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# Title: LBr. 705 · Overbeck
# Folio 10v, page id DE-611-HS-861255:0020
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 11r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=20
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000020.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 131 lines, status machine
# Lines: 131 recognised, mean confidence 0.75
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

minet alores omnium
xyE- ex ( +24772 +12XC 8y2 124 Xy -8yB 16x2B+3X) 162y) 87d + 4( +82)18yd +8x(- 8d- a
xyZ +X (3 - 17Xy  = 5X2 + 8y2-10XyB + 8y β3 +9X2 3 - ∞3 + 9Xy) + X 4 (3 82) - 8yd X(+ 8d = a b
3xy Z +3x 3 46x9 ( +3X.
517yZ-X β + 5xyZ
Formularum in ctava Dimen
sione. Reliqui ordine ad sinistram
se
subjecti persequuntur Dimensionem
sepfimam, sextam, omnemque seriem
Antecedentium Dimensionum
p geotaX7xy47E- 2Xy21795-7X  17  + 14xy β +72) -7 2β -7y) - yud 17(- a
Xy -SXdis +sXyd- 2 +9Xy2 -75Z + x β3- 4~ - 8xy B - x) +72B +79) +xd. 7 (= a b
8x92 +2(2 B B-9 +C 6x9( 4uβ + 1022 (3. 2x) + 479) 12d - 4(3-87)14yd- 8x (18d - a0
7y8 quyβ 18yβ +X2β 3X 1 ary) 18Xd- 4(d 138) -8yd- x (16 = al
 =guy Z +2X 2 + 4y2 + quy B - 4y3- 8x2 β - 4X) 187y) + 42d - 6β- 42) 4yd 4214d - 46
+5XZ2-5y2 + 4Xy β -2yB -9+2β + x3V 3xy) - x + 43 + 821 + 2yd+ X- 8d abc
XyZ- 33 3xy= - x 2 +5y8+ uxy B- 49(3- 10x(B 13X7 exys C3Xd +8(3 +2)) +4yd + 9X(. 16d-abc
aXyβ +29(3 +4u2 - ∞) +3x9) +xd- 4B 32) -2yd - X( + 8d - adcd
Exy( +47β90 +2∞3)- 4xy) 22d 43+82) 4yd +nui- 8 ab
DDD Xy( -293 = XEB - a∞Y + uXys 12d +4B= 92) 6yd- 10x ( +21 = abcd
3E D(D -EyB- X2(, + +5xy)- Sxd + 4 (-72 +2yd +8xC-8d - a b2
yβ- 2x+ (B X + -xy) 15281 2β 137 9yd- 5x (12d-ab cd
C(+ X + 3xys 15Xd 4B +62) B t. 17 (+ 2qd - abcd
X -3xy) Xd 0 132) +29d + XC 8d- a be de
xyv-5x00-32) +Byd +X (3cd=abide
d000 2yd- xC+8d- a bid et
22) +2yd. 21712d=a8 
2)-qyd +9xC 16d- ab cde
yd -bxC +20d - abi det
XC6d=abidesa
AACI Subsidiariiaosq
Q 11OxZB+ 4X 102y) qud - 8β + E) + 1yd +9X( 16d - ab
Xy 3xy- 2X2 16X92 1398 +2∞ 3.77 axyB. 2X) +7EB-3y) 17ad- 7 C= ab
g+GZ-F 4L +5G(1X -2 - Ey)-Xd +7C= a bC
Xβ (8) -3xyβ - x) 132β+2y) +Xd - 72- a bcd
XE 2Xy(3+27 -ZB +3yV- 7xd +7E- ab
S 3xyC+3x (t3C 3yb. 3x 13d=ab
4X7-32 ( +69) +97d - 21 C = aVcd
X2V (2)- 2y -Xd +7C- ae bide
XE - 3XyE -X( +38 +2y β 1X) -6d -abc
Abacus V Dimens X β  -2y3 - X) +6d abcd
X3y -3xy-XZ + 5yE + x B-5)= a b
Xy 2X E -9Z 45x β- 5) -ab
NV Dmenss. BC. N2E =2yE - + βB +5) - a bC
X Axy +2s +axE - qB- D- 2 ( 15) = abC
Xy -29 72+ 4B - a b XB=abcd
y 2X7 +2( - a b2
-3 112. 2) XE
Xy -37- ab)
X2y-a
2( -3y) +5∞d -7E = abd
yy -5xd 114(- abcde
ad -7C= avides
a -X a -9a +Za -Ba
C-abedesqus a xa -ya
a bc -2a. ( a s a3. 
Abacus 53 -haye -y 2 13∞ (3 +5XC - Zxy (3 -7X) 45+ + 7y)) 47Xd - 7 C- a1b3
Septe mersionu xye 2yE 3x β- X 2 + 8xy31 3X)-24 Hess. bxd +147 abC
yZ () - 2xZ Xyβ +4x) + 52β - 7y))-qud + 7E- a Bc
Abacu sex Dimens.
e
Xly-qxy +29- GC4XSC 09 +0d = 4. 
Ry- 2y 2 +4XG+ 2xβ. 3C 12y 3- 67) 16d - a1b
XyZ- 3x(3 32 +47+X) 120 =abc
3B 47) 19d = abcd abc a ija
XV-= aebcd
d=abcdes
X- 5Xy +Ex t5XZ SyE syB a5j= 4 ~ -2yB +EX 2d av abc- ta (a Va da
Xa- ya 1Za - ( a +) a- da + Ca
a =xa -9 a +2a= (3a 1) a - da
ab9a 2a +aida
Est vero
Xa = X- 2y
ya = Xy. 3Z
Za XZ 4(3
Ba =xβ-
Va -x B
de =Xd- 7
a XC-88.
a -xa -y at 1 Za3 - βa 1) a
a -xa3 -y a + Za
ab= ya ra+ Ba patda ha
ebc = 2a - Ba abide. )a
avide ade
(VIabedef-da
aeb -ya- za
ab -ya
b=ya- Za + βa
ab xabe  2a
2abEd xabed-(
adb2xab- y a- 2a + Ba
dcada
arocd-xa bcd = (3C
2a62-xabe a- 2Ba a b cac-xaebcde- Va
Primo daturm Specimen Inventionis.
Ergoxa 13 2xy
Ergoxa-ya -a3 Detrahaturya -xy
etus dt
aque xad  3 y+X mys
saque l x
Ergo a15 - 5X3y-
+ +2y= ab
XC+ZXy = 4X(
2 0xy
2+ 5Xy2 - 5XB - 5yt +57
Eodem ordine omnes Valores in Abaco subsidiario
notati invenientur tales quales in Abacit
primariis consignavimlus
fectentibus sit P, potentia Respendent sibi
X, 9, Z, etc exprimantur per (1)) (21) (3). Et X par (6)),  per (2), et
a, vel b, par  (1  a per ( vel b per (17; ab unt be per 2) a b orlb e per (3)
itaque XyZ dabit C (1) (y3y3
ab dabit (1)  a b dabit (1) (2)
Hinc regula goueralis consensus coefficientium in Abacis primariis
 ita in exemplo exprimetur
Coefficiens ipsius ((1 2 (3)) in valore ipsius (1) (1)
caeticienti ipsius (3) (5)) in valore psius (1) (2) (7
V= abede
aded = Bd
aibcd= Ba Varda
avcd -βa ) a
abedes-da abcdetgs -
ab pab paiee Papta bb - ra B - ya Za + β3a -Va + da - (a ab= pab va 2a a sara
Zβat + a- 2d a + Ca. ab = xabe 2a 2βa 121 2 2
a +Zda 3Ca: abcd -xabed βa 3) a 13
a 2abide- abide ) a 14d a
2a6- xab- 9a 2a 2a deaes sarides Da 5a
Proditvi Abaci) alor a1
coefficiens pliue xisq in valore ipsius a b
defficieuti pius L) in vatole psius a bed