# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/58971/text
# Catalogue record: 58971 — Quantitates imaginariae.
# Incipit: [Fig.] - xx - x
# Date: 1675-12
# Akademie-Ausgabe: AA VII,2 N. 062
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=58971&katnr=Cc2+1136
# AA VII,2: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 58–59 (from the shelfmark LH 35, 8, 30 Bl. 58-59): 4 pages, canvases 115–118, page ids 00068124:0115 to 00068124:0118
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=115
# Lines: 114 recognised on 4 of 4 pages, mean confidence 0.62
# 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 58r — 00068124:0115
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 59v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000115.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 33 lines, status machine
evantitates sna
x ∞ 14 4 4
2
2a -2
na
rax. x ∞ B
x rax + 
eX  x +.9
2
ratx rate pt
raxxx xbo
S-XX
XN-1
x
(a + Y-6+ aut
nax
6∞ Y9
dd4
a 
2a -2l7
1D 2a - Y -x 
Y
ratxx
+ rat   
ax +p9
Ealx ∞ex _
tua x s
aa x - M
a X Y.l
S- 1 B a =p co  11 cot. ergo 68
hinc patet ex cd H I. non sequi tantum cor+
Set et co r + Y-1 quae sunt quatuo rat tes
quationis cot- 170

## Folio 58v — 00068124:0116
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 59r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000116.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 3 lines, status machine
 u
b
RSACHSISCHE LANDESBIBLIOT

## Folio 59r — 00068124:0117
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 58v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000117.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 23 lines, status machine
 1e
()
ea
in
2
d
i
ut
1a
aa
d meotmadi
 ntreb
 1a
1d od aie ineat
a n saai
nidi dma si
. 59
a
 
 
mum
dndu  
ee

## Folio 59v — 00068124:0118
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 58r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000118.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 55 lines, status machine
xix.
a
2 xx +9
i
dux x 200
X + 266xx 46
e auaa
d
266 ad ep
6b x
taa x
1s
bx
x21 4
1ba + haas + ∞ 49
b2x9.
a x
 a  car -g5 + 29
e + 9
n
imo hec appans difficultas
n CF H GC, adeoque ejus quad
quadrato alterius subtrat
potest
to
unquaque linca
sitaque in
x seca
sux
posse in duas pare
at
epretms
X s 
si b, majoi quam a
Pa+S +at
AB,) X peni pote aequalis AC. AD. angulus DAB rectus. Ait
posito puncto Za quo incipit X,  et sumendam proponi. X ad partes
B, fore A tunc posita AB AX, fore AC∞ - X.. Ergo
rectangitum CAB, fore = X nempe AC in AB. Engo Jamm recta
quad ratum  AD aequale rectangulo CAB ex natura circuli Ergo DA p. X,
feripos test multiplicave, st DAB XY - 1. itaque Y- 1. Significat magnitudinnem quae quantur extr.
adu hoc reserri
s
lineam CAB in perpeniculari AD sumendam. Et notam esse problematis male a
cum sit BC. formati, ut enim aliquando quaentur ut quantitas quaesita sumatur versus AB, cum sumi
3FX. et AEK.
0
i esse contradictionem Addi enim vel subtrahi est in unam magnitudinem
debent verseris
co quis fertu addendae  ex
eere contradictione non ex magnitudine seu
aleru se Anc conjungi posse, quod est contra hypothesum
a enbus partau lao ner viticalas an ded licea sormne s, e Aen
n
additione