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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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E
S E C Y 1O N s B u S Cap. III.
75. Ee quoniam (uc prius) P = 13 , = R: F180, Eg - + = 2 Y3R9-2RG
=R9VZ, vel 2 =Y3 in Rg. Adeoque, 7. 2 = Y3:: Rg. F 9. HIOC est,
26. Ot Radius, ad excessum Diametri supra subtensam erad. 220; (leu supra
latus inseripei Prisoni;) sic quadratum Radii ad quadratum subtensae graduum 30,
seu lateris Dodecagoni. Adeoque, cum ratio R9 adt Lq Sic duplicata racionis R ad F;
7. Ratio Racii ad differentiam Diametri e lateris inscripii Frieoni; est au
plicata rationis Radii, ad latus inscripri Dodecaeoni. EL propierca,
78. Radius (Seu latus Llexaeom), e latus Dodecasoni,  excessus Diametri
Supra latus Trieoni, sunt continue proportionalia.
79. EG quia 2 = V 3 in Rg, = 2R - R V Z, In R: ErOO Frcessus Diametri
supra subtensam Trientis, ductus in Radium; aequatur quadrato subtensae erad. 30.
seu Semisextantis.
80. Eadem reperientur, bisecando Sextantem, (nam quactrantis triens, et sex.
tantis femis, idem (UnE:) Hloc modo;
8T. Si ponatur P pro Tubrensa gractuum 30, e A pro subtensa residui ad semi-
circumterenciam seu gradtuum 250: Tum, quia subrenta sextancis seu dupli arcus
E, est R; FIBO (per B 24 cap. praced) B4 = R 9 - 4+ 2949- A99 - 4R9+ 4 F99
EER99 = 4 RgAg - A99 = 4RgF. 9 - F 99. EF (resolvendo aquationeM)
2R9 = Y3R99 = 2Rg LR9V3 = 2 = VY3 in R9 = 2R LR V 3 in R = A9, e
F.9. Hoc e,
82. Quadrata subtensarum graduum 250, e eraduum 30; aequantur, illud qui-
dem summa, hec autem Differentia, Diametri  Lateris inscripri Frieoni, in
Radium ducta.
83. Tuem; Cum C = A = R V 2 subcendat, tum criplo arcus A graduum 90,
cum criplo arcuS E gradtuum 30: ErBOZ. (= A f E = RY2 + V3, =R -13F=P
est subcensa crientis auctiareu A vel L. HOC est, tam Graduum 210 = 120 f 90.
quam gradtuum 150 == 120 + 30. Ouod ante conclutum eratsBT. Wam Z. hic
loci, idem est cum A illic; e Z9( ut illic A9) = 2 = V 3 in R 9.
84. Idem eriam alias invenietur, subducto (2 = V 3 in R 9) quadrato subten-
(x graduum 30, ex (4 R 9) quadrato diametri. Ouoniam 150 F 30 == 280 Gra
dus, complent semicircuicum. Nam E ex 4 R q Tubducamus 2 R 9 - R qV 3, ma
nebic 2R g F RqV 3, seu 2 f V 3 in R q quadracum subtenta graduum 150:
adeoque et gradtuum 270.
i A C. 1LL.
De. duadrupaata Suut 
Sreus deb Lineu.
E. C L Circulo inseribatur Ouadellaterum, cujus Opposica Fatera sine A, A, C.
il
tenta simplorum arcuum) e B, D, (suibrenta dupli e quacruplI;) Diaso
nales erunEC, C, (Suhrentae criplorum.) Ot patet
Sed _e etiam patet, arcum A, hoc casu, inOrem
ese Ouadrante Circumterentia integra
2. Erso (proprer rectangulum diagonalium X
quale duobus rectangulis laterum opP
C4 = A q = B D. Adeoque
F
AC
= B. Hoc est,
torum)
Ludaratum subtensa Lripi urbud dempia
quadrato subtentae simpli arcus, quadrante mino-
S; aequatur Rectaneulo subtensarum dupli ex tri-
BI. Litus DC
cum alteram diritum, extribet reliquam.
4. Sec