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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)
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A L G E B R A.
Cap. CXII.
quaatates ACD BCD dirisO, aptetE A D Subrensa quadrantalis arcus, radio
CF Bilecta In FI: _ CeNErO FT Ecribatur TemicireMLUS ADF: FrIt (prOPter qua-
dracum rectae AD subduplum quadraci rectae AB) semicirculus AD L Cubdu-
QuE COMMUI lEgMentO AD F) relidua Lunula A F DE reliduo PriangutO ADC
aequalis. Lalesque quatuor Lunula, talibus quatuor Friangulis; hoc ct, Jua-
draco tor circulo inscripro ADBG.
IOITO; per Archimedis demonstrata; A quatur SpharX SuperFcieS, quatLIOF
Circulis in ea Sphaera Plaximis. Adeoque Flemisphaerii Superticies curva, tali-
Dus quaruor Semicireulis: calisque superticies HlemiphaeriCK Guadrans, unI LemI
Circulus A DBC elto jam Balis Femispharieae Puperficiei crrx: cujus po-
lus P, axis C P, plano balis perpendicularis, eju sque quadtrans unus LH, gu
Platio H. PC per axem cranleua BHICCCtUT.
peripheria P, expolicus arCU a.
+d0
circulo.
plus semicireut ABD; adeoque quadranti ACD aequalis. Et (dempto utrin-
Ponantur item (ob commodiorem calculum) Circuti radius R, diameter D = 2 R,
Poticoque quadrantati aieut DF A = a = = P; est TCMICHCHIUS XBB = 1 a
superticies hemisphaericae currae, aequali semicirculo ABD) quo reliduum xeque
eur expolico criangulo ADC
Ouod quum rariis modis tieri possit; per ca quae nos dudum docuimus anno
2659 (ad calcem Fractatus de Crcloide, cum EdicI, pa8. F22 inserenda ad 668)
iterumque AnnO 267O (in Fractatus de Motu Capie V, PrOD. 24.) de Fieura
Planan aequali cuivis in supersieie Spharica fieura, circulis quibusvis (sive maxi-
mis sive minotibus) terminatae. Sic tiat limplicissime:
Cum supertieier Sphaericae legmenta, Palattesto practto abseicta, sinc Axis segmen-
eis proporconalia (quod de expolica quadtrantalis Cunei superticie D P A Pariter
valet:) Si sumatuT, in axe CP, ut semicirculus Z RP, ad semicirculum dempto
triansulo Z R~ = = RD; hoc est, ut D ad P = D: sic CP ad C l: (sive.
quod cancundem elt, uc D ad D, sic CP ad PY:) planum per YL bali pa-
rallelum, abscindet hujus superticiei currae porcionem volo adjacentem, aequalem
criangulo ADC. Ouod cum, in reliquis superticiei currae quadrancibus, paxi-
ex hac: aequabitur tocum Abscittum (Polo adjacens) tori Ouadrato bati in-
scripto: Et lic centum ue oporitt. Ouod crat taciendum.
Vel sic brerius. FH Elemisphaerii superticies curra (urpore duobus circulis
maximis aequalis) = P P. Ouadracum circulo maximo inscripium, = 2. L R = RD.
Aludque ad hoc, ut P ad D. Adeoque (propcer segmenia superticiei parallelis
Planis abseissa, segmentis axis proporcionalia) Cumpris C P ad P Y uc P ad D, eric
cum cota supertictes =  L, cu pbilto ad Polum, plano L. L abscista, = R2d
quacrato bali inseripro. Sao ctat Lacienaum.
a RE: criangulum ADC = 3 R = = RD; reliquumque lemicireuli (dempto
hoc criangulo) a RP = =PD; cui aequale auterendum est ex DP A (quadrante