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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)
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DeCaleum Cntri Ceravitatis.
crat Copositum. Idem nempe quod i singulis calibus designarimus: VF ex Cal.
culo patet; ne opus HE ut lingulis casibUS IMOTCMUE.
In figuris Solidis: De Cenrri graritacis Distancia d Verrice, Similiter constat aE-
que in Planis; cx 6 e7 hujus.
Onodque hr in Plano per Biametrum d Centrum Graricatis Batis (adeoque e
reliquorum bali parallelorum Planorum Centra Graritatis; proprer omnia, quod
Fuxoonimus, plana similia, ee Similicer ad diametrum polita;) constabit ex q’hu-
Jud.
Ouod sit in ea quam dicimus d Diametro vel Axe distantia; sic item conttabit.
In similibus Planis (ex quibus conslari Solidum intellisatur) Cenera Graritatis
sune similirer sira; (quod ex 4 Cap. 4. et5 Cap. X. demonstrabitur:) adeoque
ab homolosis punctis distane in ratione lacerum homoloeorum; vel, rectarum ut-
cunque in luis respectire planie similicer posicarum; (quod ex det. T. _ prOP. 4.
FII. 6. demonstrabicur:) Cunque, ob similem, quem supponimus, planorum ad
Diametrum Axemre licum; homolosa timilium elanorum puncta sint in Diametro
vel Axe consticura: Distantiae Centrorum gravitatis à Diametro vel Axe, sunt in
ratione lacerum Homolosorum, sire rectarum similiter poticarum, in suis respectire
Planis: HIoc elt; (quod ex prov. 20. F.l. 6. demonstrabitur,) in subdluplicata ra-
tione Planorum. Adeoque: Si sexies Planorum, Indicem habeat S, vel -5: se-
ries Diltanciarum, Indicem habebit ZS, vel - ZS: Tt series Momentorum (ut
qua sunt in ratione ex rationibus Ponderum ee Distantiarum Centrorum Gravir
eis compotita, per 28 Cap. 4. ) Indicem habebie S. F ZS, vel - 5 - =S; hoc est
ES, vel = 25. EC ixitur (Potiris P, pro Pondere scu Plano ulrimo: NV, pronu-
mero Planorum, ex quibds conslari incellixacur Solidum; D, pro distantia C’en-
eri gravicatis Balis, d Diametro vel
AXC;
S F = NP, vel - - NF
5
Solidum, lire Planorum Ponderum.
ve Reoreerum: L, NVED, vet
35 =2
NPD
eD; Summa Momentorum, Sire Solidi Nomentum rel Ponde.
ratio. Adeoque dirita summa Momentorum, per summam Ponderum; prodibit
5 +
35 F =D v
5
O, distancia Centri praricaris Solidi, a diametro vel
axc: Nempe, ea quae sr ad D distanciam Centri Graritatis BaLiS, ut 2 5 f 2 ad
35. F 2, aut-
ad = 3 5 F +
2572 ad - 35 f 2; hoc ell, ut S F sad = S f L, au- 5tF
Ouod erat demonttrandum.
Cumque, in Figuris Reciprocis, quo Centrum gravicacistrabeane, non Tolumre.
quiratuE, uc = SF F sic terminus policirus, (per prOP. praeced.) Scd e- 35 F X
(ne ratio illius ad hane sic vel Intinita, rel plulquam Intinita; adcogue, propter
Intinitam, vel plusquam intinitam distantiam, Cencrum grariraris nusquam sc:)
major else debeac (seu minus negacirus) = 35, quam = L; sVC = S, quam
Z. inde constat dererminatio
POrrO; quum, in Fipuris Solidis, secundum seriem sire Directam, Cire Reci.
procam constitmris, oltensum sit; tum, quantum distet Centrum graritaris (adeo-
que de planum Aquilibrii) a plano per Verricem bali parallelo; cum, in quo per
axem plano reperiatur; cum denique, quantum in illo plavo d diametro vel axe
distat: Datur iplum Craricaris Centrum; dummodo Cencrum Craritatis balis non
iOnOrCtT, (Per 26Cap. 4.) Ouod crat propoticum. Nempeillud iptum quod in
sinsulis calibus detignâc propotuio: It ex Calculo patebit.
Denique: Duod, de duabus hujulmodi Figuris Dimidiaris, (timilibus ee aequa-
libus,) utrinque ad candem rectam contrario litu posiris; dictum elt: Constabit ex
hujus. Ouodque de iiidem (planis Coliditre) fixuris dimidiaris (aut quae harum
instar Lunt) cruncacis, aliasre mulctaris, ret apxresatis, addirur, Constat cx 27 C ap. 4.
SCT2
Cap. V