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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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De Cuamo at cradundis. Cap. V.
Eis 166. (Nec quenquam inerim morari debeat, quod (propter aciem Aa;) alricudo
in L, 5, 03 IIIa OP SIC; aeque in P, p, E, minor, quam in B, B, B, respectire. Onam-
quam enim illud omnino rerum sIc; aique, in fectione determinata, alicujus sE
Momenti: Continuaca tamen in intinitum sectione, (quod Cupponimus,) ditte
rentia eraneseie in data quaris minorem: Ouxe non modo in methodo indivisibi-
lium, sed in omni per tigurarum inseriptionem et circum scriptionem demonstrandi
methodo, nesligenda erir. Deque enim aliud produeis, qua quod centrum era-
ricaris quod in Ba, b B, rectis lupponimus; promorendum erit ultra illasus inter-
vallo quod dato quoris minus TIL. Ouod aurem ab alio, ditterentia quae data qua-
vis minor sic, ditferre demonstratur; pro aequali habendum exit. Dumque cal
dem suxponimus, tum in X, y, S, cum in P, p, E, alcicudines quae in B, b, B: Soli-
dum ex minuris adscripcum (partim inscripeum, parcim circumseripeum,) pro
vero Solido sublticuimus, quod ab illo disterat, non nili disterencia quae data mi-
nOr LIc. )
Cuneus autem Fruncatus ille, quem diximus; seu Prisina parallelis Fraperiis
interjectum: Constat ex Cuneo intermedio, seu Prismate Friangulo vB r infi-
Aerice; et biparcico Parallelexipedo, Parallelogrammis vB d y et =BEP inli-
Stente.
Oui quidem Cuneus incermedius, propter tormam, elt, ad Pgramidem aeque aL-
tam eiusdem bateos, uc 5 ad 3, Peu 3 ad 2, (elt neigue Cuneus illa parallelexivedi
illius Semis, cujus Pyramis Friens clt:) Cumque porro alcicudo Cunci, in B vel
b. Tic ad alcicudinem baleos Pyramidis in B; uc B9 lcu D B, ad BV: hOc elb, uE a
ael s: Exi Cunei Friangulo vB = insiltencis, ad Pyramidem simili et aequati Lri-
ansulo Y aP incumbentem, ratio, (ex illis compolica) ut 3 a ad 2 s. Cumque
Cunei cencrum graricatis sc in Bb, abscindens, vectus B, ZBb, (Der PrOP. 5, 6.
adeoque ipsius ab Aa distancia sic, bB f 3B V, Peu a. f Z5, (ue ex schematis in-
spectu facile colligitur;) Centrique graritans Pyramicis Z a P (ve dietum est
inde diltantia sIr Zs: Adeoque diltanciarum ratio, ut a F 35, ad 3s: Ratio haec,
cum ratione magnicudinum (3 a ad 2 5) compotica; extribet rationem Momenti
Cunci illius, ad Momencum Pyramidis (respectu ejuldem A∞,) ut 3 a2 F 2 a sy 2c
252 ACu6a 2 = 4a 5ac35
Et parallelexipedum (biparritum) cum sC, propter Formam, ad Pgramidem a-
quealcam, ejuldem balis, ur 3 adr: Sieque baleos in B vel b altitudo, ad alcitudi-
nem in B, ut a ad s: F.rit Parallelepipedi ad Pyramidem ratio 3 a ad s. Cumque
Parallelepipedi (neue biparcici) commune cenerum rearicatis tic in medio Bb:
Adeoque ejridem ab A a distantia, a f 35: (Sirque centri graritatis Ppramidis, uE
dictmm elt, distancia 35:) Diltanciarum rario, a f 35ad 25; cum ratione magni-
cudinum, 3 a adt s, compolita; extibeE FaTIONEM MOenTOrUM, 3 a = f 3 a 5acl 25,
TCu 12 a2 6 as ac
Cuncusque, Pruncaro illi Cuneo superimpolitus; Componitur ex Pyramide in-
cermedia, eriangulo Bx supereminente, (Pvramidi in Y a P simili ee aequali;) d
Cuneo biparcico, paralleloBrammis. Bs Y, rBEP, Supereminente.
Pyramidisque PriansulLVB = Cenrum graricatis, cum incellisaCuE in BB Titum.
(Talcem in pluno luper tanc crecto,) oblemdens, versus B, 3Bb; adeoque iplius
a0 Aa distancia (uc ex schemaris inspectu tacile conligitur,) a F 2s: Rrit (PrOP
ter magnicudines aequales) momenti ejus rario, ad momeneum Pyramidis L a P
(respectu ejuldem Aa) cadem quae distantiarum; hoc est, ut a F 3 5 ad 25; seu
UC 4 a Y
1d3s, Hoc cC, 1C 4 a5 - 35, 2d 35
Cuneique biparriri, cum (propter aequales bales dt alcicudines,) sic ad Prrami
dem, ut 3 ad 2; Cenrique diltancia illris, ad ceneri hujus distantiam, ve a f
ad 25: Liric momentum biparciei Cuneis ad momencum eyramidis L a P, (respectis
ejuldem A0,) ut 5 1  25 4d35: sCl 6a5 = 452 2d 35
Frso, Solidi corius, minuto Frapezio y SEp incumbens, (quod ex parcibus
jam expolitis componitur,) ad momentum Pyramidis correspondentis, incumbencis
Friangulo L a P, (respectu ejusdem A a,) est ut 6 a 2 = 4 as plus 22 a2 f 6a5
Dlu5 + a5 = 3 s2 plu56a5 f 45 2 ad 3 52: HOC cA, uE 18 a 2 f 20a 5 +75
ad 3 52. Vel (ductis omnitus in communem alcicudinem V a--B,) ut 28 a h
f 20 a sB f 7sB, 2d 3s B. Ft sic ubique. Adeogue momentum Solidi ex
illis contlaci (sire quod totam ATa, Sive quod ipsiuS partem uE ABBa spectat;
ad momencum correlpondenris solidi ex his conttati, (quod rel torum ADa, vel
iPEUS
168, 173