DelMonte, Guidubaldo - In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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1rectælineę LK. Et non dixit, quia VC ſitipſi CX ęqualis.
Quare codicem græcum ita reſtituendum cenſeo. τὰκέντ<10>κ τῶν
τοῦ βὰ<10>εος μεγεθῶν, vt vertimus.

Ob ſe〈que〉ntis verò demonſtrationis cognitionem, hoc pro
blema priùs oſtendemus.

PROBLEMA.

Duarum expoſitarum magnitudinum incommenſurabi
lium altera vtcum〈que〉 ſecetur; magnitudinem tota ſecta ma
gnitudine minorem, & altero ſegmentomaiorem, alteri ve
rò expoſitæ magnitudini commenſurabilem inuenire.

Sint duæ magnitudi
nes incommenſurabiles

AE BC. ſeceturquè ipſa
rum altera, putà BC, vt
cum〈que〉 in D. oportet
magnitudinem inuenire
minorem quidem BC,
maiorem verò BD, quæ ſitipſi AE commenſurabilis. Au
feratur ab AE pars dimidia, rurſus dimidiæ partis ipſius AE
dimidia auferatur; & eius, quæ remanet, adhuc dimidia; idquè
ſemper fiat, donec relinquatur magnitudo minor, quàm DE.
quod quidem perſpicuum eſt poſſe fieri ex prima decimi Eu
clidis propoſitione. ſitita〈que〉 AF, quæ minor exiſtat, quàm
DC. quippe quę AF, cùm ſit abla ta ex AE ſemper per dimi
diam partem, metietur vti〈que〉 AF ipſam AE. Deinde mul
tiplicetur AF ſuper BD, tum demum multiplicatio vltima,
vel in puncto D cadet, vel minus. ſi cadet; ſeceturex DE
magnitudo DG ęqualis AF. quod quidem fiet, quoniam AF
minor eſt DC. Quoniam igitur AF metitur BD, & DG;
metietur AF totam BG. Sed & ipſam AE metitur; etgo
AF ipſarum BG AE communis exiſtit menſura, ac propte
rea BG ipſi AE commenſurabilis exiſtir; quæ quidem BG
minor eſt BC, maior verò BD. Si verò multi
plicatio ipſius AF ſuper BD non cadet in D. ſed in H,
erit vti〈que〉 HD minor AF. nam ſi HD ipſi AF eſſet ęqualis,

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