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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
# Folio 349, page id 851708439:0373
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Cap. L XXXI.
A E G F B R A.
Si ACF Semisesmencum Circuli (cujus Radius AC, Diame.
teT AS,) FOTEUE CIrCA A F: produCETIX Spharx Segmentum
cujus Flementa func O HIB, O D l ac. Scd DHB = D AB
OAHI, eCD DE =O AV. = D AD. e d HC ==C AC
() A F. AF serieS (O AB, O AF, O AG:: AB 9, AE9.
AG9:: ASXATT, ASKAD, ASXAF:: A LB AD, AF, hoc est sC
ries Primanorum: ideoque =O AG X Z A F. HC O AFI, G) AD,
 AF, Scc. Clt series Secundanorum: ideoque elt =- AFX ZO AF.
tergo Segmencum Sphaerae cst ; A F X:  A G = 3O AF: =
E A F X: O FG F 3O A F. (Id quod elt cheorema jam ulur-
Dacum in menturanda Corona Aheui Cerrisiarii.) = 3 A F X:
C
OFC F IAFH X, LSOFC =IOF Cn AF~ (3Vd f AP)
quod ipsum cst Theorema Archimedis, cognita diametro. Mnod tamen (cum
praesimat diametrum cognitam) minus est ulii accommodum quam iliud alterum.
De Erusto Eyramidis eet Coni.
Sunto A, B, C, D, F, _C. Flemenca Segmeni Frianguli Rectan-. r. . 7F. - - - . . .
suli Parallela bali: Elemeneorum Ouadraca constimune trultum:
F
Pyramidis Ouadrara. Sincb, c, d, X esc. complementa legmenci .. . d . . ... -. 7..
ad parallelosrammum. Sitque A L P = Z. Fum
B9 = AA - 2 Ab F Bb, Scd Series AA, AA, AA, est AEquali- 1. C. . C...
Cq = AA - 2Ac = cc C um, ideoque = p AA. Series Z. AB, ib - - . - - .
Oc. usque ad E 2 AC, ec. Cst Primanorum ideoque
F9 = AA 2AX + XX) = 2p A Z = pAX. SeriCSBB, CC, dec. eAt
Sccuntanorum, Ideoque =-5p XX. ErgO Frultum Pyramidis
e
Ouadratae est = p X: AA - AX f G ZX = pX: AF. + SXX (quod FIL THCOreMA
DrIMUM) = SpX: 3AE + XX = (prOPIEE XX = A A - 2 AF f LF) 3PX: A9
FAF F Pg (Theorema Sccundum) = SpX: Z. A f P. 9 (Fheorema cerrium)
=3PX: LF + A9 (TheOremA quarII) 5 pX Z9 = AE. (T heorema quincum)
vel = : p, 2 44 + 2E2 + 2AF = 1 pr. 29 + A9 L E9 (heorema Sextum.)
Si Fructum Fueric Coni, positis A, P. diameeris Balium: Coliditas per Pheorema.
cum superiorum quodris inventa ducatur in 253. Pariterque mulciplicando per 2
LiOS aPEOS NUMETOS, Pheoremata applicentur Pyramidlibus quamlibet Polvedris. V).
tiigue crunt in Menturandis ratis Cerrisiariis (Anstis Fonnis dictis,) ec Arbo.
rum cruncis.
De Trusto Sphaeroidis:
Sit CBF quadrans FMip(COS, cujus semiaxes CB, CF, ee semipara.
ODt
1OCB- DCD
metri ad CB racio lic uE L act L, FrGOC NIE =, K CCB GCN E
OCiII)
OCB dC
Erxo Frullum Sphaeroidis cst = =- pr: D CB - ; D CC -
= +2OCB. + =OCB - =O CO = 5 pr: 2OCF + OHC
Ouod ipsum est cheorema ab Ouchereso primo, jamque ab aliis adhibicum invenienda
capacitaci Doliorum.
De Trusto Fusi Parabolici.
Sic Parabolae axis A, et ad axem Axplicata P divisa in parres aequa.
les innumeras; pes rectas B, C, F, ec. axi paralelas; quarum disse.
rEnEIX ab A CIMC n, 2 Bcc. uIque ad X.
EroO B9 = 19 = 2 A1 F B n
C9 = A9 = 2 Am = m m
_c. ulque ad
F.g = A9 - 2 A N + N X
Sed series Aq, Aqe ecc. Cs Aqualium, ad eoque = p Ag. F.1
2 A m, ec. eA Secunctanorum; proptet rectasn, m, dec. in dupli
co