Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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ſunt uertice, eandem proportionem habent, quam
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ipſarũ
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baſes. </
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<
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">eadem ratione pyramis aclk pyramidi bclk & py
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ramis adlk ipſi bdlk pyramidi æqualis erit. </
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<
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id
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s.000582
">Itaque ſi a py
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ramide acld auferantur pyramides aclk, adlk: & à pyra
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mide bcld
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auferãtur
">auferantur</
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pyramides bclk dblK: quæ relin
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quuntur erunt æqualia. </
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<
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">æqualis igitur eſt pyramis acdk
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pyramidi bcdK. </
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">Rurſus ſi per lineas ad, de ducatur pla
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num quod pyramidem ſccet:
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ſitq;
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eius & baſis communis
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ſectio aem: ſimiliter oſtendetur pyramis abdK æqualis
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pyramidi acdk. </
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<
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id
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">ducto denique alio plano per lineas ca,
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af: ut eius, & trianguli cdb communis ſectio ſit cfn, py
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ramis abck pyramidi acdk æqualis demonſtrabitur. </
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s.000586
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cũ
">cum</
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ergo tres pyramides bcdk, abdk, abck uni, & eidem py
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ramidi acdk ſint æquales, omnes inter ſe ſe æquales
<
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abbr
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erũt
">erunt</
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>
. </
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<
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<
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id
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s.000587
">Sed ut pyramis abcd ad pyramidem abck ita de axis ad
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axem ke, ex uigeſima propoſitione huius: ſunt enim hæ
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pyramides in eadem baſi, & axes cum baſibus æquales con
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tinent angulos, quòd in eadem recta linea conſtituantur. </
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<
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<
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id
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s.000588
">quare diuidendo, ut tres pyramides acdk, bcdK, abdK
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ad pyramidem abcK, ita dk ad Ke. </
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<
s
id
="
s.000589
">conſtat igitur lineam
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dK ipſius Ke triplam eſſe. </
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<
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id
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s.000590
">ſed & ak tripla eſt Kf: itemque
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bK ipſius kg: & ck ipſius kl tripla. </
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<
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id
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">quod eodem modo
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demonſtrabimus.</
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17 huius</
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ucrfex
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1. sexti.</
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5. duode
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cimi.</
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<
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id
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">Sit pyramis, cuius baſis quadrilaterum abcd; axis ef:
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& diuidatur ef in g, ita ut eg ipſius gf ſit tripla. </
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<
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id
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">Dico cen
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trum grauitatis pyramidis eſſe punctum g. ducatur enim
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linea bd diuidens baſim in duo triangula abd, bcd: ex
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quibus
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intelligãtur
">intelligantur</
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<
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abbr
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cõſtitui
">conſtitui</
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>
duæ pyramides abde, bcde:
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ſitque pyramidis abde axis eh; & pyramidis bcde axis
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eK: & iungatur hK, quæ per f tranſibit: eſt enim in ipſa hK
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centrum grauitatis magnitudinis compoſitæ ex triangulis
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abd, bcd, hoc eſt ipſius quadrilateri. </
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>
<
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id
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s.000598
">Itaque centrum gra
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uitatis pyramidis abde ſit punctum l: & pyramidis bcde
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/>
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marg70
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ſit m. </
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<
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id
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s.000599
">ducta igitur lm ipſi hm lineæ æquidiſtabit. </
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<
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s.000600
">nam el ad </
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