Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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contineat, ſint{quam} ambo arcus in eandẽ partem caui, at{quam} eadem extrema pun
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cta habeant, vt vult Archimedes in ſuppoſitionibus ante lib. </
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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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">Neque vero arcus C E D, arcui F G B, congruet, aut imra ip-
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ſum cadet. </
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<
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xml:space
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">Nam ſi dicatur congruere,
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congruet etiam tota circumferentia
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circuli C E D, toti circumferentiæ cir-
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culi F G B, atque adeo æquales erunt
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circuli. </
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<
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">quod eſt abſurdum, cum inæquæ
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les ponantur: </
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<
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xml:space
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">Si vero arcus C E D, di-
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catur cadere intra arcum F G B, cu-
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inſmodi eſt arcus C A D, quoniam vt
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paulo ante in hoc lemmate ostenſum
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eſt, arcus C E D, id eſt, C A D, maior
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eſt, quàm vt ſimilis ſit arcui F G B, ſu-
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matur arcus H F B, arcui C A D, ſimilis, atque adeo maior arcu F G B:
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</
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<
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">Aſſumpto autem in arcu C A D, puncto A, vtcunque, ducantur rectæ
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A F, A B; </
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<
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">productaque recta F A, donec arcum F G B, ſecet in G,
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ducantur rectæ G H, G B. </
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<
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">Itaque quoniam arcus C A D, H F B, ſimiles
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ſunt, erunt anguli C A D, H G B, inillis fegmentis exiſtentes, æquales. </
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<
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">Quia
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vero angulus C A D, angulo C G B, maior eſt, externus interno; </
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">& </
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">angulus
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C G B, angulo H G B, maior quoque, totum parte; </
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<
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">erit multò maior angulus
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C A D, angulo H G B. </
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<
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<
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">Non ergo
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arcus C E D, cadet intra arcũ F G B: </
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<
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</
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<
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">adeo maior erit arcus C E D, arcu F G B, vt dictũ eſ.</
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">_HINC_ etiam liquido constat, multo magis maiorem lineam ex cir-
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culo minore auferre arcum maiorem ſimpliciter eo, quem minor linea ex
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circulo maiore aufert.</
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">SI in ſphæra maximus circulus tãgat aliquem
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ſphæræ circulum, alius autem maximus circulus
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ad parallelos obliquus ſit, tangatq́; </
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<
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res illis, quos tangit maximus circulus primo poſi-
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tus, fuerintq́; </
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lo primo poſito, & </
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