# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/851708439:0132 # Permalink to this reading: https://leibnizlegible.com/page/851708439:0132?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 108, page id 851708439:0132 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=132 # Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000132.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine # Lines: 54 recognised, mean confidence 0.83 # 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. 6 l. B. l Cap. XXII occuxtam gna. invicem tigna - numero paria; hic vero, imparia. Adeoque alternis potestatibus Fxemplo res erit manitesta. Fx de primo casu f A F F, liquet ex mulciplica. cionibus lupra tradicis. De reliquis sic liquet; F RadiX. LF. = F.9 AL + F. 4. Ouadeatum. AF. ZAGE L AFC AgC. F 2 AF. 9. = F. C 292. F 3AF. 9 = F. C. Cubus AC +SRGC.A- 3 AF C F L. 90 tA99 = 3ACF. F ZAGF g - AF. C +A44 4 ACk +0+4L. 4 4 A F. c. F B. 99. Biqualtratum. e. Radir. c AF AF. + P. g F A9 + 2 AF. + P. 9. Ouadr. AgF. = 2 A H. 9 lC =sAgF. - 3AF. 4 = F. C. Cubus. FA94 Y SACL = 3AGF. 9 F AEC AcL F3agF9 + 3AF C F F. 99 + A99 + 4 ACF F 6AgF9 F 4 AF C F F 99. Biquadratum. eC. =AC = 2AgF. = AF. 9 Tioner eriam ex continne proportionalium natura, qua lede locandum st quod- vis membrum cujusque porestatis. Supponendo (quod ulu renire (olet) radicem binis Fiouris scriptam, quarum altera dicatur A, altera F. Ouamris enim Radix in qualvis duas partes pro libitu direlli postic; puta, y in 4. = 3; uE SIE A = 4, E = 3: Nam etiam BC A9 = 16, f 2 AF = 24, f F. 9 9: Lacienc 49 = 7 4 Actamen, in usirara Radieum extractione (quo res haec poristimum spectar,) ubi Radix binis nocis seribitur, puca 57; prior censeri solet A, posterior L; ut 5 (hoc elt 50) sC A; et 7, F. Cum itaque, in radice, siF A =5, Sed Tubincellecta ciphra sequente; A 5. sedesiplius s’erie locus secundus, seu supra monadtum lOcum prIIIS: F. 7 Sed7 (propter nullam hic Cubincel lectam ciphram) sedem habet in ip lo mo. nadtum loco. Trem in guadrato; Cum st A g = - 5X5 = 25; hOC Cs, (propter ciphras duas Fubinte llectas) 50x 50 - 2500: Sedes quadrati 25, criilocuscercius, (qui est su- pra monadum locus (ecundis.) Sed A F = 5 X 7 hoc est (propter unam ciptram Cuhincellectam) 50x7 350, adeoque 2. A = 700; Sedes ipLIuS AF = 35, adeoque 2 AF = 70, erit in loco decadum, seu primo supra Onitacum locum. Denique F g = 7 x7 = 4 (Dropter E Gnomon