# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068098:0009
# Permalink to this reading: https://leibnizlegible.com/page/00068098:0009?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 3
# Folio 5r, page id 00068098:0009
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068098&page=9
# Source image: https://digitale-sammlungen.gwlb.de/content/00068098/jpgs/default/00000009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 74 lines, status machine
# Lines: 74 recognised, mean confidence 0.78
# 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.

pars Aertiaa Methodo langentum inversae seu e punctionibus Augu si 1673
si sit figura a = X. pet: a = ax + YX, unde fies  ad P habendam assumta
a + Y
primum X absissa: - 2X = a + y P. et p = 2yX
ps
eta d
W
a + quod est memoratile, inde
et vino y = (a = a X, fiet 2X x - a X - p et quia d = L
2a aax
a sar- aex  a ax=
a +as a=aex
et erit Y= cq
44 at - ax +Ca3 - a X
2 gX. a7
vel u lata fractione per- X r. ea X X+ ca  X
 vel Y= a sa- ax +  = ax
2X sa
b, = X. Ergo a = fX.. unde si fiat. 2X = 4yx fiet 2l = X., vel l - = = p
cum Y -20
Unde res sequitur memorabilis in Hyperbolocide Cubica Reductas esse figuae romogeneas.
quod me credere facit, peculiarem aliquem hujus figurae usum esse.
3ylx
=X Ergo at - _yX, unde si fiat 3YX = y X et  P- X
jam 7 = s  et Y = 10 40 = e. = 250 , vel E-
parmloloeis ax = Y. Ego ap - 3y3 = 3aX, ego p - 3X.
u
Ce yx-a
inter quadralum termim poserioris, et rectansitum seriuinotum, duplicata, seu est differ, 2a 10 = - v2  L y - , 1 a x. ce  = 10 a X = e. Ego 1D a  - 2 Cx. et a X = 927C X fietr 69:
locus ax= a y. est momentum sinuum criculi, ex vertice.
2a xP - 2x P = 3y Ergo P - 2
=
3ax - 2X
2ax-3X
a = 7X.
3aX -2X
hoc di vidatuo y = 1B). aX = X C 2a - 3x - aX - X  8a - 36a X + 54 a X - 2 7 X
34 3X2
a = y, fet a =  sax, et a = y ax, et à = 1X
Tax
Aequatio cinaae quam Cartesius post (onicas simplicessemam putut, lib. 2. pas 37 hic asfetur
y - 2ay - ay + 2a = aXy. vel X = Z - 2y B- a + 2a. sed si hoc et,
tantum nascetur ex comparatione in unum quatuor aliarum linearum,) ordinatae recta nguli
ordinatae Trianguli ordinatae parabola, et ordinatae Eipsus Hyperbolae. Ita conchoeis ex rct
applecata ordinata circuli et H Hypebolae ad Asemiptoton, componitur.
Ait Cartesius lineas altiorum gradumu potius a Mechanica quam Geometria (oc repudiam
das, ob difficilem earum descriptionem. Id nimis verum esst. etsi iuimi excellens sit earum
contemplatio ob pulchutudinem admorandae rerum harmoniae, fatendum est tamen usum mechanicum
non respondere. Quare illud utile futurum est, efficere, utmodum quo investigare qua linea
quaelibet altion, ex ordinatis infeniorum composita intelligi possit. Sed quoniam descriptiones
ejusmodi non frerent nisi per puncta, cogitavi an non vocatam subsidium optica, descuptae va
seraratum inter se jungi possent, tantum min ita ob idque duabus dactis fante fieri potest
si algue spiatssit  pse asi iato cis otaatem s asperte otieas
uet y
2a - 37
4a + 9X 4 12a x
a+ XarX Ha
27X+ 36 ax
unde locus
2a - 3X
a a - ax + a + ax - 2x (+ 2a
ai
BIBLIOTHECA
RrOII
LiA BHODERMB
4Xy a X - 477
X. Ergo
a + Y22a
r
a ta
2yX- 2
ay
ase at
ak = yX