# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/827130880:0147
# Permalink to this reading: https://leibnizlegible.com/page/827130880:0147?run=74
# Title: An Introduction To Algebra (shelfmark Leibn. Marg. 87)
# Folio 131, page id 827130880:0147
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=827130880&page=147
# Source image: https://digitale-sammlungen.gwlb.de/content/827130880/jpgs/default/00000147.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.84
# 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.

Resolution of Problemes.
P Bould non Pem hon the compendious mays oE hi
c. f. 8. and x do arise out oF the ArH PrOCe(S OF Probleme 28
and how chac Process miohe De so improred as chacic miphe
direct rou co make Innumerable changes ot aIL chc afUFCO
Eguations, 25
FOF
TY(0= p - n
22 f- 4n- p
2Z
= 21
27 d = 4n
toreite
(e - p -. 412
f = 9n 1
d =- 9n
29 FTV F p = 2 39n  9p = 3
Andso, (For examplo, takins q = 2) 10 find v =- 2475 ∞33
25069223.
a = 2837207 - X. A. 4 1D = 244-= 247
B = 29663OT -: XXX F = 53- 247
C = 2982858 -- XXX F = 27 -: 247
D = 8785296-: a xx C = 16-: 247
50 chac by changing the Value OF C vou mashave aS grcal
Varieties rith chese Assumptae as Wich the FOrMeF.
There miehit also other very different mays OE LoMS
ehis Problema 9. V. Diophanti, Deadded. Bue iF aII Bould
bc set donn chat mighe pertivently De tritren concern
ins che suxplys OE this Defect in the Manuscripes oF Dio-
phantus, ic vould matie a large Treatise.
Probl, ZXIX. T0 End erro equictutat LMlaneles Cqual re
ore anocher in Perimeter and in Area; every onc ot cheiehdes
and perpendiculars beine co cach oF the relt as some numiber
is to lome number.
(Fran. Van Schooten, in the ZII. Section Ol is Sectiones
Miscellaneae, tells us, chac this Probleme havins been openly
propoled at Paris Anno 1633, Mon(ieur Des C’artes eave chat
Solution Which he chere sers donn. I Mall here expressit in the
Cyse oFchis b0ok, nor changins His letters, thac his work mas
beeasils compared mich chis.)