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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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Cap. III.
ANOUL AR TBIS.
in (B =) = Y: 4R4 - A4: aequabic AD. HOC est 2 R9 Aq - A94
4R9 = Ag: = A D. EF ZR9A = AC
V: 4Rg = A9: = D, ut prius. EE
RC
DEE Candtem rationem, CB - E B = L. D = ZRGE9 - F 44 5: 4. Rg = Fg.
c
2RGF = FC +: 4Rg - E 9. = D.
RC
38. Si Hic D (vel 5) Sutrensa simpli quadrante
majoris, aur etiam majoris criente, (sed duobus crien-
tibus minoris:) Tum B, C, et B, P, (auE B, S,) c.
runt opPOlita latera; e D, P, (seu D, S,) diagona
Les. Et proprerea BC. F BP = P D, (teu BC = B5
= 2P (= C.  P
=SD.) E consequenter, R
in (B =) = Y: 4R9 = P 9: aequabit PD. HOC
est, P44 = 2 RgP4 Y: 4. R4 - P9: = PD. Pt
RC
PC = ZR9P
RC
V: 4 R9 = P9: = D; uc prius. AEque eadem ratione, BC F B5
= SD (A SC accus S major triente;) FE SC = 2R45
RC
80. Sed, Si arcuS S sc major quadrante sed criente
minor: (aut arcus P major duobus crientibus. Sed
minor tribus quadrantibus:) Tum B, C, e D, S
sunc oppotua lacera; et B, S, diagonales. Adeoque
B5 = BC = SD. Ft, ConSEquentEF, 25 -
RC
(= 5 = C) in (B =) = V: 4 R9 - 59: = 5D.
Hoc es 2R959 -5441: 4R9 - 59: = 5D.
C
EF ZR45 -SC
RC
RC
(E sit arcus P major duobus rriencibus; quod cancundem est dc si estet uno mi-
E RGP = PC
RC V: 4R9 - Pg: = D.
90. A quibus omnibus, hioc oritur Theorema generale: Rectansulum subten-
sarum areus simpli e quadruxti; aequatur subtensae dupsi ducta in excessum
subtensae tripl supra subtentam simpli, si hic sit quadrance minor, aut major tri-
bus quadrantibus; vel in excessum subtensae simpli (si sit major quadrante sed
rriente minor, aut major duobus trientibus sed minor tribus quadrantibus) supra
subtensam cripli; vel denique, in summam subcensarum tripli ex simpli, si sit hic
major triente sed minor duobus trientibus. Hloc Cst; AD = B in
C =A; SI arCUS A EIL minOr quadrance aut major tribus quadrantibus.
A -C: Ei sit major quadrance sed minor criente; auc major duobus trienti.
bus sed minor cribus quadrantibus.
A. F C; Ii sic major triente, Led minor duobus criencbus.
OT. EE, universaliter,
2R9A ∞ AC
RC
rentia inter 2 Rq AC AC (quorum illud majus est, (i arcus simplex Fic quadrante
minOr, aut major iribus quactrancibus; sed hic, l Conra;) divisa per RC, ducatur
in V: 4 Rg - Aq: Productum aequatur D, subtensae areus quadrupti.
A 2 a 2
92. Ft
V. 4k9- 59: = D.
ZXIF