# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851708439:0790
# Permalink to this reading: https://leibnizlegible.com/page/851708439:0790?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 766, page id 851708439:0790
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=790
# Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000790.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
# Lines: 58 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.

C. O M N F R C F U N
Invenire duos numeros quadratos, qui partibus suis aliquoris additi eandem
efficiant summam. Fxempl gratia 16 F 8 + 4 + 2 + 2 == 3r = 25 + 5 + 1.
Inveniantur ejusmodi alii duo.
Buc T added wichal, chac P looked uxon problems oF chis nature, (oF which
it is caly co contrire a great many in a Tucle cime,) co hare more in chem ot la-
bour chan cicher ol Ve or Disticuler.
Since chac cime L have (pent no Further chouphes abouc il For being jull
chen called trom home by chie deach oF a near triend: Betore L BOc home again
P understood chac my Lord Brouneker had boch relolved chole evo, and allo a
lacter problem From che Pame hand, on irhich L understood chat (varins che
Former inguiry) MonL. Fermat did lay a orcacer Irels, as more contiderable chan
chose Former. Which problem beine boch receired and antvered, betore L heard
oughe ot ic; Y conccired ic necalels For me actum acere. Whac his LordMips
Solution oF chis latter problem as, L am noc able io cell, nor so much as Wrtiat
vas che problem; noc having any Copy ot cicher. Buc L know his Fordthip (0
vell, and his peculiar dexcericy in chinss oF chac nacure; chac P hare a vers ArOnS
prelumprion oF che accurarene(s ot wtrat he doch in lueh a way.
THaE OcHer lCTLeF OF MIONI. Fermat co vour CelF, et ertrich von incimate chac L
may expect a Copy From MI. WVhite, is noc vec come at me; ies poltible ic may be
vet lodged in my L. Brounckers hand, eo irhom ic ras tirst co be communicaced.
lcan ontr, for chac and all ocher vour noble Favours, cender vou my very hum-
ble chants, heine in no capacier ot makine any valuable retaliation; Vour revard
beins onty che conscience or jour oun senerous inclination co tieap lavours on
chole trom irtiom rou can expeet no recompente,
Mallonty add aterr mords and tiss vour noble hands. And ris buc chis;
chat since rou hare been rillins co gire vour selF checrouble, and us che hOnOUT,
eF impartine papers becrixe Monl. Fermat and ny Celt, Lchoughe it noc Whony
incongruous co subjorne a Fheorem, irhieh il ic Chall (0 scem 800d tovou, vou
may cransinit eo him eo be demonstrated, noc as a challense nor as a matier ot an
extraordinary ditticuley (For P do noc cake ic (o eobe:) buc such as in che solurion
oF ic may probably Cuorestrohim (ithe knou ic noc already) a preur handlome
Speculacion, irtrich pollibly may be nocunveleome co him. Jhe Pheoreme is chis.
Sit Ppramidis vel Coni Frustum (parallelis planis abseissum;) cujus basis ma-
jor aequetur quadrato rectae R: minor, quadrato recta P.; altitudo P. Dico. Si cru-
ribus A, P, (vel his aequalibus) constituatur ansulus graduum 120; ex circum
scribatur circulus; duadratum Racii cireuli sis descripei in allitudinem frusti du
Etum (RGF) aequatur Frusto.
The Demonstration oFie, or whaterer at any eime L Prail be in any capacies 10
Terre you in; sou may command ac pleature trom him WHO ACCOUnES IL a BreaC HO.
nour  de audo be repuree,
RieBL NNoble Sit,
Tour affectionate and verr humble servant
DOTEN W ACZL5.
Oxtord Sept. 3.
EP LSFOL. A. Y LII.
Sl. Vel. 1657.
D. Pctuicis Brouneter, ad D. Joh. W allis.
Vam, Vir Claristime, quinto hujus seriptam helterno die recepi; u d illam
ad D. Kenehmum Diebr, QuX QuaM MaEUTE POLIO ad illum cran (MICEtIE
Oua AUTeM MCMOTASd D. Kenelmo Dieby ad D. W Bite millam, ue neDIS impertIa
tur, nondum accexi, neque de illa quiequam inaudireram. Obi illaut dcpero
ribi crantmutendam curabo. Incerim en ribi, quam peris, D. Fermatet Gua toeM
cerciam, meique ad illam responsi summam; (ipsa Siquidem verba nelcio exhibere,
cum corundem nullum apud me apograptum recinuerim:) quod camen fecillem li
Ducalsem D. Whise relponsum illud eadem Forma tuisse cransmicturum. Poreris, A
ribi vicebicur, Larine candem crantmitere, (L. p. 16.) ul non lib el a ldiomale
Ansli