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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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DE SE C F 1O N L B u S Cap. II.
7. Vt subtensa Simpli areus (triente minoris) ad summam subtensarum Sim-
Dli e Dupli; sic est excessus subtensae Dupli supra subtentam Simpli, ad subten.
Jam Tripi.
8. Trem; Ouia (per 57 Cap. praeced.) B4 = 4 A4 -
(= AC) = 3A9 -
est
A9C
B9 - A
R9. EL PrOBIerCA
A44. F180 B9 - 19
R9
AC
3A -
R9
=C. HlOC
9. Tripium subiensae areus (triente minoris) dempto ejusdem Calbo per qua
aratum raci diviso: aequatur subtensae areus Triph.
20. Sed cum eadem subrenta C, subrendic etiam alceri segmenco ejusdem eic.
culi, subrentam crieniis hujus segmenti vocemus F. Fric igituIr S. A -
E C
Rq
C
RC
TF. EE quoniam CrES aECNS A, A, A; CE trES ATCS E, E, E; complent cocam
circumterenciam, (ut Patet: ) erso, A lemel, et R. Correl, complent crientem 10-
LIuIS. EL PrOPICrea,
22. Aeus criente circumferentiae minor,  residuus ad crientem, (A et F.)
eandem habent subtensam Fripli areus.
23. Ouoniam (ue jam oscentum Clt) 3 a -
=3E = = C: Adeoq: 3RgA
RC
RC
AC= 3RgF = R. c: Et (cransponendo) 3R9A = 3 RgF. = AC = F c.
Ereo (divideneo per A = F umingue) 3Rg (= 319A = 3R9F) AC - FC
A - F
=Ag f A F F F. 9. Ouod patebit, dividendo AC = FC per A = F; auc mul.
ciplicando A - F per A g F AF F F 9
24. Sed (per 6 37, 38, Cap. praeced. ) 3Rq cMt quadracum Cubcen (ae Friencis;
hoc Cst (per S TF HujuS) Tummx areuum A e R. Fr9O
25. Duadratum subtensae Trientis (seu criplum quadrari Raciii) aequatur Qua-
dratis subtensarum duorum arcuum trientem complentium, e carum Rectaneuto.
HToc elt (potico T pro subrensa crientis circumterentiae,) T4 (=- 3R9) =A4
AF  H,9
26. Sed angulus quem A E concinent (urpore Anoutus in Prience circuli, duo.
bus triencibus intiltens) est angulus gractuum 120. FrGO (Per S15)
27. In trianculo rectilineo, cujus anculus unus est erad. 220; Duadratum sub-
tensae hujus aneuli, aequatur quadratis crurum continentium, corumque rectaneulo.
Ouippe si cale criangulum inseribatur Circulo; balis hujus crianeulis erit subcenta
trieneis circumterenciae, Peu V 3R 9.
18. Si cireulo interibaur Ouadrilaterum, cujus cria la
TeTA SINE A, E, A, (Sen K, A, F,) d quartum L: Veraque
diagonalium (ver S LZ) est Y, Cutensa erientis. FrSO
per d +3, 14, 25,) Z F Y A9 (= Z A f F, 9)
ZR9 = A g. f AH. F F 9. FE, CONSeqUentEF Z. L = A H.
= F 4 e Z A = A9 + AC: Adeoque Z = A F L.
FErSO,
70. Si acerecato duorum areuum R, E, (trientem com
plencium,) addatur tercius utrivis eorum aequalis: Z. suib.
tensa aecregati omnium borum niun, aequatur summa
20. Sed eadem subtenta L lubrenaie ex una parce crienei aucto areu A, et
ex altera parte crienti auel ate L; (uE patet:) HoC Cst, arcui qui tanto exce
dic trientem (auc a duobus ribus detieic) quanto arcus A vel L detieit a
2.2. Aecreeatum subtensarum duorum areuum, qui sinul complent trientem
circumferentrae; aequatur fadnsa alterius areus qui ranto excedit rrientem
(seu defieit a duobus crientibus) quanto ucervis eorum a triente deficit.
22. Idem
subtensarum istorum duorum. Hloc CAt, Z == A f F.
eriette. FrgO,