DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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proportionaliter ab angulis diſtant. </
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4
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ſexti
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16
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quinti
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<
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Ducãtur
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pręterea à punctis KL ad latera perpendiculares
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KM KN KO KP, LQ LR LS LT. & quoniam anguli
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KMA LQE ſunt recti, ac propterea æquales, & KAM LEQ
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ſunt æquales, ut oſtenſum eſt; erit reliquus MKA reliquo
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QLE ęqualis, triangulumquè AKM triangulo ELQ ſimile.
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vt igitur AK ad KM; ſic EL ad
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Lq.
">L〈que〉</
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& permutando
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marg18
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ad EL, vt KM ad
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Lq.
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pariquè ratione oſtendetur triangu
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lum BKM triangulo FLQ ſimile exiſtere; eſſequè BK ad
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FL, vt KM ad
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abbr
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Lq.
">L〈que〉</
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ſimiliterquè in alijs triangulis oſten
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detur, ita eſſe Bk ad FL, vt KN ad LR; & Ck ad GL eſſe, vt
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kO ad LS; at〈que〉 kD ad LH, vt kP ad LT. quia verò AK
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EL, Bk FL, Ck GL, Dk HL in eadem ſunt proportione, vt
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proximè demonſtratum fuit; in eadem quo〈que〉 proportione
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erit kM ad LQ, & KN ad LR; & KO ad LS, at〈que〉 kP ad
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LT. ex quibus ſequitur centra grauitatis KL, non ſolùm ab
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angulis in eadem proportione diſtare; verùm etiam à late
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ribus in eadem quo〈que〉 proportione diſtare. </
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<
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id
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N1105E
">Ita〈que〉 cognito,
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quomodo intelligar Archimedes centra grauitatis in ſimili
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bus figuris eſſe ſimiliter poſita; nunc conſiderandum eſt præ
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cedens poſtulatum, quatenus nimirum oporteat grauitatis
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abbr
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cẽ
">cem</
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tra in ſimilibus figuris ſimiliter eſſe conſtituta. </
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<
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N1106C
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miùs conſiderando hanc ſimilem horum grauitatis
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centrorũ
">centrorum</
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poſitionem, congruum, & neceſſarium videtur, ſimiles figu
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ras ſecundùm eandem proportionem eſſe æ〈que〉pon
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expan
abbr
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derãtes
">derantes</
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;
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eademquè ratione (ob earum ſimilitudinem) circa grauita
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lb
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tis centra æ〈que〉ponderare, veluti ſi figuræ: AC EG (quarum
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centra grauitatis ſint KL) à rectis lineis PN TR vtcumquè
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diuidantur, quæ per centra KL tranſeant; dummodo in figu
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ris ſint ſimiliter ductæ; hoc eſt, vel latera, vel angulos in
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eadẽ
">eadem</
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lb
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proportione diſpeſcant: vt ſit AP ad PD, vt ET ad TH. æ
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〈que〉ponderabunt vti〈que〉 partes PABN PNCD, veluti partes
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TEFR TRGH. & hæc non eſt ſimplex æ〈que〉ponderatio; ve
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rùm etiam (vt ita dicam) ſimilis, & æqualis æ〈que〉ponderatio.
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cùm ſit ſecundùm eandem proportionem, quandoquidem
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eſt PB ipſi TF ſimilis, cùm triangula AKB ELF, AKP ELT,
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BKN FLR, ſint inter ſe ſimilia, quæ quidem efficiunt, figuras </
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