# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0506
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0506?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 255v, page id 00068196:0506
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 254r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=506
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000506.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 105 lines, status machine
# Lines: 105 recognised, mean confidence 0.81
# 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.

R semi latus rectum a; semi transversum bA. semiaxis transoerite
erit sab distantia foecrum FB = 2F, et FK = CK = f fiet
et f= Cb Y+ bb _Sab in Hyp. ubi in Hyp. et + est +, in Ellipsi + est -
jam  et sit jam AF= g, fiet AF = f -. b in Hyp. et b-f in Ellipsi
seu AF = +f 4 b 9 generaliter. Ergo g = + b ++ bb + ab. Ergo fret
g= 99 + 29b + bb = 4 bb fab, sed ita non tolluntur quae debent, potius
hoc loco 9.
pulo fore g= b + Sbb + ab ubi in Ellipsi est negativa
gy = 2aX + (a : b) xx ponamus esse  y = a  quaeritur X, fiet q
Ax sive,
aa = 2ax + (a: b) ex seu ba = 2b9 +gg. seu 9+ b = sba +bb. sen  = b + Vbtba
s
sit  RF= Z seu Z = _ b +X frit Z  id est hoc loco fe 
hoc loco Z _ sit f, et fiet 9+ b seu f = bb + ba  seu KF
quia igitur habemus AF, quaeramus et AC jam = -b - sbb +ba
itaque h = b +60b + ba seu AC retrorsum ab A. sumunns
retorsum sumumus nid est non versus B, sed versus K sumamus
AK sive b, et KD s BRF, seu KO, itaque si
AO vocetur Wh, fiet, = b + Sbb +ba. Quaeramus jam
relationem inter h et  tollento
Fempe 9 + b = 1bb +ba. Ergo
fg + 2gb (+ bb) = (bb) + ba. Ergo b =  g9: a - 29. quod rursg
quod designat tunc; cum 29 major quam a, esse b retrorsum sumendum
ut semper in Hyperbolat hinc quia f= 6b +ba substituendo pro b valorem
fier gt + ggaa = 292a: aa - 4ga + 4gg = ff, Ergo extrahendo
jam ba. Ergo
fit g,  a-g 4;, a - 29 = ff
fit h = es d gg (99) + ga (99,: a- 29
Ergo sit h- ge jam B = b licet enum scribi possit +f
quia tamen jam distinximus signa in Abb+ba, ut fgni ideo interpretama
f per + Sbb +ba) Talva deinde signi adjectione, in h = - b - f.
(89 + ag(=99, : -a +2g = h seu 2gh = ag + ah
Itaque generaliter verum manet h, esse a a esse medium
ergo fiet
a semilatus rectum esse  est med in Ellipsi e Hyperbola est
se medium harmonicum inter distantias focorum, a vertice
Adeoque in circulo osculante, succedaneo Ellipseos et Hyperbolae
seu speculo  circidista radius circuli est medium Harmonitum inter distant, as focorum
a vertice, et ulteruter focus pro arbitrio sumi potest.
D
Superest jam ut peruliari er eadem
ad dioptrica tansferamus nec
At tantum conside-
2O aud concurrentes
62 remus radios parallelos sed et
sed et a super ficie circulari  vel plana post parallelismum
64
 refractos, ut appareat, quae deinde
cujus osculantem adhibere oportebit. 4 pitus ca
a 8689 5N 936 consiteravit, quantum in
dit 90 6p oppβ668600 573205 b
en
 9200 plicae et
= molem igitur
spectando fit
b= 9di 4a
AX
s
146 899Y
de
e
1.00000000
0. 86 65254c
53971V0
26794920
v. Ao +8
10000(4
34c
40
4
 es
toc
36000f
34
5000
A80∞ pOO
840.C15040 1504o
360000) 2600d600
84. 30
90000
 1040 =- Virto
00d.
5440 = 1260 4
500
3 etiam ad
eos reolligat curva
4Nin
c
3. 4 4100
fort
B1Y
2
0
XX - 2ax taa = aa = L aa
=
recillis non
Hesperbo 20000
licaefi-
nis
differant
lcrculas
1. 7 3.E
267949
25100
0