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# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 2
# Folio 66v, page id 00068126:0132
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 67r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068126&page=132
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 82 lines, status machine
# Lines: 82 recognised, mean confidence 0.79
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

sias 3M agatur normulis 3MY inax, ilentque tangens 3A  3M3 et
vocetur AxeX et C. AY Y
eX- qua  Si vyc X Lx
ec Y (M
et 2a = M
y et M Md, +
ax axxyissem
qui a MX= LXX = yy
et Lgn
r-:queiga AA dx Am Xdx = Zydy. seu dx: ily:: dX: X. Y: ysa
x - 2 4= syu qu Ergo YR
yiia a
n MX iFee seu = a - 2 x jam trangula
crga ax=ha. a  fBM Y A, et 9A q F sunt similia, et datur ruto 3MY a YR
Erro YAL q
erus e, et eademomin
interdum, veru per radion
ati (per X et y, nunc efficiendum est ut detur per Y.seu
radium F seu Y, et ei conjagata 33M, et ei conjinaata
F3M seu g- r. seu ejus loco
eCrseu
et F3M = 4- p
 v.dea P
de
P g r - qr seu 2r -9 Est autam AF = q. e: 2. (_ p- F N
Ergo FY = X - 4 - C. 2 Ergo X jF Ergo XX - q ex + 9 C: 4 +yy
2r -p = Er-2749
49- pp = 41 99-144
similiter quia AC = g+C: 2. fier et OY = _ 4+e: 2 - X.
+arg - 49 = 2sig. rpfret XX - 4+CX + g+c: 4
r. Ope harum duarum
aequationum tollatur X et y. et quidem quadrata a se in
XX = 9+e X + gFC: 4 A yy = XX) + q. ex - q e: 4 ( yy) -(Vr-1+ Ep ppfinet 2a  = q+e quod
vicem subtrahendo fiet:
Seu = 2Cx + 4gC = qp. se  X+ P = M seu X: C- p :: 9.
ut ep: e sit E = C - p. fint AY ad OE ut A (2 ad duplicatam OF. quod
vel X. G. 2 ut
est theorema per elegans. quia igitur X = q pc q. 2e q e-p
et aq:re ep - aq2 4 eC c= 2Cp + pP = yy. seu fifit
ag: 2) - aqp: 2C(- a9.4 + a9p: 207 agpp: 4eC = yy
quia aq = bb. fiet bbl4 bb 14 1- pp: ce = yy. seu
aq. 4 _
e ess
y: b.2 :  ec - pp: C seu y =   ec- pp b: 2C cujus calculi
comprobationem habemus, nam in casu quo 3M incidit in E
FR = eg- eV: 29
Aeqeg.Ce
seu quo y = b: 2 fit sec- pp = et seu p = 0  siu differen
R et 9 et 3M A et CB et F0
cia radiorum ex loco eductorum evanescit
jam quaeramus 3esse R
+9-agx sobrigrationem laterum triangali
AFR ee:
que quanqe
quispe similis ipsi 4m2d4M
Characteristico Et quia FY= XG ∞12 et YB = =a - = X. ideo fer.
FR : C ate- q.2 19 8 X. seu a9+ Cg. 99. 29+ 4- aX
jam aqu4qe fiet
o 1qu qu 
jam x = L9. ergo ubi ut inveniamus rectam FQ cogitemus esse 3MY in FR = FQ in ZM R
dige rax
6B= eetqqeaque ergo queramque 3M. R h sest  a2 + aa: gX-  aa. qu XX + E-
seue
cuta quod verum
Hinc et FR = C9- CC: 
tee: 4 X. et in iau
quo FR = C.2. fiet
es eqq eeq + ex
V,  ax-  a:  XX + = aa - aa : gX + a a : 9q XX,
 rursus B. a: q XX + aa : qq XX = a0qXX. 1- a: q et 1 - 4: 9 = vC: c
et fiet ruisus - a: q2 F 44 : 9q XX = aCC: Y XX. Ergo  fiet
 Ec. qu. yy seu 3MR = aa F bb: ggeC- pp =
Rursus 3M ui ACXy Y Cq. y. 29924- ee TRCCX al divis per b. 29 YHG p dat FQ = ,C. 49- e9+ =Cx: bqu. 
proba: nin FQ = ∞: 2 seu FC fit p ~ 0 et X = q. 2 st y = b: 2, et fiis subse tatis sit C: 2 = 1. 2 9y - C+ +e9. 64 59q grodieru
verte 
quas (aq  su 3M_ = C. 9y Saa: 4 + CC:99 1X Ex
nonegteX  eiq. seu 3M. R: Saa: 4 + e
jam a - nasq X et a a. g = A. 7  a: g. q a = a eCX : 49
ergo X q.2, a verum 2M R =
rursu FR ~C: f9Gin
in aqq
G. 4. q p.