Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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<
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s.000375
">SIT pyramis, cuius baſis triangulum abc; axis dc: &
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ſecetur plano baſi æquidiſtante; quod
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ſectionẽ
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faciat fgh;
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<
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occurratq;
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axi in puncto k. Dico fgh triangulum eſſe, ipſi
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abc ſimile; cuius grauitatis centrum eſt K.
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Quoniã
">Quoniam</
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enim
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duo plana æquidiſtantia abc, fgh ſecantur à plano abd;
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communes eorum ſectiones ab, fg æquidiſtantes erunt: &
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eadem ratione æquidiſtantes ipſæ bc, gh: & ca, hf. </
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<
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id
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s.000376
">Quòd
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cum duæ lineæ fg, gh, duabus ab, bc æquidiſtent, nec
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ſint in eodem plano; angulus ad g æqualis eſt angulo ad
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b. </
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<
s
id
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s.000377
">& ſimiliter angulus ad h angulo ad c:
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abbr
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angulusq;
">angulusque</
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ad fci,
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qui ad a eſt æqualis. </
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<
s
id
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s.000378
">triangulum igitur fgh ſimile eſt tri
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angulo abc. </
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<
s
id
="
s.000379
">Atuero punctum k centrum eſſe grauita
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tis trianguli fgh hoc modo oſtendemus. </
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>
<
s
id
="
s.000380
">Ducantur pla
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na per axem, & per lineas da, db, dc: erunt communes ſe
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lb
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ctiones fK, ae æquidiſtantes:
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abbr
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pariterq;
">pariterque</
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kg, eb; & kh, ec:
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quare angulus kfh angulo eac; & angulus kfg ipſi eab
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number
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eſt æqualis. </
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>
<
s
id
="
s.000381
">Eadem ratione
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anguli ad g angulis ad b: &
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anguli ad h iis, qui ad c æ
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quales erunt. </
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>
<
s
id
="
s.000382
">ergo puncta
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lb
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eK in triangulis abc, fgh
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ſimiliter ſunt poſita, per ſe
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xtam poſitionem Archime
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lb
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dis in libro de centro graui
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tatis planorum. </
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>
<
s
id
="
s.000383
">Sed cum e
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ſit centrum grauitatis trian
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guli abc, erit ex undecima
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propoſitione eiuſdem libri,
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& K trianguli fgh grauita
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tis centrum. </
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>
<
s
id
="
s.000384
">id quod demonſtrare oportebat. </
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>
<
s
id
="
s.000385
">Non aliter
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in ceteris pyramidibus, quod propoſitum eſt demonſtra
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bitur.</
s
>
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