Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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FED. COMMANDINI
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ſunt uertice, eandem proportionem habent, quam ipſarũ
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baſes. </
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<
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">eadem ratione pyramis a c l k pyramidi b c l k: </
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">& </
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<
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ramis a d l k ipſi b d l k pyramidi æqualis erit. </
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<
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xml:space
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">Itaque ſi a py
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ramide a c l d auferantur pyramides a clk, a d l k: </
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<
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">& </
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<
s
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xml:space
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">à pyra
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mide b c l d auferãtur pyramides b c l k, d b l K: </
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<
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xml:space
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">quæ relin-
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quuntur erunt æqualia. </
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<
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echoid-s4173
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xml:space
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">æqualis igitur eſt pyramis a c d k
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pyramidi b c d _K_. </
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<
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">Rurſus ſi per lineas a d, d e ducatur pla-
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num quod pyramidem ſecet: </
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<
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">ſitq; </
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">eius & </
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<
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">baſis communis
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ſectio a e m: </
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<
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">ſimiliter oſtendetur pyramis a b d K æqualis
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pyramidi a c d
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. </
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<
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">ducto denique alio piano per lineas c a,
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a f: </
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<
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">trianguli c d b communis ſectio ſit c fn, py-
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ramis a b c k pyramidi a c d
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æqualis demonſtrabitur. </
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<
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">cũ
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ergo tres pyramides b c d _k_, a b d k, a b c k uni, & </
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<
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">eidem py
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ramidia c d k ſint æquales, omnes inter ſe ſe æquales erũt.
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</
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<
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">Sed ut pyramis a b c d ad pyramidem a b c k, ita d e axis ad
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axem k e, ex uigeſima propoſitione huius: </
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<
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xml:space
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">ſunt enim hæ
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pyramides in eadem baſi, & </
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">axes cum baſibus æquales con
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tinent angulos, quòd in eadem recta linea conſtituantur. </
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quare diuidendo, ut tres pyramides a c d k, b c d _K_, a b d _K_
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ad pyramidem a b c _K_, ita d _k_ ad _K_ e. </
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<
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">conſtat igitur lineam
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d K ipſius _K_ e triplam eſſe. </
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">ſed & </
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<
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">a k tripla eſt K f: </
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">itemque
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b K ipſius _K_ g: </
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<
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xml:space
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">& </
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<
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">c
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ipſius
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l tripla. </
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<
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">quod eodem modo
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demonſtrabimus.</
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<
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">Sit pyramis, cuius baſis quadrilaterum a b c d; </
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">axis e f:
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</
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<
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<
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">diuidatur e fin g, ita ut e g ipſius g f ſit tripla. </
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<
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">Dico cen-
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trum grauitatis pyramidis eſſe punctum g. </
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<
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">ducatur enim
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linea b d diuidens baſim in duo triangula a b d, b c d: </
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<
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quibus intelligãtur cõſtitui duæ pyramides a b d e, b c d e: </
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ſitque pyramidis a b d e axis e h; </
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<
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<
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">pyramidis b c d e axis
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e K: </
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<
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">& </
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<
s
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xml:space
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">iungatur h _K_, quæ per ftranſibit: </
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<
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">eſt enim in ipſa h K
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centrum grauitatis magnitudinis compoſitæ ex triangulis
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a b d, b c d, hoc eſt ipſius quadrilateri. </
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<
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">Itaque centrum gra
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uitatis pyramidis a b d e ſit punctum l: </
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<
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<
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">pyramidis b c d e
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ſit m. </
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<
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">ductaigitur l m ipſi h m lineæ æquidiſtabit: </
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<
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">nam el ad
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">2. ſexti.</
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