PAL

Ptolemaeus Arabus et Latinus

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Federico Commandino, In Planisphaerium Ptolemaei commentarius

Venice, Paulus Manutius Aldi, 1558 · 4v

Facsimile

erunt eadem ratione lineae AD, RS aequidistantes et propterea aequidistantes ipsae RS 〈et〉 BC (16 et 9, undecimi). (16, 9 undecimi)] Euclid, Elements XI.16 and XI.9 Quod cum triangula EAF, EDF sint

perpendiculariter erecta super idem planum. Transeunt enim per lineam perpendicularem EF, erunt ipsorum ipsorum] ipsornm V et tabulae communes sectiones IR, NS perpendiculares ad IN et aequidistantes lineae GP (18 et 19, undecimi). (18, 19, undecimi)] Euclid, Elements XI.18 and XI.19 Et idcirco parallelogramma erunt ipsa IP, PN et linea RP aequalis lineae IG et PS ipsi GN. Demonstratum autem est lineam OP aequalem lineae TG et PQ ipsi GU. Facta est praeterea TG aequalis ipsi IG et GU aequalis GN, erit ergo linea OP aequalis RP et PQ ipsi PS. Itaque si manente linea GP superficies OLMQ circumferatur adeo, ut linea GL applicet lineae GB, applicabit et PO ipsi PR, et parallelogramma item TP, PU parallelogrammis IP, PN. Quare cadet punctum L in B, M in C, O in R et denique Q in S. Cum igitur puncta B C videantur in punctis L M et AD in ipsis OQ, videbitur et tota superficies ABCD in tota OLMQ atque erit in tabula GK descripta figura qualis est ipsa OLMQ, ut oportebat.