# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0701
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0701?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 681, page id 851387705:0701
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=701
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000701.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
# Lines: 68 recognised, mean confidence 0.86
# 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.

PrOD. VII. DeCalculo Centri Cit aouaris.
mentorum, sive momentum totius, (respectu plani per rerricem A S, baLI paral. L B
deli,) uc - =, = NDP, (nempe, ad momencum iptius N P in diltancia D suL.
Denti, uE F ad = 5 + 2; Propter teriem Momentorum, uno eractu alciorem,
quam est series Ponderum:) Per E hujuS. AdeOque, PFOPICK =
5+2
5J =D exit distantia Plani A quilibrii (Per 20 Cap.
3.) adeoque et Cencri Cravitaris siguod est, (per 24. C ap. 4. ) = 5 L
=D; 2dc0-
que reliquum distantix maximae, (quae l’aseos est,) -  - D. Haec ilut ad il-
Jam, est uc F ad - S F 1, (in racione tinica; Propter = 5. f. x quancicarem potiei. K.
vam:) Si itaque cora distancia D (batis d verricem) ita divicatur puta in C; uE
pars ad balin, C. D, sic ad parrem quae est ad verticeni; C A, ut F ad - 5 f E; pla-
num per C crantiens, baliparallelum, est Planum Aquilibrii. Per 20 C ap. 3. LC
quidem (siuerinque ad Diametrum vel axem similiter construatur tigura) in ipso
Diametri vel aris puncto C, (per 5 hujus.) Sinminus; Caliem siquod est Cen-
trum Graricatis, in eo plano cst. Per 24 C ap. 4
Dico aucem, siquod est; quoniam, in tigura dimidiata (vel quae istiutmodi est)
Feri Potest, ur Cenerum graritaris, utur in C B intinica intellisatur, intellivenda
tamen sic ab ipso C. puncto in intinira distancia, (ut in prop. Seg. ostendetur,) adeo-
que nusquam crit.
Exempli GratIa. Si LC A DBBS Figu-
ra, ex serie reciproca lublecundanorum.
conslata; (puta, cujus rectae vel plana
Tinc in reciproca ratione ordinatim ap
plicatarum in parabola:) cujus Index,
=Z. Adeoque, ad inscriptum Parallelo.
grammum vel Prisma ADBA, (quod
lic NP,) ut F 2d - 3 F F; hoc est, uE
2 2d 2, vel 2 ad Z: nEPC UT Z NP. NIO-
mencorum eries, indicem habebie
F L vel Z; (quippe uno sradu alcior quam Ponderum, propter diltancias arich.
metice provortionales:) Adeoque torius momencum, ad momentum Parallelogram-
mi vel Prilmacis in diltancia maxima appenti, (quod ( NPD,) uer ad +-
hocelt, ut Z ad FZ, vel 2 ad 3: Nempe, ZNPD = 2N PXS D. Oistancia itaque
Plani Aquilibrii (ee, liquod est, Cencri Graritaris,) a verrice, elt: D. ejusdem-
que propierea a Bali dillancia, SD. Adeoque haec ad illam, (hoc eAt C D ad C. A,,
ut 2. ad F: vet LadZ; hoc elt, 2ad - = + L
Si sic ex serie reciproca Fercianorum; cujus Inder =3. Exie lumlla Ponde.
TUIM, (DFOPTeF -5 F F
et
ut X ad 3, hc 3 ad 2;) ZNP. In.
dex seriei OmenTOruM FL =
Adeoque (propter 3 F L =
d
Tad 3, uE 3 ad5) summa Nomen-
TOTUM ENPD = 3N PX =D. Adeo
que plani aequilibrii (_, s quod
elt, Cencri Graricaris) diltancia d
verrice, ZD; a bale, 3D: Adeo-
que haec ad illam, (nempe CD
ad C A, ) ut 3 ad 2; vel X ad
VCoap, Y CFap. V C4 4p. V C9 ap. - - DP.
hoc elt, F ad = Z F F. Atque in aliis similiter.
3NPD = 3X
Si itaque in ea ratione diridatur AD in C; Sirque Figura verinque similicer ap
plicata, ad AD Diametrum vel Axem: erit C. Centrum Gravitaris; per 5 hujus
Sin minus; Calrem planum per C. est planum squilibrii; aique in hoc, siquod
siu Cenerum Crraricaris
Porco; Flabicis hoc pacto, tum Fieura torius ADBS, tum absci UE ACB5,
RPEK
maeni.
L
N.
d.
V0dD. VEdP. V-Y. Y3dp =- DP.
1c0
ENPD = ZNPKS D