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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 279r, page id 00068194:0557
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=557
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Quadratrix.
AB sit X A sit  diameter et N semmar
et  sit AFH semicircum ferentia; AB sit
AG sit AEB sit _Z AG sit 
omnium
a Arcus AF   habebitur si habeatur summat da
se omnium LF. sit triangulum characteristicum LWF
erit LWF sim. FGE. seu LF; LW: WF:: FE: FG: GE.
seu
LF = B. 1H:, FG. seu da = Zh ax: stx - xx. et a = Lt ax: hX . Ax
e debet esse Z: h: a: H seu Z: h:  c h sax: SAx -XX : H
BC sit v. patet fore EB: EG:: BC: GF. seu Lh - Z: Lh- X . v: sLX - XX
seu ih-s ax: stx. Xx: Lh - X :: v. dhx p seu faciendo ThX - XX = y
et X fint Lh - L sax: y: Lh -x.: v: y. E v - C 269 i histx:u : 2h-x
(10
  - = h . X v: y = L sit sa X. y
Ergo Ax v. y - a F h x F ydo f vius 2G: til ax: y
Et in casu maxiaues calitudinis ponento de =0
(12)
fiet dx vy + Th. X v dy =  hhy dx
cesye ce
ex aey. 11
Eo casu quo X = =it fit v - 4 sit ex 4G. 
de =avy f
endum Eodem cusu etiam est X = Z ergo et Z-h. Et eo casu
quo Z = : h = x ex aG. 7 sit  = h fdx tunc a senth sax. 1taura siA =
= EH quod et jamcum verum esse constat.
da: dx:: = h: y
C27
seu ZN = ha
(a
Z. h: a: Y. L. h - Z: Lh - x :. v: y
(3)  v
ih - Z) = Lh - X
-dZy + dyck- Z = = dx v + dv = k - X
dZ H = h da
jam quia gy = lx - xx. fit y, 2y dy = hdx - 2X dx seu dius = dx h - 2X
Ergo in 8g. E substituendo dy. fit - dq + dx + h - X. Lh- Z = - dx V + dv =  -X
Rursus ex aq. 4 et 1. possumus invinire valorem ipsius dx. nam fiet
dx = day: h ex 1 et ex 4 fit dx = dZHy. Ergo ex 8 et 10
Leth
fit:. fd Z (t dZVF. LM - x. ih - Z = - a Z , yV +. d v hh L h - X
seu du: du = _ _ Z hh y + H. L x. L- y  + TYyV,: hh. L h - X - - t: Y
an Lin= v.   + H. d h. 2. . ita + agu.  h. i