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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 697, page id 851387705:0717
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PFOP.XI. De Carculo Centri Craouato.
planis obsgt sCcCI, Duca In Bu S  BCd. Ductis PIanis y u yZ BC5
BC D Parallelis: OltendetUr, nE SuPTa Fructo BD SB aequale Colidum B Fd V
item Frusto BDdB, aequale Solidum BDS8: Frustum igitur BS db (duorii
BDSB, BDdb, Cumma vel differencia, DtOuE ex oppoltis, vel hisdem parcibus
ejusdem BD Sumantur,) Solido Prilmatico 3788 (duorum limiliter BDr 
BD85, Tumma vel disterentia,) aequabitur. Ouod ostendendum cxat.
Sin haec duo Plana secancia, sibi invicem intra Solidum occurrant: idem hic Fie
monendum (acque similirer oAendetur) uc prius. Puta; Si BS, bd, plana (C 140.
mutuo secent in Z; eric 2 7 88 Tolidum prismaticum, aequale duorum sX d, BZ B
differentix. Adeoque de Fructo duobus urcunque Planis interjecto, constat. Quod
CTAE DTOBOTIcum.
Denigue: De Superticie Frusti, quod altirmatur; similiter omnino demonstra.
Bicur atque de Frulto ipso: Hoc prius animadrerso: Ouod Prismaris Solidire
exismatici cujulcunque magnitudo astimatur, ex ductu alticudinis in Balin; Su-
perticies vero Prilmaris, Cxlindri, Solidire cujulris Prilmariei recti (exceptis ba-
libus) Aieam habet aequalem tacto ex Lateris longicudine in Perimetrum BalIS
ducta. Onde, uc ex Solidi Prilmatiei Alcicudine e Bale cognitis, copnoscitur
Solidi magnitudo; quaque aequales habene cum Bases (urcunque distimiles,) cum
Alticudines (urcunque inaequalicer inictinata LnE,) sune incer se Aqualia: Sic,
hujulmodi Solidorum Rectorum, Superkcies (execpeis Basibus) Aream habent
coonira, li cum Laceris LongIEIdO, tum BaLS PEXIeTET, nOEX TunE; quaeque
rum Bales habene Lloperimetras, (urcunque dissimiles vel inaquales,) tum Latera
longicudine aequalia, aequales habent areds. Oua quidem ex Elemencis nota sup
ponmus, vel inde demonctrabilia.
Constructis igitur, ut prius; nisi quod e tic jam Centrum Gravicaris (non qui. Fis
dem BatIS, Sed) Perimerri Baleos: Ouoniam lingula perimceri puncta B, D, ec. 236.
in ea ratione ponderant qua distant ab Z motus axc; hoc elt, in rectarum ZB
XD, eC. ratione: qua timul omnes (propter C Cencrum graritaris) cancundem
rune acque cocidem ZC aequales: Suntque (provier similia Priangula) rectis
ZB, XD, XC, ac. proporrionales BB, DS, Cn, _C. Fancundem itaque TuNE
(per 22: EL. 5.) simul omnes BB, DS, ecc. (superticiem L rusti recti B D S B com-
Plences,) acque coridem Cn, complentes superticiem Solidi Prismatiei (dempris
Batibus) BB33. Quod erat demonstrandum.
Si rero exponatur superticialis Ongula Scalena, cum ejusdem basis Prisinatiea
Similiter inclinata (hoc urique supponimus in superticialibus, utur in Colidis id
non erat necelle,) comparanda: Similicer operabicus similis. utrobique inclinatio,
adeoque non deltruer aequalitatem.
Vel eriam, (uE in Eis. 139.) praecer duo plana Ongulam Sealenam cerminancis
UEBKS, bCd; incellisatur cercium aliquod BC.D, quod solidum secet ad angulos
rectos; adeoque duas exhibeat Ingulas rectas (de quibus procedet pracedens de-
monstratio) quarum summae rel disserentia aequabitur exposita Scalena.
Reliquaque, eodem modo demonstrantur de Frulti superticie, acque de ipto
Frusto demonstraca sunt. Adeoque constat Propolitum.
Atque hine Ongularam, quas vocant, omne senus. (Cylindricarum, Paraboli. L.
carum, _cc.) Menturam, (coonito vel suppolico Balis Centro graricatis, vel hu-
jus falcem a communi sectione plani balis, planique secanris, diltantia;) quam
magno molimine plures sunt axgresti; expedicius, simplicius, acque unirersalius,
una vice absolrimus.
Hinc eliam pacec; expoliti Cxtindri, Primacis, Solidire cujusvis Prismaciei, (ut
BDdb,) segmentum BOS B, quocunque plavo, et quocunque sicu potico, (dum
modo cocam tiguram transvertim secec, non bali intra figuram occurrat,) si Det
idem (in CC recta) punctum n vanseat; ejuldem magnicudinis elle
Duod et de Frusti Superticie (ita ut dictum est) Paricer incellisendum
Hinc eriam innoceseit difterentia duarum Ingularum super eodem plano, re.
Etave (aut curra in plano descripta) cujus magnicudo nota sit; prout Ongulx
Acies (leu planorum incersectio) propius remociutre abtuerit.
Nempen
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