# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/851708439:0431 # Permalink to this reading: https://leibnizlegible.com/page/851708439:0431?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 407, page id 851708439:0431 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=431 # Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000431.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 76 lines, status machine # Lines: 76 recognised, mean confidence 0.70 # 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. XCVI. A E G F B R R. 29. Si ab expolica maeniveline, sumatue = corius; iterumgues t residuji; ee sic Temper: Parces lic sumpra aequabune comm: seu (quod cancundem e) retiduum minus erit quoris altionabili. Nam, verbi pracie Fst0 = = z; hoc densfio, mo. nebit 2: demptoque porro ? hujus residui, manebir Z istius residuis hoc, est Z 2. dempeoque Z hujus, reliduum cercium exit Z secundi: hoc cA, ZX Z X Z. Ft Cc Lem ver. Ouod iditur (cum (c Geometrica Progressio decrescens in intinitum,) can- dem eranescet; erirque reliduum minus quoris astisnabili. 20. Vet lie, univertaliter. Ponamus, a = L = 0. Tum, demipto =, reliduum erir =. Demproque = hujus, manebit ejusdem =, hoc elt; - x = tOtius : et Sic deincepsy = X = X -, eC. Seu e e a aa c. Cum irague, per constructionem, sic = minus quam F: Floc, per continuam in se mulciplicationem, candem Fet minus altignabisi. ae sedes est 1B: Sedi B CBiSe .. 21. Idem sic ostenclatur. = cocius, est : et retiduum est : = hujus, ost a a ee aa aua Et sic deinceps. Sed cst = + = f = p ecc L dec. = + = 2. Nam hec, ad ee e ea aa aaa aa a a = + = _c. (singula ad singula, adeoque omnia adt omnia,) sunt ut act F ad c. Cum itaque sint (per supra demonstrata) . e C = -: erunt = + = + = + dec. = : - +. a = c aco aa a Similiter ostendetur: (DOsito ab = + =1:) = 2. Est enim hoc, ad = f 27 ab a abb a b = 2) ut Z ad I: adeoque j = 2. Fheus oe 11, 5: Trerumque: Posito b - + = f; erit enim ad = p 1 f. +. dc. Temper. = +- t ab aab L ac. + = +ec. = rir A + a b es FCi 1) ab,s - 2 mb Bu eE SEsE 2E. Si duae proxiecstiones sie componancur, ut sumacut in una coriuis A. hu. jusque E; hujusque ilerum =; e Ac temper: In allera, COciuS. B; e relidui sit cic cn 5 iterumque = secundi relidui; et lic temper: Agoresatum composiia progrestionis aguabie = aB. Nam posterior progrestio =. + + + c. rC. ab - b gesie 1F F 1XC 1 spectire mulciplicata in praecedentem = f - . - dideid a aa a la is sl h eF ida e c. conticie à a bV = 2 = 2. FdL iire ut 2 ad f. Et SC