# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068133:0010
# Permalink to this reading: https://leibnizlegible.com/page/00068133:0010?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 9
# Folio 5v, page id 00068133:0010
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068133&page=10
# Source image: https://digitale-sammlungen.gwlb.de/content/00068133/jpgs/default/00000010.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 107 lines, status machine
# Lines: 107 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.

1296
44
1440
Alia Methode idem investigemus, et pro literis jam numeros assumemus ac
literarum ad instar tractemus, sit Ergo Ellipsis cujus axis major AV sit 9.
nA Radius ex Foco  ad punctum  Curvae G  OG sit a
et alter radius FG 4 s
sit velocitas re GL,  circulatio GD. descensu
angulum OGF bisecans et
descensus vel ascensus respectu umbilici LD. Ducatur
rectae axi occurrens in R. erit angulus LGH rectus, item angulus , 
gu
RFR aequalika ulo Ldiquia tae vel quod eodem recidit angulus CGt
via differentia horum duorum incomparabiliter parva est, ut constat porro
pagulus FGR, vel OGR aequalis est angulo LGD, quia DGA et LGd eidem RGD
complemento sunt ad rectos OGd, et RGL. Ex F et C in GA si opus productam
agantur normales FQ, DH. e itaque ob angulos LGD et FGR aequales. Similia sunt
triangula Gst D GZF, GH Similia antem sunt etiam triangula RQF et RHO
Calculum ita instituemus in numeris supposititiis, qui simul in certo casu
sint veri AV 9. OF, 3. ROG, 5 FG, 9 -5 = 4 KH eR quia
angulus O GF bisecatur a recta GR, erit OR: FR:: 5: 4 Et OR + FR: FR:: 9: 4
et jam) OR+ FR = BOF seu 3 et fiet 3: FR:: 9: 4. et FR = 3. +: g E
per compend 4s CB- 4: 3 et OR = 35. 9 per compend- E jam  v.
jam Gq vocemus : scibetu p compendi et po quo sirbatur
per compendium 2dC  es et (R. 5 359
uc
et QR scribatur 64: 3so et RH scribatur 513t et GH scubatur 815. 410
et DHscubS. so GZ scribatur 128  et q6 2CC
 12 12 o GQ scribatur 120 1 et qR, 6, 3 sio et RH5, 3 ho
scibatur R  GZ, 12: tro et BR 4. 3Ho et 4
scribatur G8 at2. Vi0, et ZR 4: 3 sio et AH 5. 3tro et GH, 15: sio
sonbatur et OR = 313. g. scribatur per compendium FA) . 3 et
OR 5.: 32 fet 5. 32 = 3. 5:9 et 41: 31 = 3. 4:9 (negligo
Scribatur pernempendium 9: 31 = 3 10 fiet FR = 4 310 et OR = 5: 3∞ et
et GZ, 123: t1o1 et gR 44. 34H0 et RH
ubi altima _nota O. significat 3i0 esse nullius dimensionis seu esse numerum, et
secanda penultima 1, signifirat est nota rejectilis, serviens solum ad designandum
quod nuncerus sit suppositius itaque in caso vero nostro, quem pro generali positi suppo
sititio assumsimus est 310 idem quod 3.
GQ Pub abur  1222. Hor2 et
R et GR scribatur 122D: fior et GR et ZR a31: 33t
CQ scribatur 1224. Lo et _R 43, 1222: fio et qR, 433: _3sio
et Scribatur per compendium. (dR, s si  SiI: 31O et FR +E1: 320
et fiet fiet Sir. 30  3 5:19 Scribatur per compendium
GQ 1211: 510B et LR 421: 110V et _RH 531: (330 11030
et GH, 1541: f1040 et OH 551: Y105O. Jam colculo inveniamus
ratibuem CH: GH
ees
et +R: AH .. 4G et 5 et GZ:  et GQ: GH (i: BFG: 6G):: 4: 5
4: 5 et B Fg: OH :: 4: 5 et F2+ QR= F R 5, 3. 4: 9
et GH2 + OHOG seu 5 Habemus aequationes sex, quarum ope
folleadae sunt literae quinque ut restet sola sH. ex aequ. 1. et 28
A+H aGH: 5 + QR + R H = GH
ex 4 et 5 fit 4BH: 5 +ZR - 34: 9
 ex aeq. 3 et 8 fit A OH. s + 4 RH: 52 = 3. 5. g C seu
ER =- 4. 9 OH +3. 45,. 5.9 A pro in numeris: 4. 25: 10 5 + 4 25: 10,9. 5 = 3. 5, 9
152 = 81. 25: 10= 9. 25: 19 p. 2(9
4 g 1 479 32,52 10 (ser qu. 110. 5 4 4r. 9. 10
ex aeq. 3 et 8 fit AOH: 5 + XRH: 5iL 3. 4: 9
A2
en
et proinde
ergol eait
9129 4. B 3. A5-   CdEL:
5: 3+10 quod mult. per 9es et quia ZR: RH:: 4:5 fiat: ER + AH = (1 + 4 seu) 9. 5 Y 3.3 - 9. OH: g
Abcuius t est 3. 5: S10, per gda
dat ( 3 : 110
erquex seu qR+ RH 35 - g. ON: 5 et Rurjus ex aeq. 7. est
sQR + RH seu  5 QH = GH 5-4. Ergo fiet 3.5- 9. OH = 5- 4 GH
jam per cius. 6a BH = 5 - GH2, et fiet: (63.5 - 9. 5 + g H gGH = 5- 4 GH
Et 56Y2: 212H.: 3: 1
seu 9 - s. 4 GH2 = s  5. dC jam quia 4 = 9- 5 fiet 5- 4 - 5-9+5 1
G GH- S1 72: 80-3=(15 - 9 adeoque fit g - (2) 5 - 9 GH2 = 5 9 -3. seu GH = 5 F9 -32. 19 (2) 59
en SSor, et ntes OH
e2
9
etas ).9 15 + 17). Sg B9 -1 s.  3.
s abes
s -(2)5.1
GX? 9Y:: 50- 3r: f9.(D5-9
Ge 541: 11040 = G 1211 1010 + 421. 3201020
+5,31: 330 k103C G12. 1o
 proGZ scribatur
et _ZR: RH
t
eQ scribatu2. sa
 et veq
cec
enim ultimus notius, ut veri valores in certo  casu sint 5: 3 et 4. 3). scribatur
25 - 9. 25: 10-75: 10
seu Cet 
ZR+ RH = 3: si0
9
9(F4: HoZ.  5: s10H. fiet et quia GQ + ZR + RH = GH et FQ. OH:: +5, et
16
16 1635: 9. 10.5
10
n
OV tes 
FE-eCA+ Ct
_9. 4 -9 = c
AViq OF,
5 sy2: 151 -1 - 516.9: 810
=C815.110
a
6+
1090