# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0077
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0077?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 39r, page id 00068196:0077
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=77
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000077.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Eandem curvam referre ad diversos d Axes
Axes duo
et AZX
Sit Curva 8 8 Clecices duae AXX
ordinata una 8X nermalis ad Axem AX
Ex puncto curvae 8 ducantur duae narmales una d Ax AX B X ad axem
Apen
AX, serans alerm AZ in  in K; altera 8Z normalis ad
Axem AZ secans Axem AX in C. Quia rectrum Axium angulus
similibu
inter se est datus dabitur ratio laterum in triangulis AZ
C
A XC
hact cnt
8ZR, 8X C. sit AR M: R: p = AZ: ZC : C , AX: XH5 C
KA
 ZC = ZH: M C8 = yp: m fit +Z +ypB: M = b AXIX
et ita por
+ZC+ C8 = 28)
AC = Zp: m CX = yn: m fit +Zp + yn, : m = X = AC + CX = AX
X BK = Xn: M KB = vp: m fit XB + B,: m = y = GXKIKB = X8
(4
AR = xp: M KZ- vn: m fit +Xp - BR,: m = Z = + AK -K Z = AL
desideratur V sine Z ex solis y et X, unde 1 divisa per n et ex2 divrsa per p, fiet
_V = (2 + yP +X (2C - yM seu v = B ∞ _ y(pp- nn -) mm + X mn seu V - x v = my + uX
seuq
mp
mp 1
simuliter ex 4 divisa per n et 3 divisa per p fit Z = XP (-v (Y DnX +D = X(p. nA.) n.- 7
n m) nn P
m
mn m LP =mp. lm
Eodem modo inveniamus x et y ex Z et v. Et quidem invlim
t
PM
seu 7 = aX - ny
mnimus X ope aqu. 2 divisae per n, et opeaequ. qe divesae per p, et erit X = (D et ZP +B(Z)-
X = 2(p B - nn )um + mnv,: mp seu X =  mZ + tiv
en
seu
m, nn n pm 1
Similitem inveniamus y ope aeque. 3 divisae pern et Pope aequ. 4 divisae per p et ita fiet
ut (= X) + vP
n
m mia ce
L, seu
-Z(+ X) vn seu Y- vph - nn =) nm C - mnZ
Pm mp
B
2
nv - nZ
verum etiam est ob triangula rectanus AXD et A28 basis,  hypotenusae communis A 8
esse XXLyy = _ 93+ v.. sed hoc ex dictis per sase sequitua
potatu dignum  etia reciprocari X v, at Z  est enim Z ad X et y
eodem modo velatum  ut y ad V et Z. Cumque praeterca sit v ad X a et y, ut X ad V et Z
Hinc patet 7 et v esse ad relatas ad X et y, ut y et X ad v et Z. quae
est peresdegans et observatu institia leges
quidem inversio pereet an eptdignum quaesitu
Exemplum ad hibermus sit AX, Y et X8, y et y = XXt aX, i2a jam
X = Z+ rv: B et y AnB Z fint ere et y = mo. nZ: p- mm ZZ +nn DV +Emh ZVt amp Z
+arp, capp seu mmZZ + nn oV + 2m ZV tampZ + anpv = Lap mB - 2 apN Z
lese
Pp = nm +un