Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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æqualis angulo DHL, & vt KG, ad GA, ita LH, ad
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HD: ſed vt GA, ad AC, ita eſt HD ad DF: & vt
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AC ad AB, ita DF ad DE, ex æquali igitur erit vt
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KG ad AB, ita LH ad DE: ſed vt AB ad BG, ita
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eſt DE ad EH, propter ſimilitudinem triangulorum
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ABG, DEH: & vt BG ad GO ita eſt EH ad HP,
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propter triangulorum centra O, P; ex æquali igitur erit
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vt KG ad GO, ita LH ad HP: & permutando vt
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OG ad PH, ideſt vt BG ad EH, ideſt vt AB ad ED,
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ita KG ad LH, & reliqua OK ad reliquam PL. </
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>Sed ſint puncta ſimiliter poſita M, N, quæ cadant ex
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tra lineas BG, EH, iunctæque OM, PN. </
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>Dico iti
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dem eſse vt AB ad ED, ita OM ad PN. </
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>Iungantur
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enim rectæ MB, NE, quæ cum quibus lateribus homo
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logis angulos æquales faciunt, ea ſint AB, DE, quod
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propter iſoſcelia triangula ſit dictum in ſimiliter poſitis
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triangulis. </
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>igitur etiam angulus BAM, æqualis erit an
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gulo EDN; ſimilia igitur triangula ABM, DEN: &
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vt MB ad BA, ita erit NE ad ED: ſed vt AB ad
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BG, ita eſt DE ad EH, propter ſimilitudinem trian
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gulorum, & vt BG ad BO, ita eſt EH ad EP, ob
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triangulorum ſimilium centra O, P: ex æquali igitur
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erit vt MB, ad BO, ita NE ad EP. </
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<
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>Rurſus quo
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niam angulus ABM, æqualis eſt angulo DEN, quorum
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angulus ABG, æqualis eſt angulo DEH: erit reliquus
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angulus OBM, æqualis reliquo angulo PEN: ſed vt MB
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ad BO, ita erat NE ad EP; triangulum igitur OBM
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triangulo PEN, ſimile erit, & vt BO ad EP, hoc eſt
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BG ad EH, hoc eſt AB ad DE, ita OM ad PN.
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<
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>Quod demonſtrandum erat. </
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