# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/826603459:0474
# Permalink to this reading: https://leibnizlegible.com/page/826603459:0474?run=74
# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 28, page id 826603459:0474
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=826603459&page=474
# Source image: https://digitale-sammlungen.gwlb.de/content/826603459/jpgs/default/00000474.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.88
# 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.

DEDICATI
in 27r = = 296.
3) 27(9 = R9.
V9 = 3 -=R.
9) 296 (323 -C.
subtense impossibiles.
Ouid aurem e num aequationeshas (de ejulmodi mille ali-
25) omnino impossibiles dicemus: Nallo modo. Habec ecenim
illaradicem r i F 7; haec, radicem r = 8; Itc modo on
Aenlum ekt, eaEdem ad Resulam primam exisendo.
Ec quidem aequationes omnes hujulce Forma, quxe ad regu
Jam primam examinaca radicem realem habene (vel actirma-
ciram, vel salcem negaciram,) illae ad hanc regulam h exipan
cur, adimpossibile nos deducunes (hoc eAt, illae omnes in qui-
bua quadrarum Cemissis quancicaris ablolutae, majus est cubo
crieneis coefficientis cermini mediis) concra vero, quae videban-
cur illic impossibiles, (nempe ubi guadracum lemissis quan-
acatis absolucae, minue est cubo crientis coeficientis,) radiceo
hichabebunt reales. Nec ulta incerim aequatio verobigue ex
hibebieradices reales, nisi illae Tolae ubi quadracum Ceristis cer-
mini abloluci, aequacur cubo criencir coefticiencis. Oualis cA
=27r  = 54; ItCM r  T2Y  L 16. (quippciliC
gRGXO =729 27 =273 HiC 4X 4X 4 = 64 = 8 n 8.)
alixque similes. Cujus quidem ratio ctt, quia crefticiens mediu
termini in prima regula Cupponicue
3 A Ccriplum reccanguli duarum
quancicacum A, P;) in secunda re-
ro, (nOn 3 F, Sed Z R 9 hoc cA)
A9 + AE tEg. (nam, in circulo.
3R9 =T9 = A9Y A + F 9, 900d
mos alibi demonstrarimus, eAq: cOB
nicunon inueiles) adeoque quocies
concingic aequales invicem este a, E,
quod cunc erenit quando dictum
Ouadrarum dicto cuho XguacuE, nec
aliasunquar) perinde erie sire di
catur coefticiens 3A, Bre A9 f
A. 
Ir
E1
3) 27 (9 =- R9.
)254(173 =C