# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851708439:0295
# Permalink to this reading: https://leibnizlegible.com/page/851708439:0295?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 271, page id 851708439:0295
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=295
# Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000295.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 65 lines, status machine
# Lines: 65 recognised, mean confidence 0.84
# 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.

Cap. L. XIII.
A E G F B R A.
Cum enim reoregata uia (tribus 26, 27, 28, aequalia) sine in proxrestione A.
richmerica: Si inde subducatur, quod est omnium commune, 2 a a f 2 a B- f BP
ay: Relidua irem erun in progressione arichmetica, et in eodem cum intexris
ordinc. HTOC est B y, _ a B, e a B f a y f 2B7 = y v. Ouorum cum ultimum sit ma-
nitesto maximum (uc quod duo reliqua contineat e plus intuper: ) Frso vel By
vel aB est medium. Sed non B y. (Ouippe cum Foret hujus duplum duobus re-
liquis aequale; hoc est 2By = 2 a B -f ay = 2βy f 77; tOtM parEI.) EsL erxO
aB reliduorum medium. Ideoque secundum agcregatum (cujus hoc est reliduum)
elt axoregatorum medium in progressione arictmctiea: adeoque idem cum bb. + ac
= T7. EF prOPcerea b = a f B = a + B medius numerorum quaelicorum; et a mini-
MuS.
5. Excettus axoregari secundi supra primum, est, aβ - By = F.
Tertii supra secundum,
Tercii Cupra primum,
ay + 287 + 77 = 2.
aB F ay L By f y7 =2
Nam Cubduicto quod est omnium commune, 2 aa f 2 aB f ay FBB, relidua SUNE
B7, aB, aB f a 7 = 2B7 +77; quorum difterentix exdem sunt qua numerorum
26, 17, 28.
6. F.A a B = ay + 387 f 77. FF aB - 2By = ay + By + 77 = cY
Cum enim (IC e B = By = F = a 7 f 2By + 77: Si utrinque addatur rel subduca-
TUT Bγ, res parebic. L stque a L B f 7 = 6.
7. El Za = c - b. Adeoque = a + B = 6; _ b = 6 - - = a.
Ouiprecum aB = 2B7 (= 6y) sit policira quantiras; adeoque _ 0. - 27: erit
= 2 7, e = a = 7, hoc elt = a = c -- B.
8. F.I bc = 8. a a =- 8. AdCOquC a = (V 8 = 2V 2 =) 2. 628427.
Nam, PrOpEeE C = b = an CA B6 = aa. RL, PropieE aa  bC = 16,
eAt bC= 15, a a = 5; Teu BC =8, a a - 8. Ouod actirmatur.
9. FA ab - 9. 66 = 9. Adeoque c = 3.
NaM, PTOPET C = B = an et c6 = ab. FL, prOPter 6C + ab = 18,
est ab = (12 =) 9. 66 = (5 =) 9. Ouod altirmatur.
10. FIt cC = =B. Adeoque c = (V 18 = 3V 2 =) 4. 24264. F.
PFOPIET CC = 18 = ab.
FT. Es Bb = 76. Adeoque b - 4. FL aC = 1.
NTam, PrOPICE B =C; Adeoque BB = BC (= +6 = aC) =16: RL, PrOPLeK
bB + ac = 27, Cst ac = 1.
F2. F. IL aC = T2. Bb = 5. Adeoque B = (V5 =) 2. 236068.
Nam, PEOPteK a = 2 V 2, _ c =3V 2: Clt ac = 12. FL, Propter bb + ac == 27,
est bb + 5
F3. FIt aa = 18. LF a = (SV 2 =) 0.235702.
6 = 3V2
a =
(312 =) 3N 2. Et aa = 1b
T4. FIt bb = a a = F. Dimirum = + L BC.
Nam Bb = ac = aa - B0 = (17 = 16 =) T. EC, PTOBtET B = a, adeoque
B0 = a6, est bb + b0 - aa - b0 (= bB = aa) = T. Nimirum F F BC, PFOPEer
=a:
25. CC -BB = F. Nimirum, = X + 7a.
Nam cc = ab -= bb = ac (= 28 = +7) = L. AdEOque, PTOPTeT C (= B)
=b + 7, est 66 F a6 = bb = ac (= c0 - bb) = T. Nimiru, = F + 7a.
26. CC = a a = 2. Niminm, = 2 FBB + 7b. Vel 2 FBC- 7 7 a.
Nam c0 f ab - aa - b6 (= 18 = 26) = 2. FL, DFOPteTC(= a) = a + B + 7,
cA cc = bC = a a - BC (= 6C = a a) = 2. NiIruI, = 2 f Bb + , b.
Vel lic. PrOpter B = a F B, _c = b f y = a = B. f y, est b0 = ab + BB. + 3b.
Adeogne BC = a B = BB = y b, EC.
Vet Sic. Bb = a a F F F BC. F+C0 = BB + + + 7 a = a a + 2 F Bc +. 7 a, ec.
27. PosTune hujusmodi plures limitationes d circumctantiis quaestionis obser-
rari. Acque ex his illisre limicationibus dirigi vostumus in cencaminibus Fa
ciendis intra limites sie inrentos: eisque tentaminibus corrisendis prout facta
deprehendantur aue majora julto aue minora. Pari modo ac in quorientum
membris inveltisandis, aut mebris radicum lire simplicium poceltatum, (ire
aequacionum attectarum. Ouamvis enim hujusmodi processus sozusmoi, sive con-
fcturates,