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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 226, page id 1041163592:0260
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226
PHITLOSOPHITSE NATURALIS
COnPONVM Una cum.  in n a An - erit nihil. EE propcerea momentum ip.
GuSL. CCu A eric
no
An F L Q. F D.
Ca5. 5. EF cum A in A SIC A, momentum ipsiuS A ductum in
2A= erit a, Per Ca5. 3: ideoque momentum ipsius A crit q A3
sIvC = a A Z. EF ZEnCTAlIEeE SI POnatuE An aequale B, erit A ∞-
quale B, ideoque ma Am == sequale nbB, - 2 ec maA aequa
M
m-n
ICnbB SCu nbA n 2dCOquC a A n aequale b, id est, aequale
momento ipsius A 9. F. D.
Ca5. 6. Psitur Cenita cujuscunque Am B momentum cAt mo-
mencum ipsius Am ductum in B una cum momento ipsius B du-
Eto in A, id est ma A = 2 B L nbB == Am; idque sire dignita-
cum indices m ex n sinc inceori numeri vel Fracti, sive afirmati-
vi rel nesatiri. EE Par eA ratio concenti sub pluribus dignitati-
buS. 2. F. D.
Corol. T. Fline in continue proxortionalibus, si terminus unuS
datur, momenta terminorum reliquorum crunt ue iidem termini
mulciplicati per numerum intervallorum inter iplos ec terminum
datum. Sunto A, B, C, D, R, I continue proportionales; et sI
decur terminus C, momenta reliquorum terminorum crune inter
(C UE = 2A, = B, D, 2E, 3F.
Corol. 2. FE si in quaruor proxortionalibus duxe medixe dentur,
momenta extremarum erunt ut caedem extremae. Idem incelligen-
dum est de lateribus rectanguli cujuscunque dati.
Corol. 3. FF i summa vel disterentia duorum quadratorum decurs
MOMENEA laTETUM CTUNE reCipTOCC UE latOTA.
Scholium.
In liceris quae mihi cum Ceometra peritillimo Cr. Ci. Leibnitio at
nis abhinc decem intercedebant, cum signiticarem me compotem
esse methodi decerminandi Maximas ex Minimas, ducendi Tangen-
ces, ec similia peragendis qua in terminis lurdis xeque ac in ratio-
nalibus procederet. ex liceris transpoliris hanc sententiam involven-
ibU
DE MOTD