# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00067992:0049
# Permalink to this reading: https://leibnizlegible.com/page/00067992:0049?run=39
# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 30
# Folio 25r, page id 00067992:0049
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 28v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067992&page=49
# Source image: https://digitale-sammlungen.gwlb.de/content/00067992/jpgs/default/00000049.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 57 lines, status machine
# Lines: 57 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.

etiam
ab idus. m. in compositi
es
est quantitas potentia rationalisixam es
quadratum est atrabta-rab+ Y
La ole
s
 eb undo va cb at Vaa bb a ta- var - bb
Caeterum ne quis putet oes quantitates ra
dicales fortasse aliqua nobis incoonitahacte
nus raoe posse fieri rationales, sciendum eu
alidem. de monstrasse. (quemadmodum. et alias
vel ex calculo haberi pt) quod multae quant
tates sunt in comensurabiles inter se adeoque
rationem mr hale quantitates exprimi per
Namerum. 4 de surdus, id e de Meomensu
verviest
rabilis unitati. um fractus e unitati
commensurabilis q ita patet; sit fraitus
qui cuq ut 5. s dividat unitats inpartes
patet unam quintam. partem unitatis ee
mensuram comune tam fractionis quam
constat
unitatis; na munitate contineri quinqui
es, m contineri ter.
Caterum quod continuatis opaobus p integros
accedi possit ad fractos et p rationales
ad surdos suo loco patebit
1
ex irrationalibus oriuntur quantitates im
possibiles seu maoinariae, quarum mira est 
natura et tamen non contemnenda uti
litas; etsi enim ipsae per se aliquid imporsi
os universalis tractationi sub; ectarum variisque cono bile sionificent tamen non tantum orten
a
dunt fondem in possibilitatis, et quomodo
b-  bb
Nam ejusquadcum est
+a + saa - bb
+a = taa - bb
+21 a + Vua-bb in 1a- saa.
a + rac-bb in va- sa
a - bb
est rbb seu
Eb
Ergo fit hoc quadratum esse
a  daa- bb
+a = saa - bb
seu 2a + 2b
2a +26 idem
est quod erat
a - bb + va - sau - b1
Sed hoc obiter
p Ja
2b
Unde
a +Y