Ceva, Giovanni - Geometria motus

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Exemplum II.

PROP. XXXIV. THEOR. XXVII.

TEmpora ſimilium vibrationum ſunt in ſubduplicata
ratione arcuum exactorum, ſeu longitudinum pen
dulorum, quorum ſunt vibrationes. Sint grauia pendula
LA, LF, quæ ab eadem recta LF diſcedentia currant ſuſ

penſa ex L duos ſimiles arcus circulares FI, AC. Dico
tempora horum deſcenſuum eſſe in ratione ſubduplicatą
arcuum FI, AC, ſeu longitudinum filorum, aut haſtularum
FA, LA. Ducamus quamcumque rectam LBG, erit AB
ad BC, vt FG ad GI, & cum præterea velocitates pendu
lorum a quiete in A, F ſint æquales, pariterque velocita
tes æquales a quiete in B, G; erit velocitas in A ad veloci
tatem in B, vt velocitas in F ad velocitatem in G, quare
conſideratis arcubus ABC, FGI, vt altitudines rectę, (quæ
item forent in B, G proportionaliter ſectę) geneſum ſimi

lium ſimpliciumque motuum, quarum amplitudines æqua
les ſunt, erunt ſpatia in acceleratis decurſubus per FI, AC
in ratione duplicata temporum, ſcilicet ipſi arcus, aut lon
gitudines LF, LA erunt in ratione duplicata temporum̨.
Quod &c.

Tab. 8. fig. 2.

Def. 7. primi.

Idem demonſtratum eſſet beneficio imaginum, quæ vt
pote eorundem illorum motuum ſimplicium, forent etiam
ſimilium, & ſunt amplitudines æquales, etenim eædem̨
ſunt, ac geneſum ergo rurſus ſpatia, hoc eſt arcus ABC,
FGI, nempe longitudines filorum IF, AC erunt in ratione
duplicata temporum. Quod &c.

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