# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851708439:0388
# Permalink to this reading: https://leibnizlegible.com/page/851708439:0388?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 364, page id 851708439:0388
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=388
# Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000388.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
# Lines: 46 recognised, mean confidence 0.86
# 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.

L GE B R A. Cap. L XXXIX.
a = aac + ab -
 = ec. in intinicum.
Obi, praeter intinitam seriem proportionalium a diritione iptius a oriundarum,
accederet alia a dirisione iptius e similicer oriundarum; ex quibus, poltquam
Concmrrun, Runc 2 + 2, 8ec.
Similia (mucacis mucandis) in alis casibus contingent.
Pura
Sed
+c
+
aa - a c + ec.
=aa - ac F ee-
ec
Si Va diridenda sit per a = e; Ouoriens prodibir,
Si Va = Ve HC AIIaAEUE; res pariter in infinitum procedet, (quia nunquam
pervenietur ad Subducendam qua destruatur - Ve:) Sedrum, pro lerie proxi
me memorata, (oriunda ab va per a - e dirita,) accedet alia oriunda ab = Vc
dirisa per a - e seu =e. f a. Nimirum
 eve eeve e
ec. intiniie
Quorum omnium, sumiliumque, evidens et racio.
Va  ava t aava t a  dec. in intinium
LP.
X
Hujus Collatio cum Reductione Fractionum ad Decimales
 dexacesimates.
Ac in Speciebus Diritio, ejuldem naturae est (sed maxis Oniversalis)
cu Reductione (in numeris) Fractionum Vulsarium ad Decimales.
Ouam rem hic palilo Fulius prolequi liber, quoniam nescio an quisquam
me prior, eam dutinele examinaverit. Delinis ea aliquando in determinato Ouo.
tienre, Ut Z -F0, 5. 5= 6, 2. 10 = 0, 1. 4 6, 25. 6=0, 125. 20=6, 25. 15=3
Duod cum concingit, et non alias, quando (tractione ad minimos terminos re
ducta) Denominator (Tcu Dlritor) componitur ex non aliis primis numeris
quam 2 e5; ex quibus s0 componitur.
Sin Denominacor (Fractionis lic reductae) ex aliis componacur primis, quam
2 8 5, Ouoriens elt interminata. VF Z = 0, 3333 ec. 3 = 0,6666 ec. 1 =0
0009C. 2 = 0, 1818 _C. 13 = 0; 076923,0769_C.  = 0; 148, 148, 248, ec.
27 = 0; 0549054, ec.
In quo casu; haec semper occurrie concinnicas; nimirum, quod, post pro.
celtum aliquatenus continuatum, redeunt iidem numeri, et codem ordine circu-
lantur quo vrius. 1
Aliquando quidem, repetita cadera tgura lingulart;  IIL 3, 5. Aliquando,
binis liguris; ve in +, . Auc ternis; uc in 7, 57. Aut pluribus; ut in ,
Sed semper, si non cirius, pott coc locos uno minus quoc lune in Dirisore Vnicates.
Verbi