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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 102r, page id 00068197:0203
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AB, X Cb, y.
EF, Z CF, V
AG, g GE C
AH, in A n H E, h AHoA D : H ,I:: m: n: h
vel AHim A Ht
Quaeruntur valores ipsarum Z et v, ex ipsis X, y, v, g. , 2, 4
(1mO) B = CK = KF, (2d0) CK = yh: M (o) KF =
HK. n. h HH (4t0) HK A An - AK et 6to)
AX = L -XB et (6to) KB = yn. M. Ergu juventa suat quae
Quaeruntur, et fit AResimo) AK = x gnim et HK = m - X + gn:m et
(9no) KF = muh: xnch t ynnitm et () ex , per 2 et 9. fiet
Iomo) vC gh. m iin. h 4 Xn. h ynritum seu v =  th. Mr. timi) Gy A-mi 
seu (12mo)  v= my (m X) e sch Sed si
(3tio) K F = HK n: h et (ta HK = AH - AK (6t) AH = g + GH.
EX5per 6
EH (6to) GH = em: n sit AH= g. (7mo) AH = g + em:n (8VO) AK =
X = KB et (9no) KB = yn: M et ()  ex 8 per 9 fit (1omo) MX-
um
X -gn: m. Et ex 4 per 7 et 10 fit HK = g + em: n - X + yn: m. Et
(2) ex 3 per 11, fit (12 m0) KF = gn: h + em: h = Xn: h + ynn :tm, et
B3tio ex 1 per 2 et 12 fit V = yh: m = gn: h - em: h + Xnih - ynnitm
seu (7to) v = (X- 9) n: h + ystit - nn: hm) - em: h. sed f tm tan = tih
sed (15+0) ex hypothesi nm + nn = hh. Ergo ht m 16to fit
(16to) hh-nn: hm = mm: hM = m: h., Ergo ex 14 per 16 fiet
10
17 no) D = (X - gn + (y = e) m :h seu fit CF = GnGB + M) β: h
u CF. adhibitis punctis S,B,  (3 rectis GB, VB, et
qvia ergo determinabime
ratione trianguli H A 7. Ut oportet eodem modo determinari
C adhibitis rectis VB et ratione trianguli LAh, quod est simile
gno
ipsi HA ,I Ergo fiet  Z seu EF seu C= mGB + ng. h
posito G: GE: HE  m. n
similitr ergo invertendo figuram Hinc data relatione inter Z et
 substitutis valoribus, et explicando GB et VB habetur relatio inter X et y.
 non Ronamus jam porro immoto manente plano BBE ABB moperi
in eo curvam CC, q  angu 9 reco XFEF; poterunt successive
reterminari loca curvae et cuinclibet in ea puncti. Hinc si duus valores
ipsius Z, itemque ipsius B, investigemus, fiet m M:n vocemque Y, et  mot
h = rmmtn  h.  = hih m hh etum = mm t u: Est  nm = 1+ 1: 1
mm:th = mm:, nm + um = 1:, 1+ (1: rY)  et M: h = r: Ser+I
nn: hh = nn: mntin = 1:, er+ 1 et n: h = 1: srrti. Et fit
proinde Z= rGB+1)B: fitrr et v= . GB+ rVB,: Sit Ir.
itaque si curva Cc moveatur, et diverse ecudem in ea puncti situs
conferantur, fiet FGB + 1VB,: siter = (Y) (GB) + 1 B): Si + r)
et a 1GB+ rVB: sitrr = 1 (GB) + (Y) (B): Si+Y). Ergo
FGB+ 1VB, Sia r)
C Bs+ 1). sirn
est cnstans. et GB+ rV3, 1+ () est constans
GB + (V B3) FIt rr 7
Ergo t unum multiplicando per alterum inversum, fiet
1GBF YG6. + 173, 1(GB) + () (2.β,
constans seu fiet deniu
quatuor ret (Y) et,
(r+ V B: 50 8, 1+ B). GB)1)  subi to occurrunt: est B. 58, et
1t AA CB)
1 + 8Y3: 50Y (Y 1 P]: (60)
M
 et _1(). 13B)