# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/851708439:0488 # Permalink to this reading: https://leibnizlegible.com/page/851708439:0488?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 464, page id 851708439:0488 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=488 # Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000488.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 83 lines, status machine # Lines: 83 recognised, mean confidence 0.82 # 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. LL C F B R A. Sic TanS; .. 667, 5486693. 2 62, 5044427 = la15; . Cui respon. det Angulus 89, 5, 0, 17, prOxime. ErG + 2 + = -O = 179, 0,d, 17 7 tere. Cujus Sinus o,or7ASFF: nempe idem cum linu 8, 50,50, 43 Deinde; secandus sic Angulus , in r0 partes, quorum quaelibet 1. Ouaerun. tux isiCE, a, b, C, a en F, 8, B, 1. Nempe, 2360000= 6 169 Sina (8, 58, 5943, 10, 9171603. R = +:: Sin: O = O, DL745LI. L, 01694= 4. 75C Sin. B (0,5759, 43,) 0,0168694. R = F:: Sin; O =0, OF7 45TT. 1,03448- b. (816 Sinir (0,56,59, 43,) 0,0265780. R = L:: Sin; O =0, O2745TL. 1, 05264. 6 Sin; d (0, 55, 50, 43,) 0,9162877. Sini (0, 54,59, 43,) 0,0759969 Si Sinn (0, 52, 50, 43,) 0,0754752. Sin. D (0,52, 59, 43,) O,O25T243 Sinis (0, 50, 59, 43,) 0, 0148335. Praxis altera. 2,07T44 a 1,09O9T =0. 2, T2L10-) T, F3206= 13F5383 = 6 2,17647= 1. 7,20000-7 2880 313 Sit R = 1. L =0, 1. L. =1, C. A= 10. L. 180F = 179,56. = - 89. 55. cujus Tansens 687,5488693. EC, ut 2, 1. ad 0, 1: : sic 687, 5488693. aet 32,74042235 = cang; Br. 88, 15, r, 57 +. = tang; - -. Fr50 F ~ + =O = er; 178, 10, L7572. Cujus Complementum ad Semicirculum, Sc. F, 48, 58, 213. Cujus Sinus 0,0379827. ErSO, 2,00000= P: Sin; B(= 2, 47, 58, 22) == 3T4023) 329827(F, 01852 =- b. Sin; y (= 2, 46, 58, 23) = 3T2203) 379827 (2,02803 =c. Sin, S (= F, 45, 58, 232) =308208) 329827 (1,03773 = d. Sin; 2 (-= 2,44, 58, 22) = 305290) 3T9827 (1,04762 = c. 302343) 290475 296567) 293660) 290752) (1905769 =5. (1,06796 = 8 Or8 6 34 77 70 d 1891 1007 20 1027 20 (2,07843 =- B, 2047) (2, 0BOTT = 2068 2. 2 (F, 10000 = L τ080 e Flactenus Advertaria nostra. Obi duos casus expendimus: Nempe, cum L ati cudo Limbi ponitur pars Duinta, et pars Decima, brerioris Radii; e angulus di videndus, 20 minuta prima: Fanta Fere cneiBcia quantum feret vulgaris Canon Frigonometrieus. Et quidem ultima Onitas in ambisuo est; nunc justo major, nunc justominor. Radium autem (ut cgo Toleo) Facio F; (non, ue plerumque t 2000090O;) quo omnes Mulciplicationes e Diritiones per Radium Paciendae prae cidantur. Adeoque Sinus habeo pro partibus Decimalibus; quibus itaque, cum opus ell, Ciphras praemitto, quo de Unius Integri loco conster Simili procestu utendum erit, mutacis mutandio, si L acicudo L imbi sumatur in alia quaris proportione de Kaast consicudinem. Sed commontus crut (ad ricandam molelian coltes quaeettet partem proportio- nalem) uttumatur ansulus O commodae na MHaIS (Jultis minutis primis de cerminandae, absque annexis sccundis cerciitre;) acque lla quaratus Ractii maxi nt e longitudo, eodem modo quo reliquorum a, b, c, . Puca, Ly in Praxi polte. Tlore, Tumpto ut prius R = 2, ec Angulo, A = 10, Luacur Angulus O, (non Gth Illic prodit X78, 20, L,572, Sed potinis) 278, 20; cujus complemencum 2, 50; hujusque sinus in iplo Canone habetur 0,05 19022; et reliquorum item, B, 7,5, _c. Sinus similiter ibiidem sladebuntur; ut una tantum Diritione opus lic pro lingulis exhibendis; ipsaque Ractu L lonsicudo, non quidem praecise ut PriuS F, L; Ped huic proxima (qua iraque sumenda Cric) 2,09996. Nempe, Sin 19 90 17+ 264 Sin; a (= X, 48, 58 23) = 326920) 310827 (1,00918 = a.