, ad ſemidiametrum
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AC, perpendicularis, habebunt quatuor arcus BX, BF, BE, BD, æquales exceſlus, cum
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BX, ipſum BF, ſuperetarcu FX; </
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">BF, ipſum BE, arcu EF, qui arcui FX, poſitus eſt
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æqualis; </
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<
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">arcus BE, arcum BD, arcu DE, qui arcui EF, æqualis eſt. </
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eorum arcuum ſunt AY, AI, AH, AG, vt ſupra in ex poſitione definitionum docuimus,
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cum ſint partes ſemidiametri AC, inter centrum A, & </
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vt patet. </
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HI, & </
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">liquet, exceſſum GH, inter ſinus arcuum minorum BE,
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BD, maiorem eſſe exceſſu HI, inter ſinus arcuum maiorum BF, BE: </
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inter ſinus arcuum minorum BF, BE, maiorem eſſe exceſſu IY, inter ſinus maiorum ar-
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cuum BX, BF. </
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ſenſim decreſcere à principio quadrantis v ſque ad eius finem: </
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tabula apparet.</
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<
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cagoni, &
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Penta goni
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in vno eo-
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demq; cir-
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culo quo
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pacto inue-
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niantur.</
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teri in vno eodemq́; </
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demonſtrata: </
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gantur ratione alia, quæ ad plurimorum ſinuum inuentionem multum con-
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ducit. </
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ad cuius diametrum AC, ex D, centro
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educatur perpendicularis DB. </
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quoque ſemidiametro CD, bifariam
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in E, ducatur recta EB, cui ęqualis ab-
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ſcindatur EF, iungaturq́ue recta FB.
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goni, & </
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culo ABC. </
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<
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ſecta ſit bifariam in E, eique addi-
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ta DF; </
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<
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vna cum quadrato rectæ DE, æquale
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quadrato rectæ EF, ideoq́ quadrato rectæ EB, quæ ipſi EF, ęqualis
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eſt: </
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Igitur rectangulum ſub CF, DF, vnà cum quadrato rectæ DE, æquale eſt
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quadratis rectarum BD, DE: </
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, relinquetur rectangulum ſub CF, DF, æquale quadrato rectæ BD,
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hoc eſt, quadrato rectæ CD. </
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<
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DF; </
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<
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igitur maius ſegmentum CD, ſit latus Hexagoni in circulo ABC, ex </
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