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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 44v, page id 00068197:0088
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A = l -n, M =
2=M V = L - m) Trinl maxima, n minima
24 = 1 +11
31=12:, oor - 1N
23 =0d.
post tanc significationem notarum assumtarum, proponitur aequatio
resolvenda a 31 (24 -31) Y - 00. 11 (13 +31)  = 1131 ( 221 31,
24. - 31 = (00+ 11) (0or = W (1) = 00. 11A, : , 00V - UM. Fiet 00. 00Y = 00. 1 M
411. 00V - 11. un - 00. 11X,:... . = 007 - 11 n + D0. 11(V - ( - 1), :, .
Sed V- n - X ~0. Ergo fit 24 -31 = 00V - pn, : ooV -uM. similiter
24+31 = (00 - 11) (00r = 11(3) + 00I12, : . . . . F, et 00. 00Y = 10. I1 (M - 11. 00Y
Luui = U +u. un +00. 1d, :.... 20dr + t  +00. 1
CA - n -1), :.... sed A  suir = M. Eup est
Ergo fit 23+31 = 09V +1n - 2. 00. UM, :, v0r - 1(
dertio etium modo idem culculut obtineri pors
facendo eorH.umG, F = GKH E. = 3
Bor HF- 20c xoErrd =2odrvad
=ooinoo oorcipu ie +2. soru ndo H.  
umiriu
E = X5E
IIueF = teor p oir suur ieniun f. odri od 1 2
xtpurtncor viputuia +u lm m ooy R2  3 =  (- 11  .)
Hic vator obser vat popitiam inter 0 L 1I, Y
= _. eoVLIL.M = 00. 11X, :, . . . . = 00r +1E n = 00.1t (A + (n tYio GxR _=  ex VoVr + 00Y 1I N = (2 00Y. du. M     5
1. sed A + n + Y = 2Y, et
Et sit 23- 31 = 0oV + 1en  200. IIV, :, coY - 1p
(m 00Y - 1 n 1n t2. 0 m eB. MP  F.
compendio
et  ( FH60 DGHK -6)  N n GF
et Oor FH, - GKH = nN HNFG = ooVF - GK, H
10or 12
+002 F -100rV =00. N aY 3.
OSrr - 3.00uur +00. N Cn 1V-H 1 X  4 p L21
GKH - + 00r Do -oi vou L obroVi (2 ) -0or I M P Y F.  = =
Numeratores ipsorum 24. = 3L 23 +31 23- 31 31 denominator commenis GK -
Et excequ 2 sies, ereoud F V - 00. 114G = - 00. 1 Am GF 
Kk. H: K
o inour tu mooun (N) -umC=
2Wvir ovrra bbau oou p. cur vo Ex  AZ O IYII p F
GKH= ZoV-o  C)Loor ( L+B)-10. 1(mfEr):
MH Sit A+YLI
GK = (E0OVBOK COY I1e + (2l0OV OOHM = IIM, L1I M
A , cVFI = aB 1aY +  Hoc sutotum hintiplidemr per H fiet min - reit
Fumoortuma -2. M M00  )
post EH) =un, eree e oor oortoorue bost oena A-m F   t
pnoorummeum oou
 R3 2Q E n n de a .1BIXtoui
 a n
oi o t NhC 2. aeie n 4 _o CALV,
C0d 11
pt
nr.3
taref = Hn, 4300 r- 608 + 4 00 1t cnt
20dH ZV+ ∞408. 11
N +M - 2n AV  sa t  M st - in. d
87
ot5 
MaFG= (up) aeotai uo od + 2.0o r ovua
Aunar nit  ( 2. IC a 00. 11 M)
2. 10. p  
 Y  n sit n
X- VM.
sem = in 2 is
si esset m = d, sicret d A n et V =l et cuta ex differentia
retinen debet _, et firet WMM F 2. 00. Cum L00 IL (aM -X) -2uoH
praur por- C nt . m - 2b n. m
Et fet qua oder +ddu (an  Zbi d  ( F0
quod siciat i in datis sit n + V  son . n + l. n =0 seu  l = mns. 2 foletur
sed placet eandem aequationem ultimam ad hac clia ratione quae
rere, ut calcula melius fidi possit. Ex eq. 3. fit o0V F  = KH -  1 M F, G
am CC Lumoonr , = V, B8Y -200 1V +3, 0v. 11n
quod productum multiplicetur
FmaY 3 od. 11 P v0IIn
L 2. 00.1 M adr Loom 00  vo oviim
+00. 1 M a f  + 3V = 
oor, arod oripi LL. 6or dB 1Y)
(rimaer unin) frunoou
aquando hos. nos valores, ipse
ipsins GKH, et ipsius dorn
fiet destruuntur utrobique termid
qui valos etiam obser
quod superest dividitus per I1, et aequatio ordigula
o= 00. p nrar - veii nr (Omten + au p (3V + 4C) L 4 Co ur
1n = 0o1 (EntV) +00 1(2 2) - 400 =0
ut prius jam. itaque huic calvulo
cum prioribus fidi potest. Et hic
novissimus etiam in progresso ipsa
servabit harmoniam, quia utrumque
aequandum  per se harmonicum es
ne compendio sit 2(n + V: M = 13
 2V+ M, 00 : n = 15 00V: n = 14
et fier  13 - 13. 112400. 1511- 44 00 =0
 fiat n1 =  41 + L13, et fae substituendo
400. 15. 13.3
AI+ =Z 13H- 2 13
400.15. 1+200l5. 5
 ad. 14
= 44. 002 bo. 41 + ∞4I + aaq -0
et sit 41 = 9t sa  ( aaqu + s(qu . p a )) ei (C aaga eleaa)
2 A∞0. 
A 99. 4 = (4. 13, -36. 0015. 15) +417 0d. 14. 13 +51 ct. B B 2.  91 14 13
 =(2, 1d t. B+ 001 5. +3. L. 15 od. 54 ae, 5 . J. cd Ab . 1 4
sit in Hyp. et Etlipsi glatus lusoe 2t useu a Bmapor ut 72 1B
distantia socom diut ad exem mujorem pt
=- di.  et dz - - d_ a XN = dx.  u i1.
 (4X- eed, X-qqu sit 4.
1z du GX , x.
a +-b
fiet d 7 abaxi saxi X- b, X  Tansum erus 
opus erit ut consieamus ssax, Xub, X. Erit
 uo
et n - m = A = t H = C = A , sen l. B = c- b - 
etCautem est major quam b in Eillipsi
dque ( a ta (4 x :, 2 x - 494)
eque g 4,4
Vel dz- (ax
sis2 G. 2a tirt cu = X  ((ax, X - a e, X - a)
sit ee: qu = b et fiet dz =  - dx da ( (ax, X - b, X - a)
G se rcR 4i e 0S. I(arI, V) + 2 od. 1 (4) + C)- 5 00K
et 
Zordinata au minotam stdes Elemento
t ra fi 
ut cor, (0dy 1) 2d t (e r t eoituc 2teL 2. ouse e (. qei  (3) l ar
uy en quire
et vrulure ipsorm Lux
25. 41
Evrs-am dei=  dZ ((4  eet V: 149 912. fial 27=
6C2. +8 = 2r + 7
eei noc um
quiH
d t
quaenon consentiunt prirbus iitaque taculi sunt repetendi
ii FG e
eri
d0et 11, V et  _
a1. A 4 2, 41 1 B. 3 - 13013.9 (20-
i
subus ∞dr = 2i00stI + 3. donitui V, obr ubsit, 3. ooule) cris e at hilsi a pit sit a gro unilulo, fieti
A0o
quod multiplicando per hfiet siver00 Lo0Y0. t B odr vor ip
oF6 40=
aa
Undetandem sit 11h =, 00. 1. C2en+V + 00. 1 (2Y+ ) - 00r = 0 a4) + aB = 20. 1213-  00 5. 157  0015. 14. 13405. 14
terminns summus coptineas 1B, et aequatio fiet plana. Sed hac ubi non est in datis
KH = fcrN or ( od s u  = 2 ∞V. OB. IIY)
upt Ciroo upi ciei
VIN = XFM trEYI
em 4B(3.4113.3) + 3. 41. 1329 4 133:279
4000  00V
 GIAN + 40dit  + LWVrC-40dr
effici non potest
(I = qL 2(NAV
rs a
+DOV, FA
 gra tam ob harmoniam, quam ob consensum F
Pt p gp - X = 2p Y + 
+ =  X +  = l- n - n + m
fit 0 = i (a +2C 400 1An+V+
FG 
n+G = 4M + X p. 8 = e 
L - 
 fa stabit:
et dividendo per 400nr, fit
 le 
oppar
Y= N = Y - nn -
qoor F t, - (1 1) 1 300rr = 2. 0d n  H st oB.   )
aex
e.
et dour
erit l- -B, n =-a m0
A= n = -a V = l = - b R =I- n =- a - b
facinmque a = 2b fiet A = = 2b, Y = - b n = b
(D) 1Cp (00. (VtC) 4B5. 1CWVHM) 4 00dY =0 ut supra Wt = - b  t  = b
ErtA; M = - 1 2N F; n = + 1 V: (1 = 
Ut supra. quae aequatis aulchre Harmonica est, nam et ex ciq. fient xtq a 1 - 1r fB - 11 + (, et fit 11 = ( vel 11.
permitu 11. et n permutari possunt cum 00 et V (sunt ergo tes radices huous aequatianis, 1, 1, - lranesu duae aequales
sit 112 1 fiet 31 = - 7 -2b:, = 2 = 1. et ZL geaeatiur ( si a = 2b fit 12
IY= A =C
nam . bo
test munehi H
salva aegeitione
val juctitiam inter
 infncil  ta i
b infinila 
tno =
d
de nit inetae