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# Catalogue record: 547 — Lex Homogeneorum in Calculo Analysi infiniti
# Incipit: Sit ordinaria quantitas y, repraesentans (si placet) rectam, quanquam
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=547&katnr=58124
# Work: https://leibnizlegible.com/work/00068104
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 9
# Folios: Bl. 8 (from the shelfmark LH 35, 8, 9 Bl. 8): 2 pages, canvases 15–16, page ids 00068104:0015 to 00068104:0016
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068104&page=15
# Lines: 89 recognised on 2 of 2 pages, mean confidence 0.90
# 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.
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# 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 8r — 00068104:0015
# Source image: https://digitale-sammlungen.gwlb.de/content/00068104/jpgs/default/00000015.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 40 lines, status machine
Lex Homogeneorum in Carculo
efit ilti Analysi infiniti
sit ordinaria quantitas V, repraesentans (si
placet) rectam,  quanquam sub ea etiam
tempus aut velocitatem aut quidvis aliud
ascendendo
intelligere liceat. Habemus dinde infini
tam, infinities infinitam infinities infini–
teries infinitam et ita porro. Rursus
ab ordinaria descendendo habemus infinitesim
infinitesimae infinitesimam infinitesimae ab
infinitesima infinetisam et ita porro.
dddx) dox ( ax ) X) saSXS
2
X
X
ut in vulgari Lege Homogeneorum
X
_ IX) X
X3 X
Expenentes qradus tam in valgari quam iu Transcen.
dem ne nomogene
=21 e
rum ptum
seu
3
X IX IX IX) X 1X
Arithmes
Ut vero expolientes graduum sunt progressionio qc
metricae in vulgari lege, ita et in nostra nova Transcendet
Nam X dox et dx sunt p homogenea; quia
d Xdx = X ddx + dx. ergo cum ipsius X exponens
sit unitas si ipsius ax exponens sit e, utique patet
et ipsius dex sit f, siet C+1 = 2C
6
fieri
eodemue modo  Ex ddax et ddx sunt homogenea, adeoque
expositarum Affectionum exponentes sunt progressionis
Aritumeticae. Porro quemadmodum differentia.
progrossimus

## Folio 8v — 00068104:0016
# Source image: https://digitale-sammlungen.gwlb.de/content/00068104/jpgs/default/00000016.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 49 lines, status machine
exponentium ordinariorum est unitus
ita
differentia exstonentium frans cendentalitatis gradum
exprimentium es appelletur eo. Et habebimus:
Gradus dddx ddx dx X I x 1 SX ) S.
Exponentes 1-3Cd 1- 2 1-C
Gradus
Exponenles =2
= 1.
1+C0 1+2c 1+3W
X
3
d
4
ubi patet si cd faciau = 1 prodire seriem exponentum
transceldentalitatis eundem quam exponentum bulgarium
ck Re ib it sane est X homog. X dx
Et ita eodem modo SX ddx : X homog.  1: X seu X
Possunt autem hujus modi infinita aut  infinite parva
ex calculo oriri hoc modo. Sit a = V = AV tunc
(0 casu quo V et a aequales sunt fiet  infinite
parvantix. Et si esset aa = yy = Wo tunc eo casu
quo a et y coincidunt, fieret v etiam infinite parvum
Si 
ut dx2.
si esset aaa: a-y = v
posito a = y fiet V infinita. Et si sit a: aa-yus = v
et a= y fiet v infinities infinita, quasi dx V =a
et quia ex ut X
tiet 1 et v = x. siet utique
 s
= 1- c0 4 W = 3 seu 2 W = 3 - 2 420 = 1+ cd
adeoque u homous. cum (X. Et ita porro. si sit
aa = yy = bv, et a =y, fict Aobe dx hom. bv
seu 2 - 20 = 1 + W (posito v= X) seu W = 1- 200
adeoque aa - aa, : b homog. ddx
aeterum notandum est, si x sit linea in calcule
deometrico non offerri (x, sed tantum (Xdx, quae est
homog. cum X, quod tum aliunde constat, tum etiam ex eo quod
Xax homogs.  dx SX, quia illa ad hanc reducitur tum ex constans.
dx Ex habet exponentem 1-co + 1+ co ex tabulas
Ex jam
vero X sit quiddam aliud, verb. gr. utentus potest
intelligi (X, nam (x faceret gradum velocitatis. Summa velocitatum
vero
cd est 2
ipsa imri
non potest, nise intolligas dusi in aliquid, velut
plomenta corporis