# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851708439:0416
# Permalink to this reading: https://leibnizlegible.com/page/851708439:0416?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 392, page id 851708439:0416
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=416
# Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000416.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.87
# 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.

A E G F B R A.
Cap. XC. V
cibus Auentibus iplas ponit quancitates punctis nocatas in hunc modum. Sint
V, X, Y, 2 Auentes quantitates, _ earum Auxiones his notis 2, N, 7, 2, designa-
buncur respectire. Ec quoniam lx Auxiones sunc eciam indeterminacx quanti
tates, et perpetua mutatione redduntur majores vel minores, considerat relocitates
quibus augentur rel diminuuntur tanquam carum Auxiones, es punctis binis no-
tat in hunc modum i, i, j _ _ perpetuum incrementum vel decreMenEuM
harum Auxionum considerat ut iptarum Auxiones, ec punctis rernis _C nOtat
V, X, Y, 2, de harum Duxiones punctis quaternis sic v, N, y, 2. Oua ratione o
est Auxio quanticatis v, e i Duxio iptius v, de i Auxio ipsius v. Ft si quantita-
tes Auentes vet tractae tunc vel turcae, Auxiones carum siC nOtaI. OUaHEITatuI
 Vaa nu, Auxiones sunc: e Vaci xu, ee tarum Auxiones sune
: et Vaa x et lic pOrrO. His autem expolicis mechodum Tuam in PrO.
Doticione hacce problematiea tundat.
P R O B. I.
Daca aquatione, suenies quoicunque quanticates involvente, invenire puixiones.
SOLV FFO
Mulcixlicetur qualibet aequationis terminus separacim per indices singulos dieni-
tatum, quantitatum omnium Auentium, qua in termino illo continentur; de in
lingulis mulciplicationibus mucetur lacus unum disnitatis in ejus Auxionem; et
aggrepacum productorum omnium sub propriis signIS COMPONEt. aequationem nO.
ram, qua relationem Auxionum inrolret.
E X PL IC A F1D.
Sinta, B, C, a Rc. quancicates determinatae d immutabiles; _ proponatur X-
quatio quaeris quantirates Aventes 2 y, N, _c. inrolvens, puta N = x p y - ( a a Z
b. =0. Mulciplicentur cermini primo per indices dignitatum iplius x in iplis
concentarum respectire; et in qualiber mulciplicatione pro uno latere dignitatis
(hoc est pro n unius dimentionis,) scribatur a ee summa productorum exit
3 X x =  y Y. Idem Fac in y e producetur =2. N y y. Iden fiac in Z, ee produce.
cur = a a 2. Summa productorum omnium aguetur nihilo; et habebicus aequatio
3 i  = ary - 2~gy + aa 2 = 0. Dico quod haec erie aequavio relationem
Auxionum inrolrens.
St MO_S L_ A L Ld.
Sit enim S GuaEas SuInite parra, Ce LInE OZ, 0y, Ox Synchrona momenta lei
incrementa momentanea quantitatum Auentium Z, y e _: e hae quancitares proxi-
mo temporis momento Dex accestum incrementorum momentaneorum cracent
2 F 02, y F oy, N =Ox: quxe in aequatione prima PrO B,Y _  lexiprae, dant
hanc aequationem dd = 3 d X O v F 3~ 00 X x = 3 ~ 0 = b y y = xOyy - 2Xoyy
abbsbdtad 17+a2t+4tdtb  o. Subaue d
GlaliBnEM