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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 342, page id 1041163592:0376
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342
PHTLOSOPMIILE NATVRALIS
DEMOTD FO ad V. Ouare cum tempora, quibus aequalia COrPOrA Per
CdRPORON
aequalia spatia impelluntur, sine reciproce in lubduplicata racione
virium, crie tempus vibrationis unius urgente vi illa Flattica, ad
cempus ribracionis urgente ri ponderis, in subduplicata ratione
V V ad FOX A, atque adeo ad tempus oscillationis Penduli cu-
jus longitudo est A, in subduplicata ratione V V ad FOX A, &
subduplicata ratione FO ad A conjunctim; id est, in ratione in-
tegra V ad a. Sed tempore ribrationis unius ex itu ex reditu com-
Dolicx, pulsus progrediendo conticit lacieudinem suam BC. RrgO
cempus quo pulsus percurrit spacium BC, est ad tempus oscillaci-
onis unius ex itu ex reditu compolitae, ut V ad A, id cst, uE BC
ad circumterentiam circuli cujus radius eAt A. Tempus autem,
quo pultus percurret spatium BC, es ad cempus quo percurret
consicudinem huic circumterentia aequalem, in eadem ratione;
ideoque tempore talis olcillationis pulsus percurret lonsicudinem
huic circumferentia aequalem. d. L. D.
Corol. T. Velocitas pulsuum ea est quam acquirune Gravia, sequa-
liter accelerato motu cadendo, et calu luo describendo dimidium
alticudinis A. Nam tempore casus hujus, cum velocitate cadendo
acquilica, pulsus percurret spatium quod erit aequale coti alcitu-
dini a, adeoque tempore oscillationis unius ex itu de reditu com-
POTiEx, Percurret Spacium aequale circumterentiae circuli radio A
deseripei: es enim tempus casus ad tempus olcillationis u radius
circuli ad ejusdem circumterentiam.
Corol. 2. Unde cum alcieudo illa A sic ut Fluidi vis Elastica di-
recte e densitas ejusdem inverse; relocicas pulluum erit in ratione
compolica ex subduplicata ratione densitaris inverse ee subdupli-
cata ratione vis Elasticae directe.
PROPOSTTIO L. PROBLEMA XII.
Trvenire pulsuum distantias.
CorpOrIS, cujus cremore pulsus excitantur, inveniatur numerus
ibrationum daEO TEMPOTC. Per numerum illum dividatur sp2-
tium quod pulsus codem tempore percurrere posit, ec Pars in.
venca crie pulsus unius lacirudo. Q. F. L.
Scholium.
Svectat CoDOncioneo torna ad mmoeum eis e oedorum.
Eux enim cum propasetur secundum lineas rectas, in actione sola
DC