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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 225, page id 1041163592:0259
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PRINCIPLA MATHEMATICA.
225
L. IB EH
Signitatum A, A3, A, A, AE, A3, A3, A, A2, _ A = = MOMCNEA SCCONDOS.
2a A, 3aA, 4a A3 Za A 2, Za A2, =A A 3, =a A3, = a A 23
=2aR3, e = =aA respective. Et generaliter, ut dignitatis
n- m
cujuscunque Am momentum FueriE = a A m. TTEM UE GenIEX
AB momencum Fuerie 2a AB + b A; ec GenItX A. B. C: momen-
cum 3a A B, C + 4.b A B C + 20 A B C; e Cenit PE (1.
ve AB = mOmentum 3aA B = 2bAB 3: et siC in caetCrIS.
Demonstratur vero Lemma in hunc modum.
Ca5. T. Rectangulum quodris motu perpetuo auctum AB,
ubi de lateribus A et B decrant momentorum dimidia = a ec = b,
tuic A = = a in B - Eb, Icu AB = E a B = Eb A + + ab; ec quam pri-
mum lacera A ec B alceris momentorum dimidiis aucta Fune, eva-
dit A F Z a in B F : b seu AB + : a B F Z b A -+ = a b. De hoc rectan-
sulo subducatur rectangulum prius, ee manebit excessus aB = b A.
situr laterum incrementis toris a ex b generatur rectansuli incre-
mentum aB + b A. Q. F. D.
Ca5. 2. PONatuE A B semper aquale C, e contenti ABC sCu
CC momentum (per Ca5. T.) Crit e C FcC, id CA (A PrO CF de B
Scribantur AB ec a B + bA) aBC + bAC + C AB. EF par CA Fa-
tio contenti sub lateribus quorcunque. d. F. D.
Ca5. 3. PONAnEUT lacera A, B, C sbi mutuo semper aequalia; S
ipCIuS A, id est rectanguli AB, momentum a B = b A criE 2a A, ip-
sius autem A3, id est contenti ABC, momentum a BC + b AC
FCAB erit 3a A. EC eodem argumento momentum dignitatis
cujuscunque A CA na A -1. Q. F. D.
Cas. 4. Unde cum = in A sic 1, momentum ipsius = ductum
in A, una cum = ducto in a erit momentum ipsius F, id est, ni
hil. Proinde momencum ipsius = scu ipsius A CA - . FF sC.
necaliter cum in An si +, momencum ipsius q ductum in an
una