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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 258r, page id 00068196:0511
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15 Marti 1693
Bex Gy
Reductio differentraleum aliarum
ad Aparametros
102at ro vdvr u ru B.
Sit do. dque = vZ + av, : 2525 nv. sit Z =  3C+ 3HK + MIIXy, + 32OK + 3uKy +  3302 etc
(1)
et v = 400 + 410Y etc
500+ 510R etc
fit dy- 
500 + 610x +SI Xy + 520x Y521 X y + 530X3 eM
seu copendiose  et   y  3: G et Sd:5 unde
dv  5d4 - 4d5: 5 et d 2 =2 5d 3 - 3d 5L, : 52. et dv. d Z  5. d4 - 445, , Sd h. 34
 103. Sd3] 1. 4. 5d3 = 10. 3. 3d5 - 1. 4. 3d5 et set
Et ex aqu. 1. fiet.
2 10. 3. 5d3 ∞ 10. 3. 3d5 + 204 54-20. 4. 4 d5 + 21. 3. 5d4 = 11. 3. 4d5 f 11. 4. fd3( 21. 43d5) 
si jam pouamu 5 ascendere ad Xy, sed 3 et 4 tantum ad X et s in cognitae in aeg. g. non ascendtent uttra
gredum tertium sunt autem termini in gradu 3tio 10, ladeoque  aitrariae 9. Indata
geperalis Edi gradus mulliplicata per simpligent, hac clages hobet. Unot poterit stano
vero Aquatione habemus autem arbit rapias hoc casu, moluum nobem. Unot potetit e quatio
feccrimus, res succedet.
in vata ipsa prius aliquid arbitrarus
sit 3 300 + 310 Z de = 31odx 4 = 400 + 410x a ode
5 = 500 + 51O R, + sIIXy +sior d5 (2) 510 dx + SUIXdy = 520R Xdx
dy
t 3. 3 = 300 + 2. 300. 3104 +2 310 ry + 310 X
10. 33. d5
20. 4. 945 =
11) 3. 4 453
10. 300. 51gTdx 12. 300. 310 v2. 200. 310 (Xdu v2idoct
20. 400 2dy 10. 2. 400. 410151c5
i soeteo.
ich 310. 0
x aot ogex iio
300. 30013 holu 300. 300ES
400. 400
300. 400
10.3. 3d5) 10400300 stoHX 10300300 2.520IXdy 103 00 300 5IIIXB
bly 30. 400. 400
4001400f51.
300,400)
Lply 20. 40. 4uo. 21ax
11h300. 400.
Gio rvotue
Consutum)
o pouqieo  e
1173  quo
2.19. 310310, 510)
ad. 410
2. 5 v. 0)
d
Hos jam valores substiturmus in aeg. 9
315= 300 500 v. S1 . 511N) isc
44 = 400 etc 4 rex.
3. 7.  = 300. 400 + 300. 41058 +2.310. 410 xy + 310. 4105.
310 400
0,410
10.410
socis
19 2.80 g0d n
115 10 quo
X dx nlorergo 511 Ad
1 dy 220 40 10
310 100 i. 1310 :. 5i0
(16
30. 4. 715,- (2040400
.(2. 44)
21.3,0. 40C
(2i3 910. tu
45 300. 400.
6 . 700.
(, 10+03. 910
410
Cit oro).
21. 310. 400
16. 310310 510)
20, 410.410
1oqe
ina oro
 idot
 yt
Sid
nsim
SiXb
A ix
Do dei piu
13910. 406
1035t5) 10 310. 30 500 . o 3u0 510; (10 210200 510) (10 210 200 511
1. 335
l14. 5 13)
o o
( 20
r0 310, 310500
io. qu 33
i
10310710,500
213o S
288310 3
d. ). fd. 2310)
o 3
M 11 300. 460
fl. 300. 40
20. 400. Y. 2I dy M
2Hr.
 110. 300 3lo 510
4. n20400 40.
1I. o
21 0 310
10. 21030Ro
hleisio fogequ
(2 410 30 (16
Unde tandem foet aequatio 1b reducta abi sublitus tollendis sabit
9= + 10. 3uo. 3 or Sigt +. 103oa B: 5 1 (Xdx + 10. 300. 300. 5 Ufray 2. 10. 3003. 625 Y 1X
iutr A
tI130. qe
otio
3oqao. H. 3u cu.
 10. 300310 5=
10. 4c0 410.
0400
21. 500. 400.
410.20 36. 510
n. 3
g 21. 310.4u0.
0. 31o. 310. Sa0.  = 10. 310310. 50B
20. 41040.
P gionlo.
20. 4040
BIc.gIOq
2. 31csI
a 200.
10.300410. 5I1
H20. 400 410.
I1. 300. 410
21.310.400
E1 4  300, 21. 3t0 410-
Et compendiosa expressione:
3.62631.
2.10.400. 310. 540(F 1x 12. 10300 1Bs1 (t 1y 3. jig t. 41) 2
3. 20. 400910
3. I. 310 10
v. 440
4. 11. 300410
4. 21. 816. 100
canon
= 1619651 520
1. 10o
21910. 0.
ritus
x
ylys - p. 52d74
D= rm. S1ox +m. 2Scpdx un suxan +4. 2. 520 (Ardx + g. 2 510 X lx +9. 5I1 u
. ubsi ali  artitur io 10   21, 300, 310, q0o alo lias inaequ on   aquinglitetas
-Y. 52
ay +n. 510 hycy +h. 318) Y H. 511 dy Yy
quodsi ponamus p esse o, et mottieu depressa lri formula ad gradus teltium. Et hanc multiplicando
per X+ W restituetur aequatio quarti gradus tot quot prior arbitrariarum.
cum hoc canone conmparetur aequad () in pagima 3ta plagulae 14 Martii 1693 quae aequado est
pro linea sochitem exx calculo Hosurtatiano, et ob ob P, , p, p in ullimis termnis fit n2 + 273 + 56 = 61 427313
est imaginaria, et 72. 22+61 737 2. B.13(rbi
et fit 72.72 4+ 2. 612 = 0. seu 72 = 2- 62.621 aq oportet multiplacare camonem 
inferioris quadus multa
Maximi 4 termini orinatur ex solis proxime
x Cxdy et hoc in camus in 19
lu
rax
sit quambilis dicto aequationi. faciendo,
prodit VXy ex + beXyous e pax + V X A. qtou um nos suau conferendo cun temum sumur ayinors C pagnae
X dy C p 19
piu
it Vax
3drto plagula e martus sit 3. 72. 7343. 6 2. 23.73664
= + 27343. 6, u 92. B3( 6,4) seu 72,72 +4. 73. 73 = 4.72. 73
quod est possibile sem sed fit 72 - 3. 73 = 0 sed hoc rursus 9 intentum
unde calculum peragere, opus non est
400e
9tsro. 504052
Ho (209
Hoyo
520
320 o o X Yx 1C ) lBiB Xpau ut 31D oKL By, d
Jono Hory
3. 21. 3 3. H1   y H. y0 
pon lo 19q
213 eno 2 u ato 2i to 
oito su
o
1. 510d10
W, 4. 514
( e. 316. S10)
1.4.
o