PAL

Ptolemaeus Arabus et Latinus

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Ptolemy, Almagesti (tr. Erasmus Reinhold)

Wittenberg, Johannes Lufft, 1549 · 82r

Facsimile

angulum qui sub EDA, et dividendo recta GE ad rectam EA minorem rationem habet quam angulus GDE ad angulum EDA. Sed sicut recta GE ad rectam EA, ita GB recta ad rectam BA. Sicut autem angulus GDB ad angulum BDA, ita circumferentia GB ad circumferentiam BA. Quare GB recta ad rectam BA minorem rationem habet, quam GB circumferentia ad circumferentiam BA.

Hoc igitur supposito, Problema quo venatur satis exacte subtensam unius partis ut circulus ABG, et ducantur in eo duae rectae lineae inaequales, scilicet AB et AG. Ponatur autem primum linea AB esse subtensa dodranti unius partis, deinde linea AG esse subtensa uni parti. Quoniam recta AG ad rectam AB minorem rationem habet quam AG circumferentia ad circumferentiam AB, sed ratio AG circumferentiae ad AB circumferentiam est sesquitertia.