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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folio 74v, page id 00068073:0148
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si sit XY ZV. et at Zp a. 3+ vr7b. sit 3B   et X =
si sit: xye vq et n+yFa Z et  v Z aequ. b. fit a -Z. b- y p atyi beque et afX. b. B 7 a -0, b- X
Accedat: jam. =  r7 Z
soe a. Z (N. b y
Ergo XRV X et a- x
et aux
buq H T.v
arx. Ergo
b -xH v - X Y br -X
seu (abi) - brX X aequ (bar bX - bx (F X) unde quod morum eoanesat X
et fit br +a aequ 2b seu (ab2) - xbr _ - ax (+X) p (bar - b x - Xar (+ X
ubi quod norum evanescit X, et fit: br +a aequ b f ar. sive XBI velayb.
sa aequ. _, Bae aequ. B.  2S aequ. s. CZaequ. 9. Bequ. c.
Z2+ c2 r s + q. s
q0 equ B + e2.
3(β, XB78
(3) C (0) (4Z 6) a). Ergil  per 3 ets sit: cβa () sa + 
st 1
(2t5
Rursus (95 3+ aC. ergo met aqu. B9- s) item 9u cc + ( Eqat   E (B
per 3.5
et er 8. 10
(12) sc22 +5+9
eu
 Ergo βaequ.
per t. X
ut per 6 est β, se
17) 560 +6 et pro 65 ponendo valorem ex aequ. 10. fit:
Set + SeE + 45. sine β aqu. set + 45 quem valorem qungendo priori
cquse
ex aequ es. fit: cE +59 (6) F +95 adaoque eeq + crsz cs5 Sisa serqeasse rqy
Jans cE +E
g2 +52.
C9- 53
 seu C4u  C9)  C58Z SY 7 (C 9) L iy Z C se  - 9Y
es ubique dividendo per 45 fit. C2- s f7 q - 82 ut aequ. 1.
Niminum (2)S producatur dum ipsi BC productae occurunt in a. et ex punctis (2) demidantur
in βa. perpendiculares (2. 53. patet esse SB + CB aequ. C5 aequ. AH aequ
aequ. C(2 + (9S aequ AN + NHE patet etiam ob Triangula: R BD. (QA. C. 4B5
similia. fore: es B RB aideoque _ A  AN AB.
37 n 1 AD n5+ sa (8) Ba
d efa I ad H CDC A B  Ca H CB + pa H sae
poo
unde 25, sa 4 sa  (β, (3a + (a seu 85, 5A - CB ( aequ B
seu Cβ, Ba = esi sa  sa= (a pp s( f X B Ergo B F A B sa, XB+ 2YA
Ergo B per E et 3. fit AB  25. et CD
B e ergo A B AB25. et c15) Bd
eH RD
2 ergo CA p Bd C
et Cβ aequ. CA + dC ( RB Ergo CBH
aequ. Bd, CQ + RB, Q
ed ,2. + kB 25
et SBH SA   AN+ NH - CB HAH2- CB
X5 qu. y. AB Z. BCA v.
AX vocemus aqX.
fiet: + X YC  Xp B  F Z + sP.
Mitum
V+ CB.
Manifestam et jam est cum X et q item y et v aequales
nempe cum curva hochoides langit cicloidem, seu cum una circuli
per crcloidem revolutio absoluta est fieri SB aequ. 0.
et
et (B aequ. 0.  sed hiric nihil plane discimus fient enim omnia nihilo aequalia
A. H AN. NH. Alioqui necessario hinc habuissemus quadraturam
 Circuli.
ditaque vix putem unquam effici posse, ut ope
Quntilis en tansentium. Num reseodem redit si curva parabola des
vel alia quacunque adribeatur
upeerest an curvuis comminisi liceeet, ubi minima putrobiue coincidat
vel sit in eodem loco. Unaque sit analytica altera transcendens
ino si placet utraque tran scendens.