# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851708439:0368
# Permalink to this reading: https://leibnizlegible.com/page/851708439:0368?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 344, page id 851708439:0368
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=368
# Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000368.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine
# Lines: 60 recognised, mean confidence 0.81
# 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.

C F
i LL L. LL C LL
De duabus aut pluribus Seriebus connexis.
Adem de Seriebus Infinicis doctrina, est (in Intinitorum Arichmetica) Dua-
L. bus pluributre Scriebus accommodata, per = aut = connexis.
Verbi gratia. Series Laceratium,
aucta Seric Duadratorum.
da7.= 0ad
cdF + 2da
2.dT + 4 dc
3dT + 9dd
ecc.
_C.
Vsque ad DZ + DD
Summa, 3mDZ  : n D∞.
Nam Od F F d Y 2 a_C. CHL (Per GCHETALEM MCaM PTOPOTILONC SUPTA Ea-
dicam) = = m D. Adeoque 04 + E4Y + 2 d  ec. = =m DT. Oua CAt
cumma prioris columna. Irem Odd F E d d  4d d ec. = = m D D. OuIX est
summa posterioris columna. Ergo Zm D T + Zm D D est Cumma limul urri
usque.
Dux quidem Ouancitates Tunc ut Ouadrata Ordinatarum in Hyperhola: ni.
mirum
a d
L: VBI L, 2, (lacus Rectum de Prantvertum) sune quamica.
tes permanentes in eadem typerbola. Sed d (diameter intercepta) variabilis.
pro alio atque alio applicationis puncto. Oux itaque s succestire Tumpea SE
Ut O, F, 27 3, ec. Teu Od, F d 2 d, 3 d, Cc. quarum maxima sic D, Segmenti Dia-
meter; Ouaceara Ordinatarum aequalibus intersticiis sumprarum figuram complen-
tium; erit series quanticatum in ratione jam expolita. Pe, consequenter, lic crunt
Circuli complentes Conoeidem Cyperbolicam (urpore in diametrorum seu semi-
diametrorum ratione duplieata, sre uE Carum quadrata.) Sunt autem toridem
complentes Cylindrum circumleriptum (ejusdem basis ex alticudinis) maximo x
quales tinguli. Erso: Conoeides Fyperbolica, ad ejuldem balis e alcicudinis CY.
lindrum; est, uc illorum summa ad Tummam Borum; Peu, ut illi omnes. ad maxi-
mum cocies sumprum. HIOC e, ut Em DZ =5m DD, ad m D Z ; m D D;
hoc cst, uc 3Y + 3D ad Y  7
Fc, consequenter; Si sumatur D = Y; erit Conocides ad Colindrum, ut
28
ad 2; hoc elt, ut 5 ad +2. Si D = Z T, TuM CM 3 2 +. 5D
Y) ad F-
27 =3F,) ut 33d 3, leu 4 ad 9. FL Lmi.
licer de aliis casibus judicandum.
Similiter; Si Scries Lateralium muletetur
Serie Ouadtratorum. Prout sunt Ouadeata
Ordinacarum in FllipC, Circulore.
5d L  Da et
ecc.
ec
V(que ad DY = DD
Summa :m D T =- : mDD
0a2
EaL = Tdc
=4. dc
L. (quo casu ballo Cll ataaimus paralle.
lorum in Conoeide seu Spharoeide Circulorum, per Centrum trantiens,) Cru
Fst ixicur Elliprica Conocides, ad ejusdem balis de alticudinis Cylindrum; ut
Et, consequenter; Si suau D=
Em DE. = =m DD, ad n DZ = m DD: (en :Y = = D ad 
Seli 2 dd 3. Adeoque i L Mabet Hemilphaerium Lei CCphaeroeides, ad ipli
Careum.