# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/3430/text
# Catalogue record: 3430 — [Math. Aufz.]
# Incipit: Sit dt elementum temporis
# Date: 1689
# Akademie-Ausgabe: AA VIII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=3430&katnr=45171
# Work: https://leibnizlegible.com/work/DE-611-HS-957816
# Title: LBr. 130 · BurgundioTolomei
# Folios: Bl. 11–12 (from the shelfmark LBr 130 Bl. 11-12): 4 pages, canvases 21–24, page ids DE-611-HS-957816:0021 to DE-611-HS-957816:0024
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-957816&page=21
# Lines: 185 recognised on 2 of 4 pages, mean confidence 0.78
# 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 11r — DE-611-HS-957816:0021
# Scan: The same scan is also registered as fol. 12v; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-957816/jpgs/default/00000021.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 90 lines, status machine
ax
TIB, t. = +Cd 2D. Ergo 1c 2Y = ddx
sit dt con
sit at elementum temporis. Quod si jam ponamus potum esse compositum
ex impetu primo horizontali, et novis impressionibus acquisitis, patet
ore ddx Z = du d+ ut dy adeoque Zddx = dyd de dydus potent
dyndo dus deo poterit Z: a utcunque componi et Xes y: X et dy: dy et 
et deo eut ad dus, ut in ratione formala ex Z y: X et dg K: a, et dy: dx
adeoque sufficiet dici fieri Z dax = dydy, posito Z. a  forman ex _X: y et
x: a, et dy: dx. Quodsi ex problemate detur dy: dx res erit
Zadx = dydu, posilo Z: a formari ex X. y et X: a
= dydy posito adus =0
ret reducta ad
Et fingi ptt impressionem
novam pendere seu dax pendere ex  X et y simul, sed ita
C
eu
X; y, a 4d)
sed fingi jam potest impressionem novas elementianes accedere non
det detirmi constructio hinc non appatet
tantum in parallelis ad XX, seu in verticalibus. Nempe nova impressio verticalis
sit 2Yco, horizontalis sit 2Y B compleatur rectangulum corYVV, et jungatur 2Y , ea erit
Est jam 2Yk) aequalis
ipsi 1Y2Y, et ei in directum, coupleatur parallelogrammum  ∞2Y2Y) 3Y et erit
directio novae impressionis Eico est dax, io est ddy
3Y punctum curvae novum, ponamus jam dex Zddx = dtat, et W adu = atat
dusa itemque Wd per idem
dius: dax daretur per geatia sed
Jusque variantis, utei Z datur ex d si jam 3 detur ex t et a,
haberetur solutio per quadraturas. S ita
quantilat iu qua erunt
a dlx: dxdx, Xa d X: a, y: a, nam dy: dx ex datis tolli potest. Ha C ergo
dausidax habetur ex problemate Ergo habebitur
e
L
formula afsmoenda est pro talis, ut ejus differentia sit constans qua ut debeat aequari
c: a
formato ex z
1-a, posito dZ constantem
ponando jam adX
 fieret log dx = sux . X:a
addx: dxax =  Xia
quomodo hinc ductu, quae sit constans Nempe fiet
s
X
sed
a
ax.
dil
si jam fieret
Saxoxia
 7Ca per X: a, ∞: a, gia, ubi
stud per du est relat quae datur. sed vix exilus
0
ded b dx: de = B......
C
et
= , ax:
et
at:
olter dax substituendo
ittiabi deducta b
atat: W
 diferentialis datae; et tum videre an explicare
aqvalionis
plear
poteramus in aec
et similiter poddus. re inde follere dy; vel y ope
latu differentio differentcali ex
il
s
y et et W0 per R
+ et X per X X par E, ut res succodat
la lu-
componi etiam interse
dira
directionis
juro in
n
unam
curvam
et
possunt slures
cohatus
utiam potest conatur
quam
no conciui
non lu esse
parallatas, sed convergen
ses in untem punctumus

## Folio 11v — DE-611-HS-957816:0022
# The same scan as fol. 12r (DE-611-HS-957816:0023), where its text is given.

## Folio 12r — DE-611-HS-957816:0023
# Scan: The same scan is also registered as fol. 11v; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-957816/jpgs/default/00000023.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 95 lines, status machine
cebit etiam pluret conalus concipere
qui omnes Com
ptonuntur in unum,  imot nec optus est ad hoc hoc infinities nfinite
parvis, seu Clementis velociatum sufficiunt infruitae parvaasem ipsae velocitates
neru jam potest MM MN
si
sint tres rectae AB, AC, AG utcurque; placet
tamen sumere angulum BAC rectum, eumque bisecari
ab ipsa AE. sit punctum curvae M ubi Mobile
meaq
M conetur, velicitatibus et directionibus MN, in
E
it quaeratur centium gravitatis punctorum N, D
quae parllelae ipsis AZ, eC, AE
As
Hg.
 AX sit X,
men  tempus dari ex  aer dx ja
c
aeus Ae6poterit concipi
Nas
ete A
 ha si nempe ex puncto Magani
L
P, du
quae prodeunt
ut perpendiculares in AB, AC, AE, et fiet MN, dE; et M
et My, dis
dempns sit b,, si jam motus quilibet per se. in quavis harum erium AB, AC, AE, sit
ner se cognitus, habitur ex dem ips spatium ex tempore idque vel e ege ordinaria
s
hone vel supponente quadraturas ut si db de detua ex et: de detur ex Z: a, et
d
ex
a, et dt. d2 ex Z. a. possemus etiam concipere A A esse seu reprae
tempus simplicitatis causa.
Generali autem calculo prius designabimus, dito puncto
ipsisque N, p, q invenire puntum M), tam magnitui
MB = = MN, M MV= +mo
Md d9 - MQ 1. (2. Erit BS =  (1: 12) = MN: 2 = MG Y2 = MN, :2
3d = MQ12 = MN:6 et M = β+ = MN. seu erit
Z
MA = M QY2 = MN + 3MN, : 6 = MQ12 + 2 MN, :6 et pan
Et βA= 3
B
ine M V = M9V2 +2 MP, :6 Est autem MD triplum ipsiu,
M
DM) triplum ipsius Aquel M ergo fiet tandem
= Mg 12 + 2MN, : 2 = dx et DM = M9K2 F 2MP,: 2 = du
et d: dx = MQ s2 + 2M P, :) MQS2 + 2MP = M9 + _MPH2,: MG + MpY2.  possumus
e
unm omni itou ipsum conatum M9 considerere, ut compositum ex Md, et 6a seu Md et Qa. Ergo lex summandi
es
M
potest intelligi in utroque et fiet ex = dx + Ah(.2 at dus = dis + dZ(2) et Ay: dx = dv + d3. 1 , d∞ + dZ (: 12)
sex possumus
q
quod sit C et juncta MG, producatur in M), ut 
s
sit M(M) tripta MG erit directa mobilis V
s
. de xia et dg. di
+
tollatio substaituatur valor
pro 1G2
ue
_u et Y+ AZ12 =X
ponatur
operae pretrum erat
ve absolvi, et possunt plures mus nnsus conferi mnes in perpendicularam et adiozontale essi nullus
m
Et de  ponamus At2d
plana absolutus esset in A
B, et AC; ita utarqusi angulus pisus sit r. 9, fint in une stante u in altera
in honcontali ad, in verticali r de. uti ponumus Y et a constantes ets
eliam concipi. poscnl variabiles
et
pe
2
da
E 
se
se
E.
X
+
e
x
c
2
seut
A
+
e
e

## Folio 12v — DE-611-HS-957816:0024
# The same scan as fol. 11r (DE-611-HS-957816:0021), where its text is given.