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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 18
# Folio 10r, page id 00068172:0019
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quod tocs vocos
braceo
p.  Constructio problemalis num. 7. propositi talis est perfacilis
jungatur, A2B aatque ea producta ab 1A ad F, ut sit FIA, ad F2B, in ratione
data, (quae debet esse, AA ad 2Bb) juncta FH secabit 1A2A et 2B3 B
in punctis a et b quaesitis Nam ob triangula A Fa. 1A et Fb. 2B
insimilia, patet esse aB ad b. 2B ut F1 A ad F2 B id est in ratione data Scilicet
nel in duplicata ratione velocitatis qua descendit A ex. 2 A ad 1A ad velocitatem
qua ascendit B ex 1Bad 2B seu in ratione duplicata rationis A2C ad 1B
ciratum et quod statur ce
BB in sequente alculo
osif et
 BNasu praesent
patet etiam velocitatem quanaactati est de A descendendi
a vectis eA in est esse ad eam quam nactum esset descendendo libere
prAiniA, esse in dupli in sub duplicata ratione a
e 4
itaque operae
eterminetur pliarum Hit
s in pretium erit hanc rationem invenire distinctius. Natur eA. L. datur
et HL. Nam 1AL ad 1BL ut Bad A ut 1ALL 1A1B. B: A+B L
et HL: 1A2A .: HB: 1B2A:: A: A +B. Ergo HL = 1A2A. A: ATB (adeoque
AL: LH;: B: A in 1AIB: (A2A) determinatum ergo est punctum HB
calculo, determinetur am plo punctum Fadatur autem ratio .AF ad F2B seu ad
1A2B, ergo primum debet dlterminari 1A2B, cise pendet ab cB2 B et
+B+B est ad IA2A ut LB2C ad 1A2C, seu IB2B = 1ALA. 1B2C: 2A2
FM: MI A: 1AF. .(.A 1B, 1B EB; 1A2 et 1AF: eA B  F2B:.
4
B 2A2C. 1B1C. Ergo F2B = 1AF. IBIC: 2AEC = A2B . AF
ergo fiet AF E:A2B:: EA2C: B2C  2A2C:: 1AM: 1B2B:: FM. 11
Ergo FM = 1 A1B. 2A2C: (1B2C ∞ 2A2C et per 3. fiet 1AM = eA 2A C A.B:
1AM = A2A. (B2C. 2AZC: 1BGC AC. EA2C seu CAM: 1A2A:: 1B2C 2AuC
1BIEL EA2C
quod est theorema Clegans.
Nunc iAta ita investigabimus: MA
Aa = Ma- 1. A ( a M a= M. A + iAa. et FM: Ma i FM + 1AL: es M, A + LH et
fiet Ma = FM. M. A+LH: FM + .AL jam M A + HL- A 2At. 1B, C. 2AEC. A+ B
+ 1A2A A. 1B2C+ istic Arb 1BC+ EArC
et FM +IAL = 1A1B. 2ArC. AbB) + 1AIB. B. 1B2C 2AIC:
c
A+B. 1BrCA ta
seu fiet
Ergo Ma= AIB.2 AEC. 142 fl. 162 C. 2A2C. A+ B + 1AA. A. IDC + 2At EM AC L. p B. p ite
AIB. 1B.AC
Eago M
1B2C+ EA2C
A. 1RC. 2ADC AFB + + AA. A. IB.CAAC, AB. EAE
1A1B. 2ATC AAB + 1A 1B B. 1BEC+TAEE, B2C+ EAEC
ab Ma auteramus M. A fint 1Aa = Ma-M. A = (FM. M, A L FM. LHC F M. M. A 1AL. M. A
A+1AL
sed FM. MA.: 1AL. SH, unde fieret a B. quod abs. pportet in calculo ese dratum
FM. LH = 1A IB. 1A2A. A. EAECE:, ALB . IBEC+ 2A2C
1AL. A  AL. M. A = 1 A2A. 1B2C. 2A2C. 1AIB. B : A+ B.. IB2C~2AC
(AB) 2AC, + A. 2AEC= B. 1B2C
fiet 1AaACAID AC A. 2AeC B 1brC
(1A1 2A2C ArB + B. IB2CF MC
(1AID)  A. 2AC = B. 1B2C
itaque si corpesa in libra descendenti ab oppositi alterius brachii corporibus
IA2A
retardetur, erit celeritat acquisitae descenstretardato
Itaque si corpas in libra descendens ab opposito alterius brachii corpore
relardetur, erunt celeritates descensu acavis itae in subduplicata
ratione composita d et plura talia corporus in divertis,
libris a centris aeque motupuli aeque remota conferantur inter se, fait
erunt cebritates descensibus graesitae in ratione subduplicata composita
ex differentiis rationibus dufferentiarum inter celeritates proaessium
eu differentiarum inter celeritates obnitentium sibi corporum directa
Hinc si corpora A et B sint aequalia quae
sibi obuntuntur fret ista: 1ArH= 2A2C: 2A1B. quod si distinta Lacet buc
inter vires ectum reciproca
sint aequales fietusta = 22A
A unde patet etiam
quanto corporis in
brachio librae.
coleritus et
sito retardati
renden
elerit
sit libera, n
in ratione sulduplicata
ita ad iArA
1B.CnAEC
vocant p V. C