# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175906937X:0070
# Permalink to this reading: https://leibnizlegible.com/page/175906937X:0070?run=74
# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 46, page id 175906937X:0070
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=70
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000070.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.81
# 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.

+6
P R L N C E P L A
veniat Z ∞ 5. Sic e Situerit Z3 ∞ 125, erit, extraet d utrinque radi-
cecubica, Z ∞ 5. Fadem ratione, (i habeatur ZZWaa- ]- 2 ab. f- bb:
extraeta uerobique radice quadrata, tiet Z ∞a J b. Nec aliter HEA
fueriE ZLWAA L bc- L 2aVbC, erit enim Z∞a L Vbc. Non secus LIEX
Eequetur = + a L V = aa L bb, erit X ∞ V -: a L V = a a-  bb
Elis subiunse lequens exemplum, in quo omnes praecedentes
modireductiOniS (IHLOCCUTTUNE. PFOPONAtUF N22 L 3aa, 22 3a_
a2Z
DV.
:quiaisitur eorum, quae aequalia lune, ae qualia quoque
sune quadrata, tec, multiplicando utram que parrem in le quadrate,
202
124- 9a+ aZZ
A. Z2
D
. Addatur jam verinque p21 - 9 at
e Tub-
crabiatur cransterendo scilicet ipsas in alteram partem sub
a22
121- 544
2Z2 ∞V =. Ouo tacto, multiplicetuF rIESUS uEraque
pars aequationis in se quadrate, ux cranescat sigrum radicale; Ha-
bebiturque = Z +-
a24 aa2t
24 - 94+
bb D
. EIbI CIUErInqUC dematuE
27, 2c reliqua partes omnes addendo ac subtrahendo ex una
parce in alteram transterantur, quod tic mutatis tancum signis, crie
a2+ aa 2+ 09+
6b ∞
. Porroue deleantur tractiones, reducantur
omnestermini ad communem denominatorem 4bb: quo pera-
cto, Puerinque per cundem mulciplicetur, ipsum nempe deno-
minatorem omierendo, obtinebitur 4 ab Z7- 4 a aZ + ∞9 a+ bb.
Dividatur jam ubique pera, hoc est, a ubique deleatur fcque
4bZ+  4 a Z+ ∞ 9 a b b: quo Facto, diridatur uEraque ParS Per
4b = 4 a ut habeatur quantitas Z + ex una parte Cola, crieque
2+∞ Da3bb
ab - 4a bi (iverobique extrahatur radix quadrata, habe-
e
BITIE ZZ D = abV,
: d Si denuo utrinque extrahatur radix
quadraca, invenietur Z ∞V Z ab V
E quibus patet, reductionem per additionem ee luberactio
n
Pag. 6.