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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIPTA MATHEMATICA.
Corol. Toitur motus relocistimus in Medio rehcente non incidie
E TMBn
in punctum intimum C, sed reperitur in puncto illo O, quo arcuS SEEvUUS.
eotus descriptus a B bisecatur. EE corpus Tubinde pergendo ad a.
iisdem gradibus recardatur quibus antea accelerabatur in descentu
suo a B ad O.
PROPOSITIOZXVI. TITEOREMA XXI.
Corporum Funependulorum, quibus resistitur in ratione velocitatum.
oscillationes in Cycloide sunt Isochronae.
Nam E corpora duo, a ceneris suspensionum equalicer distantia,
OTcillando describane arcus inxquales, ex velocitaces in areuum Dar.
tibus correspondentibus sint ad inricem ut arcus toti: resistentise
relocitatibus proportionales, erunc etiam ad invicem ut iidem ar-
cus. Proinde A viribus motricibus a graritate oriundis, quae sine
ut iidem arcus, auterantur rel addantur hae resistentixe, erunt dif-
Ferentix. vel summae ad invicem in eadem arcuum ratione: cumque
velocitacum incrementa vel decrementa sint ut hae differentiae vel
Cummae, velocitates semper erunt ut arcus toti: Igitur velocitates,
E sinc in aliquo casu ut arcus totis manebune semper in eadem ra-
cione. Scd in principio motus, ubi corpora incipiunt descendere
ec arcus illos describere, rires, cum sint arcubus proxortionales, sc.
nerabunt relocitares arcubus proportionales. Argo velocitates lem-
Per erunt uc arcus rori describendi, et propterea arcus illi simul de.
Scribeneur. Q. F.. D.
PROPOSITIO XXVII. TMEOREMA ZXII.
Si Corporibus Funependulis resistitur in duplicata ratione veloci
tatum, differentiae inter tempora oscillationum in Medio resi-
stente ac tempora oscillationum in ejusdem gravitatis specificae
Medio non resistente, erunt arcubus oscillando descriptis pro-
portionales, quam proxime.
Nam pendulis aequalibus in Medio resistente deseribAnEUr AFCUS
inaequales A, B; ex reliltentia corporis in arcu A, erit ad resisten-
tiam corporis in parte correspondente arcus B, in duplicata ratio-
ne relocitatum, id cAt, uc A A ad BB, quam proxime. Si reli-
Stentia