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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 309v, page id 00068194:0618
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(entro E radio e desccipti sit circumferentia
positione
Circularis YY. Data sit recta quae cunque 
in qua sint puncta data A, H, in qam ex C. aga
tur normalis CG, quae sit sg, et AG sit g, EA
Ex agaus in (G, noreetis Cr H Y sit Z et X) sit y
TAX sit x HXB AVS
gu ve XX. KYC HncCXC, 9-XE et
CW = C = y. jam qu CW + AX qu Y1 = e YY
jungatur CH, 1.C . 1G
et fiet, ce +gg - 2Cy + gg + XX = 29X = 1r Rursus
quia XX + gu = vv siit exutraque aequatione
idso posito cc + gg- rr = asat, fiet ex.
vol _F + vn - 29X = 2C (∞D - XX), et sublata surdre it huit chorda GY = AG. jungum ey que rvaetur q et R)
prioribus ambabus equationibus af + vD- 29x = 2cy
v + 4997XXasGP. agXVB. _ 4 ( sit 9 retb= quosic et Etpa i sle. E eeas qu uat. sungatur itHC quae vocetur na
ttiatage gq ier cs2
ao  Acl it delpains  au ad mgntu
 coltar
sutengsi est da  voceu
quod si pro vD substituatur recta qualtam potest
qavalite
 rectare recta quae a constantem, eam potest, habet
veluti c r quae nempe recta  constante sC, (si placet)
recta Cd, pro erponendo eed, habebiitar aequatio
localis secundi grabus pene genecalis; quae si conjurgatur
cum tali  ad alium circulum. vel cum aequatione
praecedente aequationem inter X et V exprimente ad rectam
hahebiter habebuntur B et X adeoque etiam cd et X
per intersectione duorum circulorum, vel circuli et rectae
cecdeique At h Et talis quidem aequatio
Interim notandum comparatiodem aequamini localis on data isterdum nos
localis conjungit paralleta ordinatam parallelari
convirgens aequationes solides it tanc jinatius est siltalis constinctio, etsi sit possissilis
sed si velimus aequationem localem ai
ductuam
ad circulum secundum duas convergentes AY ut HX
vil secundum  et Z m tantum In aequatione proxime
praecedente secundum v et X,  substituaus p ut ad Rectam
localem feceramus) pro X ejus valorem ee + v - 3Z, D: e
sit aeo v L dcellvo -Bge 89C   Egej (bb e b v  bb Z + Blil verp -8bl. vrZ Z - Beg9g - degqq VB+ 8Cg11 221  - 0
efer
in hac explinatioa Aequatione explicata, debent v et Z inter seervure
legem homogeneorum ee gge  4C, C- 2. sed quia in hua ae quatione vecorit AH se g Alisen, g
Core tet Be beC+ egAt) NI, m
et bb g9+  fiet geem ggg ggke + gg+CC = dAgF cC + AHK gr. Ggtge Ak Kg2C + 29Xci L gL GB
cum partus et absit HG, quam vocabimus K erit C= D+X
ggraem c bb = 29e = gytac - 2ge + ee, eB = KKU-ee
et 4bb-ge = AKKY qCC = aee ergo in aeg. sec. v . Z
libi est (4bb- 8ge + 4 eC) v v prodit +(XC +KX) ess vt - appo 
quemadmodum habetur 4bbZ, ita AC ducitur in HV et HC in AY.
decu per decussationem
WV ducitur in dCge eC + 8bb  C FDC994
H: gC + bb. = - rX= 19 + 91) - ge r pot cs = ∞ rrg9C ggu gk Hinc
rrep + 9eC -gRee 499q - gk e =  - g gocc L gyrrg H9d. P gticC L yKrr
Son ((YY+gG- CC) gK F (YY +KK- c1) 99 + ( YY. 9H) eC)
seu gro ((t C)q A (HKR - cc) gg + g -rrgg M (gK WrKK - gK + 2gK (rgt (99 ))
2 GGHKH9H
seu zon (g9-cct9 f(G(a +I) gCC = (CCt VTAKK)GK _ = rrKK + 2gggK)
ud si Bv(99 - CC + 2gK) 99 - CYYLGK)KK - rrgK
1 QVY olee = cc)gg -ggKK CK   rrtk  (YY+ KK) gK, + A
aei livee  es  = v2V (C3993 9itV- B00 st ( CGd ctir. Accgt. 4 99 a) 3b. ).
seu 62
re steotud quon
Ubi e est vel summ
ipsarum g et K,
posita X affinuta
sim AG et HS sumtur
partes si G cadat intra X et D
anas potest esse excessus per
agius respectu al aeriys
sit quadraitum suma
vocetur b, erit  ec = bb
super el normaliter erigatur radius RCjungatur GR
super ipsis A et GK _ describantur semircirculi RMC
etTB, et ili l accommodetur chonda CQ= ARC, et
 rr+ cC-99, et gu 9G + CC. tr = a F) YYHCC- KH = ab H
+qubxx- aqtgx tat 20
p Ut habita est aeq. v 2atwrnete =o
ita tial  rad A  E+ A ppBY Aast aug -0
2af -4uc
299-2
n nat
∞ KKGg KKgH ZGKGTgt
 agKbhgat
Kgg gRCC
snbo rgsenserg gik. Muxx
seu duns rataa
-rgk ccgK
eg = 99+gk