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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 310r, page id 00068194:0619
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seu 4tZ an(+ee 4
KK+CLLrr = ac
rY+CC+KK = nn
differentia inter
rr et ce vocetur du
99 + kk vocetur ii
si inter AG, et HG media
proponalis in AH suma
tur G5, et jungatur
Cs, viceturque d fut
~ N = cC + oK
ad Circulum
Si velinus aequationem localem secundum duas convergentes
AY et XY vel secundum V et Z tunc tantum insaequatione proxine
praecedente pro X substituemas CetDV - ZZ,:2C, a unde pro
XF substitustur V +Z + C- 2V1ZZ + reevr- 20122: 4 ee. quod
acta faciendo, ex v 2atDv, ete. fiet
 ge V-egeeerr-Saegfee + 4 bl V - 8bb v0 ZZ
deeatvD
+ 4bb (V
eged
ogervvr-gacdt ov + 4bbZ
+0bb eerio
+8ge 22DP +8a C9fZZ + 4bb+ - 8 bb ee 22
+8aC2Z vV + bbee sp +gatger
-8b65
geeat
+ Aeeaat
8bbees2 Bateceu
+4bbC
easge.
 4bb-9ge = 4cc(494 89g- 8gH 4 4ee = 4CC - agg- ggk- AKK taKK t + eC
1d. FCit
=. 4cC = 4e0 + 4KK + 4 Ce = 4CC + AKK. = app. Unde prodit apMV
unde provenit 4pV 4 pp V respondens ipsi 4bbZ+, stu per decussationem
ob vvZZ fit ge - bb = g9 + gk -99 +CC = CC+gK, et fit (8 CC + 8gK) vV2
ducitur AY in HC, et HY in AC
0b72 ft af g. bee = (991C - rr) (99+gX) - ( (cc 199) (99 + KX + 2gK) und sit
unde  sit -8 (rrgG+ CCKKH (99 + CC FrY) GK) ZZ sen -G(Bg ulet r.d. ar B Sig 
Ob vr sit eeat f geee t geas - bee = (rt t.gH.) r+ (5- 99) + (99 F9L) (gHXK 
9+ (Ccg9)- rrgg H 9 30
(9g+ KK + 2gK) (YY + CC C99 + g9+ gk - gg -cC) +. (99 +94)
dd n
g9 +CC LYY) =
q9gGCC +KkTCKHCGtNignFXggCLC un  tadin d 
ob vZ fit   debet resolvi 4e, aaff - 2af eg + bbee ande fiet auff -1as eg + bb =
qu (9gtec-rr) ret ruggue  Errgg + (CC + 1) (99 + KK+ 29K) - 2 (9grec r1) l
rr+ 9g = 
akk = CX OX
4((29kce
-8 (rKK F Ccg9 + ggKK = gK (HK + CC + YY) vV seu - B(DD KK Hx tuggt ung H) v1
gorrt qu cdt 9
drbe (+ ) 4 99ccle
V
 2NICCC Errgg  + ucqus teckiKt. rccyH +ggg gghX (+ 299gB gea geurus rg uous
EA= 4eC (ggHK + CCCggHKK) + arrgK + qu (+ cc _ + nr)) et fiet tandem
aequatio +qu    e  vr Z L 2 ggl t ep - 2rrg 97
+ (bb2
AppB +2 0 a brZZ - 2 cc99 vV
IVKK
RngK.
cc KKL
mink)
=DCCKK) 99
=eetrr
X99C2a.
 +2 G rceii
dgrk
mimgte
gtr gK
5N = CC + 9tC
DV= rrga qu. AR.. cebii
paspini Yr + cc+g4
e=9 + K- AH EXX = rrikt nd nn = rr + cc + kK
i ggrtck
ubi pp = cC+ KK = qu. G(B)
in qua aegratione, v, q tractantur ut Z, K; at Y, C, ee s edem mode se habent
ii = Gg+KK
bb = CC +gg = qu. GR
Utrinque. Et ad ec si permutarentur V, 9, cum Z X respectiae maneret aequatio eadem.
Habemus ergo lo decicut aequationem localem ad Circulum
secundum binas convergentes ordinatus convergentes, pa quitu qualum quarum
cum non nisi quadrata dentur; erit Circulus locus ad aequationem secundi grad indeterminata
secundi gradus binarum indeterminatarum quae iclationem excrimentem, quae
cum eadem con quarum  una cum constante posit v altera cum constante
issit Z. Itaque 2 ad problema per convens binas convergente construendum
Conjungi possunt vel hini circuli, vel binae rectae ut in pagina prima, vel du
Sed cum problema
bin circuli ut hic; vel rocta cum circulo, ut ibi et hic
est solidum, et per rectas et Circulos construi nequit, identificatio aequationis
localis cum data no ut coefficientes inveniaatur, nos ad problema solidum
ve non succedet nos vel ad impossibile , vel ad constructionem problematis solidi
praeliminaris, ducet; adeoque constructio fiet vel impossibilis, vel inutilis.
potest ad huc augerio varictas coefficientium in constructione locali si vit Z, ve
si pxponatur  X angeatur vel minuatur per datam, ducta parallela ipsi AH; vel si Z au V aut augeatur vel minua
irculum tervenilt. Sed nunc ad sectianes condias pergatum
sim AG et HS sumtur
partes si G cadat intra X et D
anas potest esse excessus per
agius respectu a aerius
sit quadraitum suma
 rr+ cC-99, et gu 9G + CC. tr = a F) YYHCC- KH = ab H
s Eridatur CR
ralius angulo ad CG
RG volctur C
abet eoder
tit pr- Ce+ (R
recto, et puncta
erit U=er+C
irtertg=mm
ageaas