PAL

Ptolemaeus Arabus et Latinus

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〈Commentum in Almagesti minorem〉 (C.1.7)

Florence, BR, 885 · 109r

Facsimile

Almagesti Title in upper margin, possibly added by another hand F

〈I〉 Omnium recte phantium verisimilibus coniecturis etc.

〈…〉 17 lines left blank, evidently meant for a commentary on the preface of Book I F

〈I.1〉 Demonstratio prima. Demonstratio prima] d. prima i. m. F (all demonstration numbers are in the margin) Data circuli diametro latera decagoni, pentagoni, exagoni, detragoni atque trianguli omnium ab eodem circulo circumscriptorum reperire. Unde manifestum est quod, si nota fuerit circuli diametrus et prenominata latera erunt nota, corde quoque que residuis semicirculi arcubus subtenduntur erunt eque note.

Sit circulus ABG, cuius diameter ADG, centrum D, a quo per undecimam primi geometrie erigatur DB perpendiculariter super AG divisoque DG in puncto H per equalia per decimam primi. Ducatur BH que maior est DH per nonam decimam primi et minor AH per septimam octavi per tertiam primi resecetur de linea BA equalis linee HB que sit HZ. Ducta linea BZ dico quod DG est latus exagoni et DZ latus decagoni et BZ latus pentagoni ab eodem circulo circumscriptorum et nota. Probatio: cum DG que per correlarium 15 quarti sit latus exagoni et semidiameter circuli est nota, quoniam 60 est latus exagoni notum et divisum in H per equalia cui additur DZ, quare per sextam secundi ductus DZ in DZ cum quadrato DH equatur quadrato HZ, ergo quadrato HB. Sed per penultimam primi quadratum HB valet quadratum BD et quadratum DH. Ergo ductus GZ in ZD et quadratum DH valent quadrata BD et DH. Dempto ergo communi quadrato DH remanet ductus GZ in ZD equalis quadrato DB et ita quadrato DG. Sit ergo ZG prima, GD secunda, DZ tertia cum ergo ductus