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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 3
# Folio 8r, page id 00068156:0015
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secta, modo non situm sit ut in intervallo inter
A et B, erit AB pervenietur ad ab A ad B, tendendo
ab A ad B F et ab F regrediendo ad B, imo
seu hoc codine FB + BF
 Si Hamen oelimus rem ordine punctorum semer
desicnare em directionem sic dici potest
universaliter FB +BF
Imo etsi  cadat F in intervallum, tamen
universaliter dici potest A F - BF = AB. Nam cum
BF progressus ad easdem partes cum A, est negatious pocasu
 cas et ita moles addendo fit AF+BF = AB.
jam inveniamus ZA2B ex 1A1B. Q
(2d0
Nempe () 2AF - 2BF = 2A2B et 1AF - 1BF = 1 A.B
puncti, addendus est motus regulae et puncti si ferantur ins 1A2 A = FA- ((A)  A 1AF- ZAF. Et (po) 1B2B = 1BF- 2BF
1BF =1AF 1AB Et per 2 fit 5to) 1BF = IAF- 1A. B
Et per 1 fit (6to) 2BF = 2AF- 2AB quibus valoribus 5 et 6
substitutis in 4. fit 1B2B = 1AF- 1A1B - 2AF + 2A2B
ubi pro 1AF- 2AF substituendo A2A per 3, _ altique ex
seu si a progressu
ipsius A auferatur progressus e apsius B, idem fit quod
sotus Regulae sit 1AA 1R2R . erit 1A2A =
poprius
et fiet 1R2R + 1A2A = 1A2 A motus puncti A totalis
7mo fiet (800) 1B2B = 1A2A = 1A1B + 2A2B seu
fiet (9n0) 1A2A - 1B2B = 2AB 1AIB - 2A.B seu
mosse 1A2A + 2A+B = 1 A1B + 1B2B
pascitur
motus puncti in Regula sit 1A 2A. firt 1AEA
C sit centrum gravitatis commune ipsorum A et B
sitque et AC + CB = AB. hinc 1AIC + 1C1B = 1A1 B
et 2A2C + 2C2B = 2A2B. 1A, C +  1C2C - 2C2A = IA2A
seu 1AIC+1C2C = 1A2A + 2A2C at 1CEC+ ECLBC iCrB
et 1C+B + 1  B+ 1BdC, = +  1CB+ 1B2B - (1 C2C+ 2C2B
quae duae aequationes differunt relegando, vel quod eodem
redit pro A substtuseo  2B et cntra et pront C substat atur 2C et contra
redit pro I substituatur 2 et contra; et pro A substituatur B
Omnia ergo redacta sunt  ad A2A + 2A2B = AB+ 1B2B AC+ CB = AB
1AIC+ 1CZC = IA2A + 2A2C et 1C1B + 1B2B = 1C2 C+ 2C2B
Conjungamus jam duos motus situs novus 2A3A + 3A3B = 2A2B + 2B3B
A 2A2C + 2C3C = 2A3A+ 3A3C, et 2C2B + 2B3B = 2C3C + 363B
comparando A2A = 2A3A et 1B2B = 2B3B ex hypothasi seu A(2) est constans et B(B) estg
C2C = A. AFEAT C- 1ErA Ergo 1A. A 3A A = 1BEB- 3B- B
Ergo 1A2A - 2B.B = =BB 2A3A - 3B2B. Erqu seu  A(A) - (B) B est onst.
ergo B et AB - (B) A) est const. Ergo AC + CB = (C)A) - (C(B) est onst.
est autam AC ad CB  ut (O(A) ad (C)(B) Ergo AC - (C) () est const.
et CB = CAB) est const. jam 1C2C est  = 1A2A + 2A2C = 1C1A
1on
const.
Ergo 1C2C est const. seu 1C2C = 2C3C
Hactenus phorographia de de libavimus
nunc ad Pynamica nomnilit transeamus. Reperio
ascripto
omne punctur signo 
omnis linea positiva
scribatin
rum
egto
ordine contrario
hoc prius non ob.
servatu
Fin uno motu
adhibits soli
punctis mobi
A, B, C