# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0597
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0597?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 299r, page id 00068201:0597
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 298v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=597
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000597.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 100 lines, status machine
# Lines: 100 recognised, mean confidence 0.87
# 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.

donae
sive ut rectangulum CA in DR, aequetur ati VADPV. et rectangulum CAFs, aequetur
zonae VAFNV, exea  nspatii et rectangulum CA in HT aequetur spatio
NAHM V. ita enim, to cu corpuscylindrisum cujus basis AHTA figura logarithmi caltitudo A
aequabitur ungulae cujus basisquam AHMY) per plano per seminormali per Et M abscissae
elindio
spatium Hyperbo
seu summa ommum spatiorum loganthmis proportionatium, ergo aequatione santo ante
inventa: sum. Log. + Parallepiped. ex CA in CAH aequ. CA in VA HMV i o pro summa
Loyarithmorum, seu ungula quamdixi, substituatur CA in A HT A fiet:
CA in AHTA + CA in CAV aequ. CA in VAHM, et demta altitudin ommumi s
communi CA, gura transponendoque erit figura Logarithmica AH 7 A aequalis
eit AH TA + CA in CY (AV. aequ. V A HM. Ervi icalculo, ita enim ratum AHTA
foret nullum c CAVY VAHM.
nd + l + a + + 
ap an
bin
12b b2, 36 15. 4b
12b 12 1. b 5. 5
+-
12 + 13.
12b 123b
13
Pn
itc 
14 et
en dCX
in 2sapi eu rina Ergo pa  ex es n3
i Ergo n- sutata
et na a sns1 B la
Ergo X du p al +. 
Ergo vdn
eb+n
aatS
ergo na-asndt Bab
et diri ab an
Ergo _n + sn dl , l et an + nat B al.
abtan
et bdu + naTB b dl. et b an d
b - n
ex eb
Ponatur C dn aequalis vel prostartionalis ipsia a. posito ab. esse potentiam Hyperbolae, erit
12b 1,2,V 1,43, b3
et bcdu aeq dC  V. sit can aeq a. fier:  sitque ab. potentia
Ayperbolae, erit ab y. sit CA,, b. et AH, n. eii _CHb.n.  et HMp ab
b -n
b - n
ab an y aeq adt,  sive se in spatium
Hyperbolicum VAHM. ducatur recta AH. vel rectangnum erectum VAC, baseos CA, altitudinis VA, consta
ed quoniam res videtur jam regrediamur:
6-n
folidum gereratum constabit exmitai rectam ulis parallelepipedis quorum per plana basi perpendicularia sectum
constatit ex paralle lepips, quorum altitudo AY bais communis AV, bases  exigna quadrilinea, NFHMN
PDFNP est quonum vel p D( NP, vel, vel quod idem est rectangula NFH
seu differentrae logiritus
proximorum, posito FA HF, FD et. esse infinite parvas. Quoniam rero in infinite parvis, quadrilinea
haec a rectangulis HFN, FDP, non differunt, rectangula autem haec su ord inata Hy perbolae
in ipsas _n, vel FD, differentias numerorum. Hinc habetur aequatio inter ordinatas Hysrbolae in differenti
numerotum, et inter differentias logaritdmorum
Cinfinita
res rectur abinitio ita repetetur
absoluta et geometrica sine suppositatoganidimium constnct
Constructio autem haec est:
CeC. Luadratura figurae Logarithmicae.
regu est sint primum numeri ps decsn CD, CF, CH. eorum Logari thmi DR, Fs, FT,
m  spatum
suintis
q quadrilineum nmmero novissimo assumto βT (vel CH) duobus pumeris primo
CA, et novissimo βT (vel CH), asumptoto demque CB et (asymptoton enim habere manifestum ess
ac curva AT comprehensum esse df aequale rectangulo sub primo numero assumto
et AC) sub numero no primo CA, differentaqe  et n C), differentia numeri novissimi
3Y vel BT vel CH, a suo logarithmo CB vel HT. Numerum autem primum voco, cujus
Logari ust CA cujus logarithmus hoc loco assumtus est infiniteparvus sive nullus, faniam in A curva
intelligatur
centro C. asymptotis CL. CA. describatur teni eA R ABsibulbatur per punctum  descutr
normalibus
 VP NM, cuius ordinatae AV, DP, FN, Ht M. _c, et quoniam
axem secet +
et quoniam spata VADPY, VAFNY, VAHMY, logarichm it  pro DR, FS, HT
Hyperbola sequile
proportionales sunt. Quodita fieri ponatur ut constat, ponantur autem ita
esse proportionales, ut rectngulo Zonae sint aequales rectangulis sub loganithmis
aequetur
respondentibus, et altitudine communi AV, exempli causa, aut unoritimem
Qonae VADeY et ita in caeteris. Ergo differentiae Zonarum, ur PDFND, NFM 
 aequabuntur differentiis logaritmorum in VA ductis. Ponantur jam differentiae sexonarum seu quadritmea
honarum esse in finite parvae,  differentiae numerorum DF, FH, infinite parvae
V sint; patet (et facile demonstrari posset) pro his quadrilincis exignis DN
FM assumi posse rectangula FD _H N rectangula ergo haec differentiis
AFN er
ogdinatis Hy perbolae, in differentias numerorum, et ordinatae Hyperbolae, DP, FN, erc
frunt ex potentia Hyperbolae seu rectangulo CAV, divisa per numdros, CD, CF etc, exempli
gratia Cgu agui cert. cvetar Fos. apui  ea u aim td. atitem apo. A) in 8
et snan-andlgaba
Cexigna
exempli causa rectanus.
FDP, rectanus ulo VX m
posito erunt enim B5 et
similes, etiam infinite
parvae