# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0763
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0763?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 743, page id 851387705:0763
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=763
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000763.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
# Lines: 64 recognised, mean confidence 0.88
# 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.

PFOD. XVI. De Calculo Centri Cravitatis.
Verum potest de hoc idem Ingulae semilesmento B V A insistentis, aciem ha. FiB
Bencis Aa, momentum respectu iplius A a, lic adhue aliter concipi. Nempe, Si 259.
recta omnes ip(i AV Parallela, Semileomentum BV A complentes, ducantur in 260.
quacrata distantiarum liarum respectire, d recta AV: (hoc elt; propier aequalia
quae supponimus parallelarum illarum incerstiria; in seriem secundanorum, ut 0.
4, 9, c. quorum maximum sic remorissima parallelarum distancia quadrata:)
Nam rectarum quaelibet in diltanciam Tuam ducta, extribet parallelosrammum ci
dem insiltens in Semiquadrantali Ongula expolica; idemque icerum in candem
distantiam ductum, exhibet istius parallelosrammi momenuum respectu AXIS AV,
Peu Aa. Adeoque simut omnia, illius parallelosrammi momentum.
Ouxque de Oneula dicta sunc; solido ejuldem plani B V A convertione im-
vertecta deleripro tacite ( ex praemonstrais) accommiodari porerune. Sed de tris
tractenus.
13C
Progredimur ad impersectum Sectorem, Sectoris plani B a A eirea A a. impersecta
convertione descriptum; Onsulamque huic correspondentem. Ouancum scilicet,
in tis, Cenirum gravicacis diltac ab Aen convertionis, ANC, seu plano per actem
Ongulae perpendiculari.
Ouxe Friangulo B Va intistie semiquadrantalis Ongula aciem habens A a Ps
ramis elt; Cujus rertex a; Basilque criangularis ipsi B V insiltens. Centrique gra-
ricatis diltantia ab Aa, 2X35 = =5. (Ouod eodem modo octendetur, aique in
SO. de Pyramide criansulo BV C incumbente.) Ejusque magnitudo (per 5S
DrOP. Praced. ) 3s 2 h. Adeoque momentum respectu A a,  S B = 553 R =  SV
Ouod quidem addicum momento Onsule Sémisesmenti BV A (SO. invento
SC 3  35VR = = 25 R f 1353V; exhibet Semiquadrantalis noulx sectori
BaA intistentis, aciem habencis Aa momencum respectu iplius A a, 30 A +
8SV R =  12
Edemque sic habetur. Semiquacrancalis Inoula Prianeuls B C. a, aciem habens
Aa est item Pyramis cujus vertex, a; Balisque Friangularis (ipli C. B insilten.
tiS.) Centrum graritatis ab A a plano distat, Z BV = 35; adeoque Cencrum PY
ramidis inde distat, 3X35 = =s. Adeoque, propier magnicudinem 55= R (per S S
DrOP. PrxCCd. ) momencum, =53 R. Acque hoc Addicum momenio Onsula BC.A,
SP. InVencO,) SCR f 552X2; extribet momentum Onoula Semiquadiantalis
Sectori Ba A insistentis, aciem habentis A a, respectu iplius A a, SC R3 F 35VR
 i sR. OF prius. CFujusque duplum, elt Semitolidi corrclponcentis mo-
mencum.)
Acque hoc Ungula momentum, per ipsius magnicudinem divitum; hoc est, per
VR = F SS=R, (Der S S. PFOD. Praeced. ) extribet hujus. Ongula Sectori
Ba A insistentis, aciem habencis A a, distanciam Ceneri gravicatis ab A a plano,
ZC R f 35V R + 25
8v R = 45
Adeoque Semitolidi correspondentis, distancia Ceniri gravi.
cacis est ab Aaconvertionis axe,
ta ut 4 R ad Z.
SCR + 3 50 R + 25 P: nempe aet illam Vnsu.
2V RP F 52 D
dimiliter otendetur, Ongulae Semiquadrancalis Triangulo B A V intillenris
aciem habentis Aa, (qua etiam Pyramis elt,) Cencrum sravicatis ab A a plano
dictare 2x35 = =5; magnicdinem este ss =V; momencum respectu A a,  53V.
Acque hoc ex momento Onoulae Semilesmenti BV A (S O. invenco) sublacum;
extibet Semiquadrantalis Ongula, Segmenco AB A intiltentis, aciem habentis A a
momentum xetpCC A a Se P3 = 35VR == 2
le
Vel etiam; Dnoulae Semiquadrantalis Friangulo B A C insiltenris, aciem haben-
is Aa, (quae vel eyramis, vel lalcem duarum Prramidum agcregatum vet ditte
rencia, quarum communis balis criangularis ipsi B V insistic,) Cencrum gravicario
similiter ab A a diltare, 2x35 = =s; magnicudinem, 5S2 R; momencum respectu
Aa 225 P. Atque hoc ex momenio Ungula Sectoris B AC (SP. invento)
Be R3 = 85VRZ Subductum; relinquit se R3 F SsV R 2L , +53 R, momencum
respectu Aa Ongula aciem habentis Aa, ipLI AB A, Scomenco insiltencis. VE
Prius. (Flujusque duxlum LC R3 + + 5V R2 =553 R, momencum semisolidi cor-
respondentis.)
EIIdGuE