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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 147, page id 175905688X:0169
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=169
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000169.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 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.

que I
linchi
Aplitu
el au
et 
set
IIIes d
11
litate
c
. Ca
GueniI
EBRVM PRTMVM.
E radicum extractio, quae pro Divisionis a
quadam specie haberi potest.) Ouandoqui-
dem eadem terme proportio utrique operacio
niconrenit. F.R enim in Dirisione, ut quotiens
i ad unicatem, sic dividendus ad divitorem. In
 extractione rero radicis quadrarae, uc radix, ceu
quotiens, ad unitatem; ita datus numerus, ceu
diridendus, ad radicem, ceu dirilorem. Adeo ut radicis extra-
etio dirisionis species sic censenda, in qua dirilor quotienti est a-
qualis; vel etiam, in qua radix inter dacum numerum de unitatem
est media proportionalis.
Veletiam si una sit, quae vocetur unitas.) Per unitatem in- D
cellise lineam quandam decerminatam, gua ad quamris reliqua-
rum linearum talem relationem habeat, qualem unitas ad certum
alIGUCIM NUIIMCTUII.
Vieo commodius ad numeros referatur, quamque commu-C
niter pro libitu assumere licet.) Sic enim, exempli graria, datum
aliquod rectangulum eransmutandum in quadratum: Si pro uni-
cate lumatur latus unum, quod libuerit, de inter iplum de reli-
quum inveniatur media proportionalis; crit ca lacus quadraci, da-
to aequalis. Reque hâc ratione latus alterum ricem gerit alicujus
numerise quo radix quadrata est extrahenda. Adeo ue manifestum
Sic, Problema propolitum, nec non media proportionalis inter
duas datas lineas inrentionem, nihil aliud esse, quam li un a line a
2sumpea prounitate, ex reliqua line a tanquam numero extrata-
tur radix quadrata.
Vi ad ipsas inveniatur quarta, quae sit ad alterutram, ut D
est altera ad unitatem, quod idem est atque mulriplicatio.
in mulciplicatione enim est: uc productum ad mulciplicandum,
ica