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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 4
# Folio 9v, page id 00068076:0018
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ei b raeterum calculum sine ileo compendro pinendi qu ch. nunc exqui i
vacat. Porro vileamus etiam an non utilite pus  extrahatur. radix exx iar +de. set nempe
sint Lv + de - r+ odY a + rh av  sit se h:  dv = de: 2dh = at: 2 sit db= 2d
et t 2dm dL: da fit dv= Ergo dv + de = deto: 4 ati - ete: 2 + dt: 4 + de =
= de: ah + de: 2 + dh: 4. Et Sdv = e = de: idh + ih: 2 = y 
seu de + dh = 2 dh y. sit I C = p: q h= m: n y = et v: co.
fier de Q  (:) man - nam eog + m B(pdq - qup  Con = 2 vqt  man-nam n. sed
Catis hinc apporet nihilo faciliorem hac ratione prodire calculum, quam praecedente.
Redeamus igiturad paginum praecedentem, ubi erat aequatio Lman-ndmt2) edg-gap nh = c n9Y
et faciamus primum nt cq fiet ( q) = Cn fiet ( Imdn. namc h + L) p.q 4ap h2= con isaque si
ed et n non assurgant ultra unum gradium aequalio assurgit ad ftum, debet aute s alterntiu
in vel p assurgere ad secundum; vel ambo, ob , ob co et n habemrus arbitrarias
ob m et B habemus sex vel 4. sed compendiosi calculi causa, sint saltem 4 ut sit p unius guadus
sit ergo Cd= ff +2F9X + gg XX et m= k 10 + ux +12X et p = 13+14X et n = 15+  lX
vel omiffendo 15, ut contrahatur calculus videamus au liceat facere n=  tantum, et habebimus:
Man-nam = 10l +
X +eC
uIx.
2. 12 17
Est autem hh = ae + 2abX + bb XX
2tla. -4. 10. 12. P abC x- 2. 10. 12 12b ex Y
Ergo (2)m dn -nam P R2-. p10P a c + 218 abix +18 PbCX
edunepo dam bingit
Pan -nap = 3l + 1 4lX - 12lX = 131
(0=
Ergo  pdu -naphi . - - . . -- -  13Pa + 2. 13. P’abX + 131 b X
+. Pa C .. +2. 12 Pabex tul 637
C14
2 t et f9X- e + 2X
Et con.. . . . . sed video em quae aequalio debet esse identica. Sed res non succedit
+1lX +2IX
seu m du + nam = (N 10L + 2k. 13 (X 4+ 1EL X cujus quadr = =_ZEI  + 4. (. 10) 12KIX + 2. 5.102 u L2
compendis autam cansa fiamus h.  h = X pdn- nap - a2 1(4 14 1∞k F19  + 4 1eK X t4)LKIX3 + 12I2XY
n = K+ + 4KIX +6K VX+ 4K V X + 
CCo N = +s K+ 4 a fKIX +6fK (2X + 4PKBX + fVX 
2f9k. 18fgKI. +12f9KI. + 8543. + 2f914 25 . . . .
+ggK+. +4gXL. + 6g4Y. + 49413. + gI2X
aequ
aG
1man. nam
1du n sli =.
Himeo de successu. ideo absolvere nant calculum opera pretium non est
qui calcutus non difficulter absolvetur; sed cum videam naturam plecaque quae lento compendra respuere