Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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FED. COMMANDINI
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æqualibus baſibus, quorum axes cum baſibus æquales an
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gulos faciant. </
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<
s
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xml:space
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">Dico ſolidum a b adſolidũ c d ita eſſe, ut axis
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e f ad axem g h: </
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<
s
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xml:space
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">nam ſi axes ad planum baſis recti ſint, il-
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lud perſpicue conſtat: </
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<
s
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">quoniam eadem linea, & </
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<
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">axem & </
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<
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di altitudinem determinabit. </
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<
s
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xml:space
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">Si uero ſintinclinati, à pun-
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ctis e g ad ſubiectum planum perpendiculares ducantur
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e k, g l: </
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<
s
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xml:space
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">& </
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<
s
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xml:space
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">iungantur f_k_, h l. </
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<
s
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xml:space
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">rurſus quoniam axes cum ba
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ſibus æquales faciunt angulos, eodem modo demonſtrabi
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tur, triangulum e f K triangulo g h l ſimile eſſe: </
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<
s
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xml:space
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">& </
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<
s
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xml:space
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">e k ad g l,
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ut e f ad g h. </
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<
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xml:space
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">Solidum autem a b ad ſolidum c d eſt, ut
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e K ad g l. </
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<
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xml:space
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">ergo & </
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<
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">ut axis e f ad axem g h. </
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<
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xml:space
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">quæ omnia de
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monſtrare oportebat.</
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<
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<
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">Ex iis quæ demonſtrata ſunt, facile conſtare
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poteſt, priſmata omnia & </
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<
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">pyramides, quæ trian-
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gulares baſes habent, ſiue in eiſdem, ſiue in æqua
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libus baſibus conſtituantur, eandem proportio-
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xml:space
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nem habere, quam altitudines: </
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<
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<
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xml:id
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xml:space
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">ſi axes cum ba
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ſibus æquales angulos contineant, ſimiliter ean-
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dem, quam axes, habere proportionem: </
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<
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xml:space
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<
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cimi.</
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enim ſolida parallelepipeda priſmatum triangula
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res baſes habentiũ dupla; </
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<
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">pyramidum ſextupla.</
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<
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cimi.</
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<
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<
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<
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xml:space
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">pyramides, quæ in eiſdem,
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uel æqualibus baſibus conſtituuntur, eam inter
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ſe proportionem habent, quam altitudines: </
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<
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xml:space
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axes cum baſibus faciant angulos æquales, eam
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etiam, quam axes habent proportionem.</
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