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# Piece: https://leibnizlegible.com/api/records/37799/text
# Catalogue record: 37799 — De calculo logarithmorum hyperbolicorum
# Incipit: [Fig.] CA ⊓ I rectang. CX
# Date: 1676-08
# Akademie-Ausgabe: AA VII,6 N. 048
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=37799&katnr=Cc2+1430
# AA VII,6: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-vii-6
# In the Akademie-Ausgabe: AA VII,6, p. 506 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdVII6.pdf#page=506
# Work: https://leibnizlegible.com/work/00067993
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folios: Bl. 121–122 (from the shelfmark LH 35, 2, 1 Bl. 121-122): 4 pages, canvases 241–244, page ids 00067993:0241 to 00067993:0244
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=241
# Lines: 353 recognised on 2 of 4 pages, mean confidence 0.75
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 121r — 00067993:0241
# Scan: The same scan is also registered as fol. 122v; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000241.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 160 lines, status machine
Quoniam ergo demonstrationes nostras experientia confirmatus habemus, nec amplius erroress calculi metuerecoginu, jar
operae pretum erit Cogarithmam binarii Hypertolicum invenire. CA p AV, 1. ut ante AD, 1. cirt CD2. quaeat loganthmus binaru, seu spatum
AADEV, sive YD. quod ut facilius invenionus iti procedere intile erit C iAgit  ent spation WH. lognalhumus ab si quem invenimus esse 11437 vel 2 874 ita ut eror
non sit o. sit CH  C7  sit C. H CrH Csq
erso l qua C7H p 19
Cau
CsH
CcH cyt
140000 240
71 et CD est  vel 20000odo erit DqH (e CD- Cr1)  512829
odima potentir ab il
pal: 194871
d. et eius quid. dpu 162993503 141 (100 0a  b. B7 Cr H
10000000H
et eus culus d eit  134830736299898789. Quibus potistanibus a d. opus habebinus ut nex patelit 1000800 900 0o0io
lotuus ed.   eit.   et quia CA, CiH. CrH. CqH Es usq ad Coy H sunt continue proportionalis, erunt spatia V. H, 18 2 H,
12R3H H usque ad op 7 H aqualio, erxo spatium Vy H, eit seplustum spati. Uiti, seu erit 160118 Ergo ad imenendum spatium VD logarithrm Binam oupertoliam
  HD, vocetio d eui DEp ex summa omnita ordintur
100
sufficis imenidi superest inveniri tantur spatium residuum 3 R D. vel 7HE.). id vero ita fier: C9H voretur 3
inter ex hR7H, ex Ed. tr nmas pati 1. k d erit   + 3 pa dc it quonim a eAt cinater  et 5 citula 19. sie 2. tit d cinli  et n  se 
ca sei seu  error ent longe miner quam ooo, si trubus prinis terminis, utemur. est autem id - +
3  5F2d = 35d + 203. et pro f ponendo 2- d (nom CiHse CD - 2HD)
fet F n 4 - ad + d. et P⊓   EY P= Nndr 63 - d3 er d5 +d= 4d + 3 0 in 6 d52 14d. 14d24505 Fa 0sd p ad - 33. l3 5o  61- 5d3 8 ex
portis (Fd- 35d + 2d3
(53 1
1od 0000o 
 +343 pasen 244 - 304 + 1143 0d 0+ 24 d p 1230789600000000000000 4 48 4
14d = 24d+ 643
erit v
+2
22
+48 - 72 d 4 36 d = 643
199677689966760094004
1 28- 72d + 35 d- 643 + 11d35 _ 14835780992 18386679 436l A .. 369236889000000 4100 0000
30 d 78898074972300000000
5 Ergo 1152375 16312 8998d 617B ent area spati, 7 RD ita it Ercq sit min quas o  115337510312699γ896679 6dE 80gIr4+17299390
n
4440 149786554 8960607266 logmichuro habuimus n. sed  sed quoniu error uniter 
isque teptuplicatus est, adea
 factuq o  ello
d aele erit logarilhmum inivenre paulo exactus. praetog. Log. I est tqu 400o  5000vo 600vieo quatuc uiorus ter mdui redere 192.asta in 
11437
571850)
129
571861
4003047
6
fici. 120000 861
Eodem modo 11533751
100
444014996
10c3 
est
237164266,73160421183067. loy. 10a
69314718055994529 1417191750 log. 2
230258509299. +0456240) 78700 Log. 10
10936(2288604 0g. 33 oaa e a
00000
vrvuvue
5718617 953 1 0666
o
10= 200 3000 40000 B s A 
1900000
11429
qua
el
v
95310(6466 lpg. . 2) 517 95310166
100000090d0ven
1000,000000
335
A1200d - 600-
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i
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log. bineri
1600
4
15 nt in 1e en 4f
2
a  edrima mdin rod 2. FC F c_ 1 1 1633164
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60v 0,006 11
6B0 A
1661211662606560000000023G
A4X ∞x Ay6SA
A24014796Y
pam 2681 5538
90
d
 i de
d
c1 A
240000 24400
10, 240 00 100
4u. 000 - 70000
400000
AA X 
4, 24000 1F00
d
+24630
Ssb∞B
13i: 3603
At seo:
22874 1143
244000 1120000
25976039
785 667 171162
7
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11437
571850
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871

## Folio 121v — 00067993:0242
# Scan: The same scan is also registered as fol. 122r; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000242.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 193 lines, status machine
t   AY.
CAB 2. F rectanu. CXY aequ quad. es. suie L
it CXe i. eut ARr L.  et CXF 14 4s et 27) Xp   p  in  10 1o0o  ruvooon
50000 Cx  BeB. A 24 19296. 17  24 13,4 V. 124. 3
qu
quare spatium VX p 3. 4, 000  = 13,400 + grs. 0 = 1, 2, 3  24000 = 1200 + 90 - 6 1  - 1 06
240000
40000 1000o
es auten l B +o ergo l’e oo et 7 43 17 1000 i 1 0bo
ergo si addamus l. -+ habebinus tam prope ut errorsit mina quam
N 114327 C0. er 1437
120000
s et redicendo aed unum denominalorem ((446) 8 864 d c0 - 360202 + cst
1496016430953
005281645045
70897585400
exerbec2e4
42563027590453
ergo M L. L+
31728 (3
u s
10269203303494983 fr 103680000,0000
nen I quaeramus a logurithmum itupertolicum numeri
120000000oiu A
942563(027590453
1114048 00 00, 00001000 0
ergo spatum VX eut
2400000000
10368100019, 0000, 0000 A1
1 942563027590453
94 275630 27590453
differentia:
portuo quae Logunthumoctum tabularium esse deber. Sit ergo CX
101 H 1+ i
121000
.2BF 4 )1937
Ises  jau ex dato s Z, l. eut ANEin. B =  +  C est  , to
437
56800,00000C
ia so
20000
24000
excestus parto maxt quam
por non est.
520240
 ut duos
6 23880794
10058
0365
1028
114048
11940397
 190000,0000 (4200090000
Loga
114370000 boligs  
Jam Logentumus Tabutaris ab L est difcrentia inter logertBomum ab 11. qui est 10413927 et lognictuntum  ntim. By b. ab 10c  ad 194039
0do
 erit
203000o 4000o puo etc seu
At supraloganthumus Hyperbolicus ab  erat 11422, vel 114370000 er lognitimus Hy prbalicus ab i
Et loganchnus Tabularis ab ist est disserenta inter logaribimam ablioi, qui est: 2004q e et tognitmam abioo qui estre dooee quae differentia est over  2tt B log. Tab. ab. 10.-
Ergo LRatu Log rab. ab i
ad Leg. Tab. ab 10r H
  4 13927
100000
0 so 43214 que ratio debet esse ae qualis Rationi Logaithmorum Hy plibolicorum supra inventae. 114370000
Ergo multiplicando percrucem dibet cinitr prodre idem
11940397
41927
8342779
23880794
107463573
35821191
42161508
11940397
47761588
qy42+ 52709019
(4942 385180000
00 0006752901
1194
1338
134
huo res accuntius discylienda
114 370000
31
45740
+912585 180600.
et enor
+ 4242585180000
A9 42 45270981 9
01 1940397-
42. differentia inter 494245 2709019) qua prodeunt
et 4942385180000
0000067529019
ergo error est 0000067529019 vel 000067529019
non im log. Tab. ab 1
Eog. Hyp. abie +3214 in 11940397 
413927, e 1in14370000
ad Log. Fab. ab 10) ad Log. 1y ab. 10 posterior e nor si ponimus log. Tub. ab.  o
Con. trp. ab1ot
ad logitab ab 1 R loy. brq ab i
unus scilicet si quari lus ponendo Tabulares aeccuratos pontmu: loy. Ayperboeteum ab 11. ex datis duabus Tabularibus
e Hqprvolico ab 10 quarimus; alter si contra. suntque hi duo onors inter se   43214 ad 11940397
sed utrobis modo certum es ertorem esse minorem quam 700o
Nam 43214 in 11940392 est  quantitas
quam sumndo sumendo 43000 in 11940000 fit 513 42 (0000000. est pr 67529019 faciendo 2000000
fit errormin
6753
1342000
BAZ00∞  7 602
A8 23
Jam β1342000+
Ergo error non est
Se pro 413927 faciamus 413000. fit
45748
Ueno cuno modoero est tmraguar  alleri adur quad
LH o F LY + et LH  B LH 1 , ut L7 18
LY
LF 10t
67530000
sin sumamus 413927 in 114370000
5000 4 11437
183
348
47234810000000
et pro67529091 ponendo 70000000
enora ein minor quam
1d est minor quam
imirum si quaeramus logerichumam ion pertoliaum ab I ex datis Tabuleribus ab in et 10 et Hyperbolico ub 10c fit
prspriore
600000ctr 422,
19 4 ~0297, Ai3D qdeber essep 11917000d  
I 12,00090000n +3214
1200000080
 uo d quatilatus est et reducendo ad communem denominatorem fiet: t
B.4942452709019. quo posteriore 
4942385180000 differentia est
257529010
51 856800000000
nentus ex assimtis tabuleribus es cedis cum qui virecti ex ipsa Hypertole inentus est8G
1
8 698,0000,0000
11940397
27854
Quaeramuscontra LH ab 10. ex dato LH ab H ex LF ab 102 ex ab  per LH dt B) E7 +ot, LA  4321a, 14 370000  nteresse eecue
Feducndo ad communem benominatorem fier pro priore , 4 +94045 16gor9 et proposenba  A LT id
4942385190000
4892  0 13
4967124 100011003
=12 0000vo, in 45
2967124,0000000
sa diffecutia Logerithmus. Aquitolius ab dies inventus ex assimtis Tabulmribus deficit ab eo qui diresti ex ipse Ayuibola inventus est.
496124 000806
13124
es
ex spatium VAs 1 200  3d
1572
130804959
54829814
32414907
10oep
1308049694
15634783
392614907
523219876
0804969
13080496
470897818 4 0000)
100000
inver
erit XDp XZ  ,3, 4 0000
=14q
864
12c
10364
328
C
loganitimos ubtamus, quorum eadem
e YXB
11437. 1 F 10oco  a 43711. H 1
e
36ao A 11422 98
5748
508092
413927
unithmum yperborocum
soliu a
13080 +9
144090000 20 1aglo1on30+5 2
2. 34, 6 - . 390 + 6119,0 - 111 3  24 000000 - 1200 00 + 800 - 6
1,2,3,4, 0000000000
13214
86428

## Folio 122r — 00067993:0243
# The same scan as fol. 121v (00067993:0242), where its text is given.

## Folio 122v — 00067993:0244
# The same scan as fol. 121r (00067993:0241), where its text is given.