# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/85138403X:0099 # Permalink to this reading: https://leibnizlegible.com/page/85138403X:0099?run=74 # Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmark Leibn. Marg. 103) # Folio 83, page id 85138403X:0099 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=85138403X&page=99 # Source image: https://digitale-sammlungen.gwlb.de/content/85138403X/jpgs/default/00000099.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine # Lines: 50 recognised, mean confidence 0.85 # 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. DE CISSOZDF PrOD. 64 _ 73 drithm. Infin.) Fodem modo si respectire duca cur eadem series v a, in seriem a inverlam, hoc etF in seriem : D= a: vel D= = 2 a D + a, ACF Peries D= Va = 2D a V at a Va- vel D= V a = 2 D V a + V a3, quae est ad seriem Aqualiu, sivecoridem D= V D vel. V D, uc = - 4 F = 2d r, sive uC 16 ad 205. Fcsimiliter, R eadem series V a respective ducatur in ali: 8 series inverlas, prodibunc hae rationes subjectxe. Nempe h series Va ducatur inverse in series T. a. rationes = hoc est e 4 15 277 a2 16 105 2X274 a a. 14 96. 11 768 _c. ProdibunE 945 103950 etc. 2X2X4X6 2X2XAX6+B1 3X5 3X5X7 3ZGX7X9 3XGX7XGXI Y _Co Si vero hi loci pro paribus habeantur, ex suppleaneur interjecti Loci impares; ponendo, in locoterrio, (inter I e a,) proserie a in V a inverse ducta, rationem F ad 2D (PeF PTOB. 167. Arith. Infin.) Sicur ratio loci quarei mulciplicac rarionem secundi Per 3, e hanc ratio sexti ver Z. 8c. manifeltum est (ex consecu- cione seriei) rationem quinei mulciplicare rationem certii per ex similicer in reliquis. Nempe series Na dusta inverse in Ceries rationes F. Ya. a. Va. a. Va. ec. dabie L, 2 E 2X2 2 X3, 2X2X4 + 4 2EI 3 21 3X52_ 6 3X5X72 4 X3 X Z 6 Unde, in praesens negorium hoc salrem seligendum est, series Va e V a invicem inverse ductas, ad seriem aequalium, sive ad D2= V D EOtICS SUPEU, UE - = X 2 2d 2; sive uE T ad 41. 11 Deinde, uc seriem va jam perpendimus, xerpendamus sini- sirer seriem v’a. La nempe ducta in seriem a invertam, hoc est, in D = a dac Seriem D V a = a ~ a, vel D d ae = a cui conrenic ratio 5= 7 ad 2, sire 4ad35. Ersimilirer in reliquis. NemDe