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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 21r, page id 00068197:0041
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10. 11. 10. 21)2 10. 2-
1.26-
14
qu (10 2) + (10 ab
21. 211
H B qu. (1B + 20) 1. 21 + qu (I1 +21) 1020 + qu 11+ 21) 00. 00 
seu 10non 2 + 1. 20 20 (+ 2. 10 11 20. 29) + (10. 10. 1, 21+ 20. 20. 11. 2. F 10, 20. 104 4 10. 20. 21. 25 = (10.10. 1 21 + 2. 10. 11. 20 21 f 11. 1. 1024 2. v1 201)
fit 10. 41 - 1. 20 = 1 11 + 21, 00 B: a)
erit
Extermino Z puodit idem hoc solodisutmine, quod pro 1, 21 tonitur 1, 22, ut fiet   g 2 t 1. 6. rar 2. 13 2. . 2 Z (1B A tront oproa, 00no d 10. 22 - 21. 20 = (12 + 22) 00 AB. a)  Ergo per 2 et 3 aequantur
10. 2 - 20
10.21 - 1120 ) 10. 21- A 20. seu fiet
11 + 21
12+22
 quod jam tum verum est quia per aeg. 1. est 21 = 22
10. 22 - 20
itaque ex aequ. 1 et 2, sequitur aequatio 3. adeoque sufficiunt aequationes 1. et 2
1 + 72
spes est successus, cum formidine tamen oppositi, quia hac ratione
non tantum ad quadraturam rationalem, sed et ad valorem quaesiti ratio-
ratem devenitur, quia non aliae occurrunt prationales quam vac et a san
quod si ergo res non succederet, haec alia via succurrit: (imo per eventum haec via minus succedit)
quaeritur ((X_, Xt. , X+.) sit X taB + YaG X = quadeato ab Yao + taq, fiet
quod identificetur
et X+b in X+C. assurget ad . X .  + (xX +..) 10G
quadrato a Cxk +C fxt. ) aO + (X + ) La D Z faO +2 Ya. sed ita assurgetur
sed si itaque faciems identificimus illud quadrato
ita _ _a(D OZ + ab debet aequari in a  + B 10G + ac
solum ad X.. + XX (0C
a 44 +9107
debet aequari A aF + quadrato ab a T +  108, fietq
aa (nM + 2a B OQ ∞ AA NM  + 2a Ta S0q sit _ constanti ratione ad D
8804 F a (C) YOq
a 
N~Oq
seu a - g Y6, fiet
H = 2e ta (b +C),: 2
a0+
et fit na p +B80Q + aabc + a n (b+C)  e B00Q + a (4 pp + 6r) + quib HC))
ubi  (∞ + 8) D et B = 2D et aequatio ultima,  explicando fiat divisibilis per 43+ a t tat
vel per BD ataq BD+89, qui ducta sBrag, fiet in Sd s J ABt, fiet
quoducta n  AB. L AP  co (et Y 1 BD + q AB + qepa o quam aequationem identifica
aequationi 1. fiet
as Us = OQ (1 na) et aa  t a C (trC) - = (4 p +4 B (brC) + qu brC)) = 4(1 Wr) 0gd +99pa
PWC0 D
+810D
 mothooubi si r= a, evanescet per sen gradus quartus  ubi si r= a evanescet (npad seu gradus
deleta
restituantur
quartus; su et faciendo eo constantem, et g(1 7r) 0∞ + 8Ya =o seu faciendo
= 4e  (9. 60) (a)  evanescit etiam gradus sends tertius,
et rest
a m (b+ C) (1 - 2) + qu (btC) = egco (9. c) (,  YY)  quae est secundi gradus expli anda et dicendiine
compendio pro O+  scubitur  h, et ex aequ. 1 agret.
plicis
X = ad + a Z + 2a fOQ x = quadrato a 1OD, + YBG seu X = CD + D8 + 2D 10Q
Pad (, G3B + 2 (bc) ED + qu sbr )a
a Et PD, DD  EhDD + 43DOG + aabc + a (brC) DE = 42 9BOG+ prr
uo ad secundum gradum, et fiet t- = Dt + (b+C)a +
ubi explicando O, D et  per X et dubstituendo valores assurget x non nisi ad secundum
enor
gradum, et fiet aequalio divellenda est in tres, vel suficiet Dperi X, et uhi sufficiet
am S d sumi pro x, et O et e explicari per D vel x ita adsunt bras literae quatuor
re sumamus peia meretur: aX = qu. a Y0D + YDG seuax = (O +4)D + 2910G, compendiofiat G= O+ D, fiet
ax = tD + 23sCQ, e jam ax tb inaxte, debet erit tD + 25 109 + ab, in, hD+ . Y10q + ac et prodibit
pro, etsiciendis tribus aq9.
aann + 2a na (OG
+HFD + 2hDD(OZ (~ quadrato a vel) ~009
+ 4∞G DD
taE) bic
aabc
+ a (btdD 1OG
(() qua
sit N = r Y D fiet
1 = 2 D + (b+C),: 2Y
ex aM +O under th WD + atD (brC) =tt DB +4BC (6+C) L) +  u (btC) rr BCq
_x ex AHH
in per e+ D, ita Enum O+) esset constans quodlicet
aabc,
et haberetur ejus valor quoniam hic sole sufficit ergo ut faciantus OZDt aabe  a qusbrc)  Yr DDOQ divisilier
vidamus an effici possit, ut haec aequatib sit divisiois  per 
per  3+D, sed hoc non foret mecesse, s. totum destiu posset, seu si fieret r ra, et dabc 2t at (qu br c),  unde fiet a bc = b+e
seu 16 16 bc = bb + cc + ibC seu bb + cc 14 bc =0 seu bb - 14bc r4qc = 4 cc - rec seu b - rc = 3
seu b= b: c= 7 4Y3, verim ita res rediret ad casum speciatem E Equidem non si faceremus unia
sed redcundoa quod non sustulissemus. sed si voluissemus _ facere D in at
constante ad +9, que 
per
od efficiemus
em divisibilem
hanc formulam mulliplicemper AM + ipCo, ubi quae libet litera graeca est formula quales planetae sunt, este uuct plicado fiet
in feissemus aequadem divisibilem per t seu pr D, faciendo
hh M +
2 X
Faciamus hanc aequation
DD, 4aa DD = AM. Ergo nn reduci est constanis rationis ad DB; ob tt
4arr (b+C) D - 4 a (brC) D = aa gIpCo +  47 (rr- aa) DD, et habemus QVC
tion  et fandem fiet ( qarr (b+C) 4D- 40(b+4)4) - 424 (rr. aa) D = 16VY, C∞ DD + drraabe
qu(btC
et
f. 21. 10. 207
seu Exerpino
20. 21 11. 20
20, 20. 11.213
= qu (u+ 21) 00. 008. a