# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0463
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0463?run=74
# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 443, page id 851387705:0463
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=463
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000463.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.89
# 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.

EFOD. C L. XD
ENFINTTOKU
L AO P. CLXZ.
Theorema.
CFries duae, in exposita Tabella, nempe Monadicorum, et F acerati
Lum facile interpolari poltunt (locis interponendis quotlibct;) in-
terpolicis scil. illic quor opus est, unitatibus; hie, cotidem mediis A-
xithmeticis.
Puca, Ei placet unum ubique numerum interponere; erit monadicorum series in-
texpolata, E, E, E, E, F, F, F, Fy F, E, T, T. Lateralium rero 5, 1, 12, 2722,3,33,
4335,52,6. vel Z, 49272927 333,4, 2,5
6.
Racio patet; quoniam numeri lunc illic aequales, hic Arichmetice proportionales.
SC FZO L. ZV M.
Deliquae aurem series non ita Facile interpolantur, nih invento prius cujusque
fexiei prorio charactere; quod sequencibus propolicionibus invectisabimus.
e ROP. CLZXL
Lemma.
DRopolcu  Inquirere, quam habeant rationem numex Tpiangu
laresus adt suum latus.
Illud hoc prosrectu inreltisabimus.
2. Si puneta cocidem, quoc numerus aliquis
triangularis postulat, debira forma criangulari
dispOnAnEUE, _ reCtIS COnjUNGANEuT, ut in ap
Dolico Schemare; manifeltum elt toram figuram
Triansularem in toc criangula diridi (tam tou,
quam incer se Limilia,) quot est quadracum nu-
meri laceralis unitate minuri, ( quod A opuS LIt,
demonstrari potest Cx 29C 6.) Adeoque l ipLuS
numerus laccralis sir h erir numerus triangusorum parricularium : J = Z: = 72 -
. Snum porum criangulorum quodlibet habent res angulos, eric horum an..
Sulorum numerus 31 2 = 61 + 3
3. Nocandum elt ad corius tigura eria puncta angularia, non nisi toc anovlos
adjacere (nempe ad singula unum:) de propterea illi rres anguli occupant eria
Duneta, Peu 3 l.
4. Ad reliqua puncta in laceribus, cerminancur anguli cerni; quorum ixirom
quilibet occupat triemem puncti. Sune aurem intermedia illa puncta lateralia, in
quolibet latere 1 - 2, erso in omnibus 3l -6, (nempe proprer eria latera;) ee
anguli ad haec incermedia puncta adjacentes 9) =18, (propter ternos angulos
ad ringula puncta;) quorum quolibet occupal urieucem punctis seu + P; adeoque
omnes occupant 3 = F
5. Ad religita qua tupertunc puneta, inera aream tigurae, terminancur anenti
seni (ad quodlibet nempe Pex,) qui propierea occupant sextancem puncti. Ouot
aurem iIII sune ansuli, sic collisitur. Tocus angulorum numerus cst (ut dixi-
US) 312 -61.F3: FTInC SI LubduCaNEur 3 (ad cocius Fgurxe angulos potiu)
e 91= 18 (ad puncta laceralia adjacenres) manebunt 312 = +51 F 18; 9ui
elt numerus angulorum ad puncta incra aream terminacorum. Cum vero no-
cun uibet decupat sexlatem puncti, Are S P; occupabunt hi omnes
R. K H 2
Denique,