Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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ctiones circuli ex prima propoſitione ſphæricorum Theo
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doſii: unus quidem circa triangulum abc deſcriptus: al
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ter uero circa def: & quoniam triangula abc, def æqua
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lia ſunt, & ſimilia; erunt ex prima, & ſecunda propoſitione
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duodecimi libri elementorum, circuli quoque inter ſe ſe
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æquales. </
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<
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">poſtremo a centro g ad circulum abc perpendi
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cularis ducatur gh; & alia perpendicularis ducatur ad cir
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culum def, quæ ſit gk; & iungantur ah, dk perſpicuum
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eſt ex corollario primæ ſphæricorum Theodoſii, punctum
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h centrum eſſe circuli abc, & k centrum circuli def. </
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<
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niam igitur triangulorum gah, gdK latus ag eſt æquale la
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teri gd; ſunt enim à centro ſphæræ ad ſuperficiem: atque
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eſt ah æquale dk: & ex ſexta propoſitione libri primi ſphæ
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ricorum Theodoſii gh ipſi gK: triangulum gah æquale
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erit, & ſimile gdk triangulo: & angulus agh æqualis an
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gulo dg
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K.
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ſed anguli agh, hgd ſunt æquales duobus re
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ctis. </
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id
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">ergo & ipſi hgd, dgk duobus rectis æquales erunt. </
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& idcirco hg, g
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K
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una, atque eadem erit linea. </
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<
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h ſit
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centrũ
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circuli, & tri
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anguli abc grauitatis cen
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trũ
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probabitur ex iis, quæ
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in prima propoſitione hu
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ius tradita ſunt. </
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<
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">quare gh
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erit pyramidis abcg axis. </
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<
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s.000841
">& ob eandem cauſſam gk
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axis pyramidis defg. </
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<
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">lta
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que centrum grauitatls py
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ramidis abcg ſit
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pũctum
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l, & pyramidis defg ſit m. </
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<
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">Similiter ut ſupra demon
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ſtrabimus mg, gl inter ſe æquales eſſe, & punctum g graui
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tatis centrum magnitudinis, quæ ex utriſque pyramidibus
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conſtat. </
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<
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id
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s.000844
">eodem modo demonſtrabitur, quarumcunque
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duarum pyramidum, quæ opponuntur, grauitatis
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centrũ
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