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# 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 751, page id 851387705:0771
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PFOD. XVI. De Calculo Centri Craviraris.
idem habet respectu F A momentum, quod habet ea cujus acies F A respectu ra.
(proprer alticudines e distantias reciprocatas:) hoc CAt, (uE modo)  50R
-55 R = ; 5v: Adeoque (proxier magnirdipem Sy R = 3 5V = 35V R + 35
Per SN. pEOP. Praeced.) distancia Ceneri graricatis d FA, erir + 2 X- 25 R L 3 s2 ~
ec d 7 
42 R + 45
42 R2 F 10S R = 3 5 V. ideoque momentum respectu 7 a 5 5D R=
4VR F 45
-5~ R + 150
Eaque momenca, momentis respectiris Ongula Semisesiento B V A inssentis,
aeiem habentis T ag (3e R3 = 35V R = = s R F a 53V, d 3C RE +85VR2  15 X
25.V, UESF.) subducta; relinquune Ongulae Segmento A B A insistentis, aciem
trabentis ra momentum respectu F A, 3CR3 f = 5VR2 =  sR; _ respectu
raq ZCR3 F 5V R= F 2S P; et (propier magnicudinem, ZC R ? f ZSVR; per
SH. propoluionis praeced.) DiMtancia Centri Braricaito L. X4, 30 F + sV R L 25
e d r
( BCZC R = 45~
15eR3 + 75V R  253 11 eri setes is) S. WP : SLTIOI reICt
1Ci X2C R 4 4 5VDeSC CISCSOT) O MMAS
Fademque Sermento a Ba respectu rectae ra aCCOMOdantE, quae Segmento
AB A respectu P A; e vice verla. (Nempe, pro an Substimendo a = 38 t a;
ec pro v, Tublticuendo B = 2 R - v.
Pula; Segmenco a Ba intistens Semiquadrantalis Dnsula aciem habens ta,
magnitudinem habet z a  = = 5 R = Z SBR = = R 2 P - = a R - 35 R + 55VR.
Momentum respectu Tan 3 a R3 - 85 R3 - 8s B R + S R = 1 R3 P - 3a R3
= 55R3 +352 R F in se R; respectu F A, 3a R - 85 R3 +  sB R2  5. R
26 R3 - 3a R3 - 25R3 -  5u R 2 -  5 R.
Er; Seomento a Ba insistens Semiguadrantalis Ongula aclem habens FA, mas-
nicudinem habet Z a R 2 = Zs R   S sBR =  R2F = = a R= = 05 R 2-
55VR:
Momentum respectu ran 3aR3 - 35 R3 + 2 S B R 2 = in S R = 1 3 R3 Z = 3 a R
2aSR3 = 2 5V R 2 = = 5 R; e relpectu TA, 3a R = 35 R + + shR:
=  S R = 16 R 3  = 8a 2 - 2 5 R - 4 5V R2 + 13 s R.
Fxtribuimus icaque, expoticorum sectorum sphaerieorum, de Segmientorum,
Ongularumque eo spectantium, et correspondeneium Solidorum seu Semilolido.
rum convertione factorum, cum magnicudines, cum momenta respectu Planorum
aliquot expolitorum; corumque Centrorum graritatis distanciam à duobus Caltem
planis sibi inricem non parallelis; aeque in quo tertio per Ongula aciem Peu con-
vertionis axem ducto, neurri priorum parallelo, idem reperiarur: Adeoque (per
PrOP. 26. Cap. PraeCed. ) ipsa graricatis Centra decerminarimus.
Ouaeque ad calcem Propolicionis praecedencis monuimus; etiam hic monenda
erunE: Nempe, haec omnia aliis Sphaera portionibus, simili methodo accommodari
DOSTC. Puta, quae de Sectore B a A (ad verricem terminato) ejusque Ingulis, _c.
dicta sunt; Facile accommodari posle sectori D a B (duorum ad verricem cermina-
corum D a A, Ba A, difterentia,) ejusque Ongulis _c.
EL prouc hic qua de Ongularum auc Solidorum magnicudinibus ee momentis
AOCEHTME; d recta ra, ad T A vel BV, transteruntur; simili methodo, haec aut
tis similia, d recta A a, ad FF vel Ba, CranStETTI POLETINE. Aliaque quae lic
xradtuncur, mille modis ampliari.
Duxque de Ongulis Semicirculi, ejutre porcionibus; Sphaeraque, et porcioni.
bus hujus; dicta sunc; ad Ungulas Semiessipleos, et porcionum hujus; Sphaeroci
des hujusque portiones; Facile accommodaneur. Nempe li incellipatur axium el
lipleos alter Aa, alter Da: manente Aa = 2 R, (adeoque AV = 2, V a = B;
erit Da in ea ratione 2d 2 R, qua est ad Aa; majore quidem si sie Da axium
Major, (adeoque Sphaeroeides convertione deseripem, Sphaerocides lacum;) mi-
nore, si sit Da axium minor, (adeoque Spharoeides loneum, convertione de
Scripeum:) _ BV, in endem ratione ad s. Adeoque, quoties BV in caleulum
venit; pro s, substituenda erie alia quancitas, quae sit ad hane, ut est D a ad A a:
d pro s, alia qua sit ad thanc, ut in duplicata ratione recta Da 2d A a: _ in
reliquis pocellaribus similicer, mucaris mucandis.
F
Fis
460.
2.
9