DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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<
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104
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uitatis cuiuſlibet trianguli eſſe in recta linea ab angulo ad di
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midiam baſim ducta (vt Archimedes demonſtrauit) & inſu
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per in eo puncto, quod dictam lineam diuidatita, vt pars ad
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angulum reliquę ad baſim ſit dupla. </
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<
s
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">Quare hoc prius ita
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demus. </
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13.
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huius.
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<
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">PROPOSITIO.</
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<
s
id
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">Omnis trianguli centrum grauitatis eſt punctum in recta
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linea ab angulo ad dimidiam baſim ducta exiſtens, quod li
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neam diuidat, ita vt poitio ad angulum reliquæ ad baſim, ſit
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dupla. </
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</
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id
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type
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<
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id
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N13ED3
">Sit triangulum ABC, in quo ab an
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fig48
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gulo A ad dimidiam baſim BC re
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cta ducatur linea AD. Ducaturquè
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ab angulo B ad dimidiom baſim
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AC linea BE, quæſecet AD in F. Et
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quoniam centrum grauitatis
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abbr
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triãgu-
">triangu
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</
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li ABC eſt punctum F;
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abbr
="
oſtendendũ
">oſtendendum</
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eſt lineam FA ipſius FD duplam eſ
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ſe. </
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<
s
id
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">iungatur FC. quoniam enim AE
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eſt equalis ipſi EC, erit triangulum
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ABE triangulo EBC æquale, cùm
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ſint ſub eadem altitudine. </
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<
s
id
="
N13F01
">Ob eandemquè cauſam
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abbr
="
triangulũ
">triangulum</
expan
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AFE triangulo EFC exiſtit æquale. </
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<
s
id
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N13F09
">ſi igitur à triangulo ABE
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auferatur triangulum AFE, & à triangulo EBC triangulum
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auferatur EFC; relin〈que〉tur triangulum ABF triangulo BFC
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æquale. </
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>
<
s
id
="
N13F11
">Rurſus quoniam BD eſt æqualis ipſi DC; erit trian
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<
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gulum BFD triangulo DFC æquale, ſiquidem candem ha
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bentaltitudinem. </
s
>
<
s
id
="
N13F1B
">duplum igitur eſt triangulum BFC
<
expan
abbr
="
triãgu-li
">triangu
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li</
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BFD. Quare & triangulum ABF trianguli BFD duplum
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exiſtit. </
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<
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id
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">quia verò triangula ABF FBD in eadem ſunt altitudi
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ne, idcirco ſeſe habebunt, vt baſes AF FD. at〈que〉 triangulum
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ABF. duplum eſt ipſius FBD; ergo portio AF ipſius FD dupla
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exiſtit. </
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<
s
id
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">quod demonſtrare oportebat. </
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</
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