Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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AG, AH, AI.</
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<
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<
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recto minor, cum ambo ſint duobus rectis minores. </
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<
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ad H, ſint duobus rectis æquales, erit AHI, maior recto, ac proinde angu-
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lus I, in triangulo AHI, recto minor. </
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<
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AH. </
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AH, maior, quã AG. </
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AH, & </
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tiã tangentiũ CI, CH, arcuũ maiorũ CF, CE,
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maiorem eſſe differentia HG, tãgentium CH,
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CG, minorum arcuum CE, CD: </
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differentiam ſecantium AI, AH, arcuum ma-
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iorum CF, CE, maiorem eſſe differentia LH,
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ſecantium AH, AG, minorum arcuum CE,
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CD. </
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<
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erunt & </
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inde angulus IAG, ſectus erit bifariam per re-
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ctam AH. </
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ad HG: </
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maior quoque erit, quàm HG. </
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<
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<
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">DVCTIS iam FM, EN, DO, ad AC, perpendicularibus, nempe fi-
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nubus rectis arcuum CF, CE, CD; </
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vt in expoſitione definitionum dictum eſt. </
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eſt, quam NO; </
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adhuc maior proportio AO, ad NO, quàm AN, ad eandem NO. </
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multo maior erit proportio AO, ad NO, quàm AN, ad MN. </
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uerſionem rationis, minor proportio AO, ad AN, quàm AN, ad AM: </
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eſt, maior proportio AN, ad AM, quàm AO, ad AN. </
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AN, ad AM, ita AI, ad AH; </
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<
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<
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quoque erit proportio AI, ad AH, hoc eſt, ad AK, quàm AH, ad AG,
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hoc eſt, ad AL. </
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<
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">Diuidendo ergo maior etiam proportio erit IK, ad AK, hoc
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<
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eſt, ad AH, quàm HL, ad AL: </
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<
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ad KI, quàm AL, ad LH: </
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<
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AH, ad KI. </
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<
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<
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ad eandem LH: </
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<
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AH, ad KI; </
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<
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<
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dum. </
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per augeri ad finem vſq; </
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cidit, vt ſupra demonſtratum eſt. </
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exceſſu porgredientes, &</
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gentium æ
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quales ex-
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ceſſus habẽ
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tium inæ-
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quales ha</
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earum inæqualiter ſeſe excedere, exceſſusq; </
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<
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iorum Omnium item ſecantium ſegmenta extra quadrantem eſſe inæqualia, minoraq; </
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<
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illa, quæ principio quadrantis ſunt propinquiora. </
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<
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EF, æqualibus, oſtenſum fuit, rectam IH, maiorem eſſe quam HG; </
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<
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HI, auferatur recta ipſi HG, æqualis. </
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<
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