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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 SECTIONEBUS.
Cap. IV.
duum 18) POnatuE F.: Tum (per 5 52. Cap. praeced.) A9 f F9 F AF V2 -= 2B9.
ErGO E 9 = AEVZ =2R9 = Ag. EF (Resolrendo Aquationem) V: ZA9
F 2Rg - A9: (= V: 2R 9 = 5A9:
= =AV 2 = F
50. Sed A9 = 5= VRq: adeoque ZRg = ; Ag - 3 = V5 RG (Semis qua.
drati subtentae Sesquiquintantis seu graduum 108;) hujusque Radix quacracica
=R9 =  20F 12 R. FCS AY2 = AY: = RY5=15 -Y: 5 - 15: P
Crgo. Y 20 F 12 - 2Y. 5 = v5: R = F, Subienta erachum 18: ue prius. Hloc
cAt,
5T. Subtensa Sesquiquintantis, seu graduum 208 (quod est Majus Segmen-
tum Radii extrema e media proportione secti, ipso Radio aucrum,) Ducta in
Y2, (nam YS F =RV2 = YF0 +
=R;) Dempta subtensa Duintantis dudia
item in Y 2, (nam R V3= = in V2, =RV: 5 - V5:) Sequatur Duplo sub-
rensae sraduum 28. Elujusque Semis, est ipla Subcenta. Vet
52. Differentia Subtensarum Sesqui quintantis e Duintantis (Peu gractuum
108 de readuum 72) Divisa per Y2: Squatur Subtensae eraduum 18. TTOC
CA Disterentia illa est porestare dupla (seu Duplum porcst) hujus subcentae:
Peu Ouadratum illius est Duplum Ouadrari hujus.
53. Sed, Subsensa duintantis e Sesquiquintantis (hoc est graduum 72 8
graduum 108, qui simul complent Semicircumterentiam) inter se Multiplicatae
(seu harum Rectansutum) per radium divisae: sequant Subtensam Dupli ar-
cus utriusvis. Nam (per 6 0. Cap. T. ) H) A F (B. HIOC el, Subcentam ora-
duum 244, e Subtenlam gractuum 226. HIoc cst, Biguincantis, aut Priguintan-
iis; (quorum subtensa CMt cadem.) HOC est, =  VEV: 5 = VS R 9
=R B + V5, v V5 = Ry5 +V5 HoC C
54. Padius ductus in V3; Sguatur subtensae sive Biguincantis, sive
Triquintantis. Hloc est, Subtenx gractuum 244 aut Gractuum 226.
55. Hujusque Ouacracum, Subduetum ex Ouacraco Diametri, relinquit
ER4) Ouadratum Subcentae graduum 36; (quanto gractus +4+ deticiunt
d Semicireumterentia, _ gradtus 226 candem superant: Nam 180 = 144 = 36
= 216 - 180.) Ejulque Radix quadtacica est ipta subtenta, Y. 3=  5 R4.
15
R. HoC eAt,
56. Seementum Majus Radii extrema ex media proporcione secti, est Subcensa
eraduum 36. Hloc elt, Semiquintantis, seu Laceris inseripei Decasoni.
57. Sed ostentum est (5 38) si hoc Radio addatur, (hoc est Subren(a Bra-
duum 60, seu Laceri inseripei FTexagoni,) Fiet Subrenla gradtuum 108, Teu Tel.
qui quintancis. Ergo,
58. Recresatum Subtensarum eraduum 36, e graduum 60 (hoc est, L ale.
rum Decagoni ee Fexagoni) Siquatur subtensae gractuum 208; hoc eAt, Sel
quiquincantis, seu Prium Decimarum.
59. Si ereo Subtentae practuum 36, Y5 = = R, aditacur Subtenta exaduum 208,
=R; sC YSRq seu RY 5. HOc est,
60. u-