DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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rectælineę LK. Et non dixit, quia VC ſitipſi CX ęqualis.
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Quare codicem græcum ita reſtituendum cenſeo.
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τοῦ βὰ<10>εος μεγεθῶν</
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, vt vertimus. </
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*</
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<
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">Ob ſe〈que〉ntis verò demonſtrationis cognitionem, hoc pro
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blema priùs oſtendemus. </
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<
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<
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">PROBLEMA.</
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<
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<
s
id
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">Duarum expoſitarum magnitudinum incommenſurabi
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lium altera vtcum〈que〉 ſecetur; magnitudinem tota ſecta ma
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gnitudine minorem, & altero ſegmentomaiorem, alteri ve
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rò expoſitæ magnitudini commenſurabilem inuenire. </
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<
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nes incommenſurabiles
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AE BC. ſeceturquè ipſa
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rum altera, putà BC, vt
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cum〈que〉 in D. oportet
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magnitudinem inuenire
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minorem quidem BC,
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maiorem verò BD, quæ ſitipſi AE commenſurabilis. </
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<
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id
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">Au
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feratur ab AE pars dimidia, rurſus dimidiæ partis ipſius AE
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dimidia auferatur; & eius, quæ remanet, adhuc dimidia; idquè
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ſemper fiat, donec relinquatur magnitudo minor, quàm DE.
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quod quidem perſpicuum eſt poſſe fieri ex prima decimi Eu
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clidis propoſitione. </
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<
s
id
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">ſitita〈que〉 AF, quæ minor exiſtat, quàm
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DC. quippe quę AF, cùm ſit abla ta ex AE ſemper per dimi
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diam partem, metietur vti〈que〉 AF ipſam AE. Deinde mul
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tiplicetur AF ſuper BD, tum demum multiplicatio vltima,
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vel in puncto D cadet, vel minus. </
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<
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id
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">ſi cadet; ſeceturex DE
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magnitudo DG ęqualis AF. quod quidem fiet,
<
expan
abbr
="
quoniã
">quoniam</
expan
>
AF
<
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/>
minor eſt DC. Quoniam igitur AF metitur BD, & DG;
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metietur AF totam BG. Sed & ipſam AE metitur; etgo
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AF ipſarum BG AE communis exiſtit menſura, ac propte
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rea BG ipſi AE commenſurabilis exiſtir; quæ quidem BG
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minor eſt BC, maior verò BD. Si verò
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n
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marg54
"/>
multi
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plicatio ipſius AF ſuper BD non cadet in D. ſed in H,
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erit vti〈que〉 HD minor AF. nam ſi HD ipſi AF eſſet ęqualis, </
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