# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851708439:0300
# Permalink to this reading: https://leibnizlegible.com/page/851708439:0300?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 276, page id 851708439:0300
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851708439&page=300
# Source image: https://digitale-sammlungen.gwlb.de/content/851708439/jpgs/default/00000300.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.85
# 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.

E G E B R A.
ap. L. XII
DP = 2BD = QBP = b Byp = 2: b .c. = Dbpy - b.
20b bb = 000120b = 66
eB = (R DP = EP APF = 0 i2 21 - 0 -) 2Y5 - 50
Ergo (deletis - c5 ubique) a a c = 240 = bbc f 2b0 = 2Y6.
Et (transponendo) a ac - bbe = 246 = 2b6.
Et c at
BB
2a. = 26e
2.
c
de
ErgO dre (= 2r6 == a a C = 2a6) = aaC = a de (PFOPteF de = 26.) FF
dr=aa - a d.
Hoc cst, r =
e
m
EC = CD.
Invenimus igitur cum Cennum cum Radium peripheriae DD, ad cujus singula
puncta cocunt AD, BD, ut crat imperatum.
Ouodque non aliud aliquod (in eodem plano) punctum sit (Prxterquam PC.
ripheria DD puncta) ad quod coire porsunt (ab A, B, Punetis) tales recta; ta
cile demonstratu elt ex 7 primi Fuclidis. Adeoque hac peripheria, locus e (et
adaequatus LOcus) talium occurluum in eodem plano.
Si autem eadem peripheria, circa F F axem conversa, describat sphaericam si-
perticiem: lingula hujus superticiei puncta praestabune quasicum. Ouique jam
elt locus ad circumserentiam cireull, cune tier locus ad sphaericam superfiiem.
CONSTRVOTTO.
Si sumatur itaque (in AB) ut m F n ad m SIC AB aet AF: Trerumque, ut
M = n ad nn HC AE ad FC: Centro C, dittantia CL, deteripta peripheria L.DD,
Cst LOcus ImPCratuS.
E. X E M P L. V M.
Si sit m adn ut Z ad 2; sirque AB = +5: Tum eric AF = 3 AB = 3; e
BE = 2 AB =6. Et nE (3 = 2 =) F, ad 2; SC CrIE AF = 9, ad FC = 78.
AdCOGuE AC = Z7; BC = 12; L. P = 36; AE = 45; BF = 30.
DE Y E R M P N A F1O.
Y. Manisestum ellu ex Analyli; oportere rationem dacam m 2d n, este inaqua.
litaris racionem. Nam, PEOPIeE r =  a; hOc est, ut m - n adt n (seu ut
a = b adt 3) sic a (= AF.) ad r = CD: E eNet m = n adeoque m = n = O: F0-
Fet r = FC infinita. Hoc est; quae pralumitur circuli circumserencia L.D D, de
generarer in (perpendicularem) rectam infinitam.
2. Omnium, AD  BD in ratione data, brerissimas esse AE, BF: (nam, hisce
breviores, non perrinserent ab A ad B:) omniumque lonsillimas AF, BF: (nam
si forent his longiores, et in ea ratione earum disterentia major Foret quam latus
AB, ut cui jam aequatur; adeoque non possent ad D coirc: quoniam, AB F BD
simul, non minores esse debene quam AD.) Veroque calu, (breviltimarum, intellige,
ee longistimarum,) degenerat criangulum ABD, in lineam rectam; cadence
BD in ipsa AB salcem producta. Priori quidem, per replicarionem (ipsius
BD super BA) in BF: Polteriori, per explicationem (iplius BD in conci-
nuatione rectae AB) in BF.
Libet hic subjungere Problema quoddam, non magni quidem momenti, nec
magnae disticulcacis; led spcciminis loco pro ejusmodi Lurellisacionibus insticuendis.