Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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FED. COMMANDINI
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<
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xml:space
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">Itaque quoniam duæ lineæ K l, l m ſe ſe tangentes, duabus
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lineis ſe ſe tangentibus a b, b c æquidiſtant; </
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<
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dem plano: </
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xml:space
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l m æqualis eſt angulo a b c: </
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xml:space
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">& </
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<
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xml:space
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cimi</
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gulus l m
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, angulo b c a, & </
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<
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<
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lipſi c a b æqualis prob abi
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tur. </
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<
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xml:space
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l m eſt æquale, & </
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<
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xml:space
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a b c. </
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<
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<
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ſam, & </
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<
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<
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lelogrammi a e communis ſectio ſit o p q. </
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<
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xml:space
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f q per h, & </
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<
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<
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xml:space
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">nam cum plana æquidiſtantia ſecen
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tur à plano c q, communes eorum ſectiones c g o, m p, f q
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ſibi ipſis æquidiſtabunt. </
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<
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xml:space
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<
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xml:space
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">æquidiſtant a b,
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l, d e. </
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<
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guli ergo a o c,
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p m, d q f inter ſe æquales ſunt: </
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xml:space
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<
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cimi</
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æquales qui ad puncta a k d conſtituuntur. </
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reliquis æquales; </
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<
s
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">triangula a c o, _K_ m p, d f q inter ſe ſimi
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lia erunt. </
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<
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xml:space
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">Vtigitur ca ad a o, ita fd ad d q: </
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<
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ut c a ad fd, ita a o ad d q. </
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<
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<
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a o ipſi d q. </
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<
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">eadem quoque ratione & </
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<
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">a o ipſi _K_ p æqualis
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demonſtrabitur. </
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<
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xml:space
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<
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ſimilia inter ſe aptétur,
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cadet linea f q in lineam
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c g o. </
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<
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">centrũ gra
<
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<
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">per 5. pe-
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titionem
<
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Archime
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dis.</
note
>
uitatis h in g centrũ ca-
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det. </
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<
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f q per h: </
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<
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<
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c o & </
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<
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g h ducetur: </
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<
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neam m p etiã per n trã
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ſire neceſſe erit. </
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<
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niam ergo ſh, c g æqua-
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les ſunt, & </
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<
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</
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<
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<
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<
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neæ, quæ ipſas cónectũt
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c m f, g n h, o p q æqua-
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les & </
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<
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