# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851708439:0881
# Permalink to this reading: https://leibnizlegible.com/page/851708439:0881?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 857, page id 851708439:0881
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=881
# Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000881.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.90
# 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.

Noble dir,
t
P 15,
etC U M.
F P LS LOL A. ALV.
D. Renelini Dieby ad D. Zch. W allis.
Receired lately From Mon(. Fermas, che enelosed iritten paper, (Ep. 46.) wvich
a detire tromhim to conreish icromy Lord Brouncker and your selF. L’hove
von have receiredmine oF che 8. (Rp. 42. ) and 25 oF Mar. A main exrand oF
ihis present Letrer is humbly co take my leare of you For lome monchs; For I am
crelons soins a journes chac will tatre up all chis summer ac che lealt. When l
return to Paris, L Will sire vou acconne ofic by presencins my humble respects
unco rou. In che mean cime L ceale turcher trouhlins rou, and remain
Noble Sir,
Pour most humble and most obedient
servant, thas hiehly Bonour et h you,
R L NF. L. M D
E PIS TOL A XL VL.
D. Fermatii ad D. Renelmum Dieby.
Praecedenca inctusa.
Llustristimos Viros Vicecomitem Brouncker de Johannem W alliscum quaectionum
numericarum a me propolitarum soluriones candem dediste lesicimas libens
agnolco, imo et saudeo. Noluerunt Viri Claristimi vel unico momento impares
Pele aut itoras quaestionibus propolitis contireri; mallem ipsos de quaestiones dignas
laboribus Anslicis ltarim agnovisse, e postquam adepri iplarum soluriones fuillent,
eriumphum eo illustriorem egisse quo cerramen magis arduum apparuisset. Concra-
rium ipsis risum elt. Id sanc glorixe Mlustristimae e Ingeniosistimae narionis con-
donandum. Verum ut deinceps ingenue utrimque asamus, latentur Cralli provosi.
iis quaestionibus satistecisse Anglos: Sed lateantur riciltim Angli quaestiones iptas
dienas tuisse quae ipsis proponerentur, nec dedignencur in Posterum nUIerOTum
incesrorum nacuram accuratius examinare e introspicere, imo de doctrinam iltam,
qua pollene insenii ri de subcilitare, propaeare. Quod ut ab illis libentius impe.
Tremus, Diophancum iplum ec celeberrimum illius interpretem Bacbetum ad aucho.
ritatem rei proxonimus. Supponit Diophantus in plerilque libri q’ee si qualtioni-
bus numerum omnem incesrum vel esle quadratum rel ex duobus auccribus aut
quatuor quadratis compotuum. Id sibi Bachetus in commencariis ad quaeltionem
3am libri qiperfecta demonstracione allequi nondum licuisse taretur. Id Renatus
ipse Descartes incognitum sibi ingenue declarat in E piltola quadam quat prOPe-
diem edendam accepimus; imo ec riam qua huc perreniacur difticillimam ee abtru-
Fistimam esse non dittitetur. Cux isitur de propolicionis illius disnitate dubice
mus, non video. Ejus tamen perfectam demonstrationem d me inventam moneo
Viros Clarissimos. Pollem e pleralque adjungere provolitiones non solum celeber-
rimas, sed ee tirmissimis demonstrationibus probatas. Fxempli caula.
Omnis numerus primus qui unitare superac quaternarii mulciplicem, est compo-
ficus ex duobus quadratis. Flujusmodi (unt5, 13, L7, 29, 37, 4.c, erc. Omnis nu-
merus primus qui unitate superat ternarii mulciplicem ele compolitus ex quadrato
et iriplo alcerius quadrati, tales Lune 7, 23, 29, 31, 37, 43, dec. Omnis numerus
primus qui vel unicate vel cernario superac octonarii mulciplicem, componitur ex
quadrato ec duplo alcerius quadrari, tales TUNE 3, 1L, 17, F9, 4. 1, 43, 8c,
Sed e praecedentem Bacheri propolitionem generalirer olim Domino de soint
Croise propoluimus, ejusque demonstrationem non ignoramus.
Omnis numerus inceger rel est criansulus, vet ex duobus, aut cribus iciansulis
compotts.
Flt quadratus vel ex duobus, tribus, auc quacuor quadratis compotics.
24949
1650.
Paris X9 Zune