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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. TTI.
AN GUL A RFBUS.
Tubrensa eripli areus; et 4 P-
P
RG
R9
cripli: Hoc est, excetus Tubrena Simpli lupra Subrensam cripli.
65. Sed arcus S (quadrans auctus minore sui LCgmentO F.) cum BONE CATo vel
minor vel major triente, PrOuLarCUS F. est major rel minor quam 3 gradus: Sub.
Aa
censa cripliareus erieu vel-
A95
Si major, 5 -
Sc
R4
- 5 = 35 - =, h arcus S sit minor criene, vet,
R
A95
RC
= 45 - =- erit vel
Summa (ut560, 62, 62) vel Disterentia (ut 564) subrentarum simpli ee dupli;
Prout S major eltaut minor triente.
66. POrrO: Cum ance oltensum sIE (52) quod, in quadruplatione areus, qua-
drante Ninoris, SIcC g = Ag = BD; eo quod subrenta Tripli major st quam
subrensa Simpli; adeoque C, C, diagonales, et A, A, latera oppolica: Jam Si arcus
quadruplandus sic Major quadrante (sed minor eribus quactrancibus) ut SuNEar-
cus P e S; Tubrensa Simpli major elt quam Tubrensa Fripli. Iam, potito arcu
simpli = Z A (es A minus quam Z); eriplus exit Z F 3 A; hujusque subrenta cadem
cum Cubtenta areus Z F 3 R. (nam incegra rerolumo, hoc catunil ralet.) Atque
hic (quamdiu A manet minor quam +) remocior erit (vel in defectu rel in ex
cellu) a semicircumterentia (adeoque minorem chordam poltulabit) quam = F A.
67. Acque hinc Fc, quod, in hoc catu, P, P, (aut S, S,) tume diasonales; et
C, C, oppolita latera. E consequenter, Pg - C9 = BD, (et 59 - C9 = bD.
Adeoque 2 C9 - D - 39= C9. Hoc es
58. Duadrarum subtensae arcus quadrante majoris, sed minoris tribus quadran-
sibus; dempto quadrato tripli arcus: aequatur rectaneuto subt
ec
quadrupti.  Adeoque per harum utramris dirilum, exhibet reliqu
69. Sed P F C in P = C, aequat P 9 - C 9. Adeoque B. P F C:: P = C. D.
(e similiter, B. S FC:: 5 - c. D.) HOC est,
70. Vt subtensa dupli arous, ad Aeereeatum subtensarum tripli e simpii (qua-
drante majoris, sed minoris tribus quadrantibus:) sic earundem Disferentia, ad
subtensam Qua drupti.
7E. Cum igicur subcenta cripli arcus P = = F A C crience majoris) sIC
eCC 6P 42 F 9Pq: Si HOC auFeratUIE ex
= 3P; cujus quodratum est
R9q R9
Pq reliduumque (P q - C 9 =
PCC
SPa4 = 8 P 4) dividatur per
R92  R4
B = = V: 4Rg - P9: (ue supra, 87 Factum est catu limili; ) prodibir
e9 = C9 - Pc = 2R9
RC
per =; et quoriens hujus per 4 R 9 = P q seu per = P 4 = 4 R 9; et randem
resticuatur mulciplicatio per V: 4 R g - P 9.
72. Et proprerea (mutata aequalicare in analogiam) RC. PC = ZRqP: : V:
4R q - P g. D.
23. Idem continget s SumatuT arCUS S = 2 F F. Ouamvis enim tieri possic ut
sit vel major vel minor trienLC, PTOuL P. CA major vel minor quam 30 practus; adeo-
que subtenta cripli, vel = = 35, vel 35 =: Non tamen inde quiequam,
hoc calu, mutatum erir; quoniam, ucroris modo, hujus quadracum eric idem. A.
BC- ZR95
RC
-S9: = D. Et RC, SC = 2R95:: V: 4Rg - 59. D. HOCCst
74. OE cabus racii; ad subtensam areus, quadrante majoris sed tribus qua
drantibus