DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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KC ad R. ac propterea lineæ OPQR inter ſe ſunt æquales.
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Atverò quoniam ita eſt AC ad AG, vt AG ad O, & vt
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AC ad GH, ita GH, hoc eſt AG ipſi ęqualis, ad P. rurſus
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vt AC ad HK, ita HK, hoc eſt AG ad
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ac tandem vt
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AC ad KC, ita KC, hoc eſt AG ipſi ęqualis, ad R. erit
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ad omnes conſe〈que〉ntes ſimul ſumptas AG GH HK KC,
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hoc eſt erit AC ad eandem AC, vt AG ad omnes ſimul
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OPQR. vnde ſequitur omnes ſimul OPQR ipſi AG ęqua
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les eſſe. </
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<
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">Ita〈que〉 quoniam ſimilia triangula in dupla
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pro
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portione laterum homologorum, erit triangulum ABC ad
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ALG, vt AC ad O. eodemquè modo erit triangulum ABC
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ad GMH, vt AC ad P. rurſus ABC ad HNK, vt AC ad
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Q, & vt idem ABC ad KFC, ita AC ad R. triangulum
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igitur ABC ad omnes conſe〈que〉ntes, videlicet ad omnia
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triã
">triam</
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gula ſimul ſumpta ALG GMH HNK KFC, eritvt AC ad
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omnes ſimul OPQR. hoc eſt ad AG. oſtenſum eſt igitur,
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quod propoſitum fuit. </
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2.
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ſexti.
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1.
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lemma.
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29.
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primi.
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76.
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primi.
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ex
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17
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quĩi
">quini</
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.
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ex
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præcedẽ
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ti lemmate
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19.
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ſexti.
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ex
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ti lemmate
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<
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number
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61
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type
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">
<
s
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">PROPOSITIO. XIII.</
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<
s
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">Omnis trianguli centrum grauitatis eſt in recta
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linea ab angulo ad dimidiam baſim ducta. </
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Sit triangulum ABC. & in ipſo ſit AD
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ab angulo A
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ad dimi
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diambaſim BC ducta. </
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<
s
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">oſtendendum est, centrum grauitatis trianguli
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ABC eſſe in linea AD. Non ſit quidem, ſed ſi fieri potest ſit punctum
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H. & ab ipſo ducatur HI æquidiſtansipſi BC,
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quæ ipſam AD
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in I.
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Deinde diuiſa DC bifariam, idquè ſemper fiat, dones relinqua
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tur linea
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emph.end
type
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italics
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D
<
foreign
lang
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grc
">ω</
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>
<
emph
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minor ipſa HI. Diuidaturquè ipſarum vtra〈que〉 BD DC
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in partes æquales
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D
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; parteſquè in DC exrſtentes ſint D
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">ω ωβ
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β</
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Z ZC; quibus reſpondeant æquales partes D
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O OB.
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&
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a ſectionum punctis ducantur
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OE
<
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>
G
<
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>
L
<
foreign
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">ω</
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M
<
foreign
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">β</
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K ZF
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emph
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æquidictan
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tes ipſi AD. & connectantur EF G
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k
<
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LM quæ nimirum ipſi BC
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æquidistantes erunt.
<
emph.end
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cùm enim ſint BD DC interſe equales, iti
<
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dem OB ZC æquales; erit DO ipſi DZ ęqualis. </
s
>
<
s
id
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N1374C
">quare DO
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ad OB eſt, vt DZ ad ZC. Quoniam autem EO FZ ſunt </
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