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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 143r, page id 00068198:0285
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Applicemus hoc ad problema aliquod, quile est minimam ducere adsectionem
sit punctum q in quo minima ducenda ad sectionem
oneam sit 24 2ax + axx = gy dat adx +  xax = ydy
quae occurrat axi in 
seu dy: dx = a + 4x, : y = HB: BCscuy et fiet
BT = a + =X jam AS sit s et SQ sit C et
erit SI = H B + AB - AS = a + = X + X = A5 et
=a _+ AS vocetur +, et fint su = atbx -+
et fiit atbx = =, : C = a + ZX,: y seu atbxy- fy = aC + ca X
seu ac +aCX + fy - atb xy = 0
Explicentur X et y per
valores supra inventas fiet, multiplicando totum per m, aequatio
fnac ppss + aC ps ap tac ps arco
o=q uipseps trepsrse p s(rqu aa) Co
a
raeppss + 2aapp S∞ + 2aa prs Ed
i 6 ap (rq aa) ).
mato rsar g0) hadens
cuse
+ pp 84 +9 rro C0 + 24 pr 9 Co 7) debit
= rr ss Cs 8. (q. au). C0eo - 275 (9 - aa) GC
quae aequationes duae spriore per n arbitrariam ut factum multiplicata) inter
et per n multiplica
+4 Ceppss-rau epps  raa eprs
se composita, debent dare aequationem ad circulum supra positam, tam
Et quidem tentabimus  an effici possit, ut circuli quaesiti centrum, sit ipsum punctum
9. ita enim non alio opus erit, quam ut ex comparatione compositae aequationis
Ad sunt aequationes sex Titerae vero arbitraria m, Y, 4, e, gk  quod si jam
e
circuli Centium _ sit datum  idque sit Q, erit 25 seu C = B(B) seu q
ob AS etiam datam erit = k + h fiet R+h = t + Ba. sed his duabus determi
nationbus factis, resstarent tantum quinque arbitrarae, quod suo sex est quitionibus
++a
efficiendis non sufficit, Ideo manendum est in terminis generatibus
comparabuntur eco
B
 pr , cocd inveniendae sunt ret q
restant h, K, e, 4 et notandum est alias
nullas arbitimias ingredi terminos illos altiores itar, hic esse difficultatem nam
et
Ope
tiam p- Sggtaa, et s- srr+ aa
modo Et si aequ resolutio nos non altius ducat quam ad sonicamsolidum
problema, poterimque hac ipsum efficere per sonicam datam. His copparationibus
adeoque
alsorum absolutis nulla erit pro infelioribus difficultas ubi hleas arbitraria sunt
tent aucentum
sufficientes. sed hic fuccurrit novum e intabile unxilium, nempe ad
scopum nostrum non desiderari ipsas  e co, sed sufficere eas fingi,
Adeoque sufficere quod possibiles sit illa inclinatio, tum ipsius ER ad AB, tum ipsiqus A ad E
quaeritur ergo Hinc si arte
eliqua effici posset, ut in tribus aequalionbus resolvendis evanescerent r et q
per quam aequatio reduci possit ad circulum
Non tamen  id loco hoc loco videbur
sperandum, etsi alias sortasse succedere possit. Et ita opus erit parie ret
et m
et m, hres esset confecta
 n = lam 4 pp q uo) tam ant plers. 2a pY + 2Y5 (rq. a0).
- nY = -m H + Y
  =na = - mA + v -n β = - m (n + B
erit  _ = aapB Frrss A = atb aprs  = a pp - rrss
B= aarr + (Yq aas. (= arb ar srqpaa) B B - a’ yr- (rquaas.
y = 2aapr + 2Y5 (qqu au) 77 - a be sap (rg aa) VE 2 pr - 2Y 5 (r qu aa)
lares
n  = AM - V: a
n = (M - D,: B
ergo A Bst M - B13 - X ( M aB
seu m = a - B: asp. β
et n= 426 (= 1  a7 - L2o  d 
un- 62 +2
Quibus valoribus m et n, insertis in aeq. F - nV = W fiet Adr - βV - (Y 2B+ H) pe = ( in - BX
sitesset 7 = 0 caderet ER in EB, et fret L = 0, _ = 0, Hto et aB  = B~ ) sed tunc non esset utrobiu eco
aut feret pro put quod utsudu
Conicam