PAL

Ptolemaeus Arabus et Latinus

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Almagesti minor

Paris, BnF, lat. 16657 · 85r

Facsimile

⟨a⟩d ad] From K ZH, inter que statuatur medium ZD, cuius proportio est ad DH tanquam BD ad DH. DH‌2] DA K Quare coniunctim ZD ad ZH sicut BD ad BA. Unde habemus propositum.

⟨I.9⟩ Si in circulo continui arcus sumantur et uterque minor semycirculo, dyametrus producta a communi eorum termino lineam rectam reliquos eorumdem terminos continuantem secabit secundum proportionem corde dupli arcus unius ad cordam dupli arcus alterius.

] The first figure from P has some mislabeled points. The second, better figure is from N 3r. Fiat ergo GH linea perpendicularis super semydyametrum BD et sit medietas corde arcus duplicantis arcum GB. Item sit AZ perpendicularis super eandem dyametrum et sit sinus arcus AB. Quare fient trianguli GEH et AEZ similes.

⟨I.10⟩ Si unus arcus notus in duos dividatur fueritque nota proportio corde dupli arcus unius unius] sup. lin. ad cordam dupli arcus alterius, ambo ipsi erunt noti.

] The line ZD has perhaps been erased. Sit DZ perpendicularis ad cordam arcus AG noti. Qualiter Qualiter] Quare K totus triangulus ZDA lineis et angulis notus. Item proportio GE ad EA per premissam et ypothesim nota est. Ergo proportio coniuncta GA ad EA addita unitate denominatori proportionis disiuncte fiet nota. Ergo AE nota, ergo EZ et DZ et ED linee note respectu dyametri circuli magni. Ergo omnes anguli trianguli ortogonii EZD noti noti] corr. ex nati sunt per circulum ei circumscriptum respectu duorum rectorum, ergo respectu quatuor. Dempto ergo angulo ZDE nunc noto ab angulo ZDA prius noto, relinquitur angulus EDA notus. Quare arcus AB notus, ergo et reliquus GB notus.

⟨I.11⟩ Si ab uno termino arcus semycirculo minoris linea ipsum arcum secans educatur donec cum dyametro per reliquum eundem eundem] eiusdem K arcus terminum extracta concurrat, fiet proportio linee preter centrum transeuntis ad partem sui extrinsecam sicut proportio corde dupli arcus de quo sermo est ad cordam dupli arcus illius que que] quem K educte linee includunt.

] The first figure from P has lines erased. The second, better figure is from K 15. Esto igitur GH sinus arcus GA cui equidistat BZ sinus arcus BA interclusi lineis concurrentibus, quarum altera GBE preter centrum transiens arcum GA secat, altera HAE secundum dyametrum extracta. Fiet ergo triangulus GEB GEB] GEH K totalis similis triangulo HEZ HEZ] HEZ K partiali.

⟨I.12⟩ Si arcus dicto modo divisi lineis ut prescriptum est donec concurrant eductus eductus] eductis K maior portio portio] sup. lin. nota fuerit et