# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851708439:0196
# Permalink to this reading: https://leibnizlegible.com/page/851708439:0196?run=74
# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
# Folio 172, page id 851708439:0196
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=196
# Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000196.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 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.

E.
F B R 
iena =, ver duo siena -, quae se invicem sequamtut. Ommino crracum elt.
Onde Schodienius (ad cum Jocum) solal manlan esse regutam ad eas aequa-
Cap. ABII.
rem limicanda Bulo, quae raclices omnes pabla reulbou bit, naattao latt.
tm.
Ouod quo manisestum fiac, hanc Expono aquationem,
2t + 643 F TZF ∞ F 7993 X = 35878 =0.
ductam in ~ = +8 =0.
quae Pacie 23 = 12 ~2 + 3 43 - 5 ~ r F 4.5 - 645804 = 0.
Prima harum, per eam regulam, Quatuor haberet radices Pegatiras; Secunca,
unam Afirmaniram; adeoque Terria (ex binis illis composita) haberet, unam
Attirmaciram, et quatuor Negatiras. Sed d, per eandem regulam, hae quinque
Forent ACirmacirae omnes; (quia cocidem lune cransitus a f in -, et a - in F.)
Regula igitur erac Limitanda.
Sed, lic limicata, nondum viceo quin vera sic. Sed Demontlrarione in.
diset.
 Loi faisas (hoc est, negariras) quot vieibus ibidem deprehenduntur duo
tiones quae producuntur ex suis radicibus in se invicem ductis. F80 ac cas Cal
Ci A P. XLII.
De Parriori sectione sexta; Nique de Mulsiplicandis
es Dividendis radicibus ienotis: adeoque de
 Radicis nondum cognitae mutari postit ralor (mulciplicando auc diridendo)
L in quacunque ratione. Ouent _ in hoc lequituT Cartesius.
Dico, multipheando aut dividendo: uamis enim solam Mulciplicationem di-
serte nominet; utramque tamen incendic: quoniam idem est Diridere Per 3,
et Mulciplicare per 3: Sicue idem est. Suberahere 3, _ Addere - 3.
Et similiter Fuchdes, Racionum Compositionem explicat, non autem carun-
dem Divisionem aut (ut loquuntur alii) Diminutionem aut Subductionem:
Duoniam ex ratione expolica, puca = seu a ad B, F. ximere rationem c ad d, tan.
rundem est ac Componere cum ratione d ad c.
Fractis Surdisque vitandis.
rEctione Sexta (quae est primae partis ulcima) Ostendit (primo) Ouomodo
Parriori mechodus hac in re, Exemplis melius parebit.
Sit expolica aequario aa = Ba = c0.
TIOC clb 2) +0  tC
Si mulciplicanda sid usus kadix per 2: Musciplicat  LGulos tujus ter-
minos per tor respectire numeros continue proporrionaleo i Propolta ratIONE
AE