# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0761
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0761?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 741, page id 851387705:0761
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=761
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000761.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 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.

Prop. LVI. DCuam Centri Cravitatis
Verum in horum Semisolidis, solidisre impersecta quaris conrertione deserio.
tis; Vnoulisque correlpondentibus: nondum decerminancur ipla Centra; ut qua
L13
259
non in ipto Arc polica sunc, sed alibi, exrra axem, in planO per atem Iai 160.
Feunte.
Cum tamen in quo per Axem convertionis, seu Aeiem Ungulx, transeunte plano
constiruta Linc, jam constet ex s G prov. T2. hujus; (nempe, in eo per conversio
nis axem plano quod solidorum, conrertione tactorum, arcum convertionis bile.
Cat; eoque per Ingularum aciem plano, quod bisccac ungulae alcicudinem:) AF
que in qua quidem hujus plani recta, jam lic determinatum; nempe in eis quoxum
Axis seu Acies eA A a per Centri graritatis distantiam, a ra, T A, BV, ec
e in eis quorum AXis elt Za, F A, vel BV, per ejus ab Aa distanciam: Id F0-
tum superelt, uc in quo iltius rectae puncto sicum lic, determinemus per ipsius a
convertionis axe distanciam in eis qua convertione describuntur Solidis; ee, in
Ungulis, per discantiam a perpendiculari per Aciem Plano. (Unde iplum grari
cacis Cencrum determinarum ii contat, peT PrOP. 26. CaP. Prxced.) Id ducem
sic axcrectimur.
OE Sectorem Sphaericum incesrum, B CBA, S A, (plani BC. A cicea rectam
Aa incegra conversione deleripri,) sic ejuldem semillem seu Semilectorem Sphae
rieum, aliumre impertectum, (convertione dimidia, aliare impertecta deseriptum, )
incellisamus ex Pyramidulis (similibus e aequalibus) componi, (juxta det. I.
Cap. 4.) Ouarum communis vertex lc Sphaerae centrum, Basesque compleant
Superticiei Sphaericae porrionem Semisectori huic, Sectorire imperfecto, convenien-
rem: nempe Frilineum Spharicum, quod Sectoris Basin appellabimus,
Cunque (per s hujus) Cenrri graviratis in Pyramide, diltancia a vertice pyra-
midis sic 2 corius alcicudinis; Pyramidularum illarum omnia Centra graritatis
(aequalibus ab inricem distanciis remoca) incelsisancur complere Simile Prilincum
Spharicum, ut b a Hig. 265. Cujus radius sE C b = ZC. B = 8 R. Cujus cum Cin-
sula puncta, (urpore aequalium Prramidum Centra gravicaris,) aequaliter onerata
reputentur; idem erit Prilinei hujus, ipliusque expolici semisectoris, Sectoritve
impertecti, Centrum graricaliS; (Per 76 Cap. 4.) adeOquC, capcundem ab A a con-
vectionis axe distabit.
Ouod de limiliter accommodabicur Onpula eidem BC A Sectori Circulari infi-
stenci; Cujus utique (pari ratione) Cenirum gxaricatis idem erie aeque Suverti
ciei Ongula Cylindracea areui b a insistentis aciem habeneis Aa; adeoque tancun-
dem ab A a Pe penMlait plano aalo.
Est autem (per S V, W. BIOB. 23.) Semiguadrancalis Ongula superticialis, ar-
cui B A inlistentis, momencum respectu iplius ao; idem acque Tumima quadrato.
rum linuum rectorum ipsi A B arcui conrenientium; adeoque aequatur facto ex
BV a semisegmento, in R ducto; hoc elt, (prOpter BV A == ZC R f 3 5V, ver
SF. SPrOP. praeced.) ZC R F 35V R: Aique hoc, per Ungulae superticia lis maoni-
cudinem diritum; hoc ell, (per SN. (. prOp. 13.) per v R divitum; exhiber iltius
Ongulae Superticialis B A, diltancium Ceniri gravicaris ab A a. = -
 + Z5. Ad
cogue (propiet CB =  CB = Z R) areui b a insiltenis Ongulx supertieialo, e
propterea (per jam demonstrata) Ongulae Solidae ipti BC. A insistemis, aciem ta
8b  +35. (De, specia
im, illius quae tori A Da semicirculo intistie, ingula, distancia Ceniri pravicacis
ab Aa, PFOPter 5 ==0, ad eo que  = 4 = Z P, _ v = 2 R, exi
Eademque eltet diltancia Cencri graricatis Solidi, impertecta ejuldem BC A cir.
Ca Aa convertione deseripri, ab Aa convertionis axe; dempra CurratTA. oSCc
propter curraturam, minuenda est pro ratione quam habet ad, convertionis aveun
chorda sia; (Der PrOP. L4. hujus) hoc est, in Semiconvertione, ut 2 R ad 3~
seu uc 4 P ad P; (et in aliis convertionibus similicer, mucatis mucandis, in ratione
Chorcae ad Arcum;) Adeoque Semisolidi, ipsius B C. A semiconvertione circa A a
deseripris distantia Ceneri orar lais a convertionis sue Axe Aa, ef( 3 a  + 3 sV
et
(L speciacim, quou semiconrertione Semicirculi A. D a dascribicur, Hemisphaerii,
distancia Cencri praricatis ab Aa, elt 3 R.
d’acque
t