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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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Cid . L
ANGULARIBUS.
246. Differentia Quadricuborum Crurum continentium eulum eraduum 244.
aut 22. Divisa per Differentiam eorundem Crurum: Vel Summa duadricube
rum Cirurum continentium inculum craduum 36, aut 208; Divisa per Sum
mam eorundem Crurum: Seu (quod eodem recidie,) Biquadrata Crurum lin
priori casut) Ona cum Tribus Mechis proportionalibus inter ea Biquadrata; AUI
(in posteriori casi) Biguadrata Crurum, Ona cum Medio proportionali inter ea-
dem Biquadrata, Dempris Primo e Tertio erium Mediorum inter eadem pro-
portionatium: equantuir 20 Biquadratis Radii circuli cireumscripii. Atque, Llaec
ad Biquadrata Basium suarum, respective sumptarum subtendentium neulum
ractuum 244. aut 36: Sunt, ut 4 ad 3 = V5: Sed subtendentium Anculum
oraduum 72, aut 208; ut 4 ad 3 = V 5. AUE, ut 8 ad 6 - 2Y 5; e 8 ac
6. L 2V 5. Hoc cA, in Duplicata ratione ipsiuS, 2V 2 2d V5 - + = V: 6 - 2 V5:
ixliulque 2V 2 ad V5 F L = V: 6 + 2V 5.
247. Paque L alera, concinenr hos qui sequuncur angulos;
Fatera. Gradus.
1 F
H, A.
MI, F.
1I.
244.
Lacera. Cradus. Latera. Olacilio.
L, A.)
1.
M, L. C
At N.
16.
Ex quibus, Ouatuor priora Paria, sunc signorum similium: Sex Polleriora,
Dissimilium.
243. Fadem Aiquationes, postime sic eriam considerari. Ouoniam (per S FTO,)
SRg4A -- 5RgGH. = sA9 AC - 5RGF C - Ac9. F H C9. FrgO (diri(IS
omnibus Der A = R, ILCXILINGUE pEr SRG,) erit R9 = A 9 f AH + F9-
a94 F ACF + AgF 9 + a P C + F. 49. Ee (per cranspoluionem)
5R9.
A9. F AF. F E g - R q in SRg = A99 f. ACF f AgF g f. F 9G.
F49. EC similiter; (quoniam M, A; et M, L; e Ly H; trabene icem similia.
Signa)
M9 L MA F A9 =RG in SRg; = M99. L MCA L M9 Aq F M AC F A99.
MI9 F MIE f L. 9. R q in S RG; = BI99 LMCF F M9F 9 Y MEC F E99.
L. 9 F L. N F N9 Rg in 5R 9; = L, 99 + L. CN + L. 9N4 + L. NC + 199.
25O. ErCO, In Trianeule Rectilineo, cujus Crura coniinent Aneulum praduum
24q (UE A, L.;) aut 72, (uE MI, A; vel M, E; vel Ly H;) Si duadrata Cru
rum, corumque Rectansulum, Dempio Quadrato Racii circuli circumseripti: Du-
cantur in uincuplum Quadrari ejusdem Radii: Quod prodit, aequabitur Biqua-
dratis Crurum, una cum Fribus Mediis proporsionalibus inter eadem Biqua.
arata.
25I. Similicer ostendecur (ubi siena Crurum sume Distimilia) quod,
L9 - L A F A9 = R g in SRg: = F 99 - Z CA F L gA9 - L. AC f A99.
Ng = NF F F g - 2 9 in s Rg: = N 99 = NCE F NgEq- NEC + F99
Mg -NIL F L. 9 = R4, in 5R9: =M 99- M CL f MGL, 9- NLCI L99.
NEg - MN F N9 = R9, in sRg: =M99 = MCN. F MGN9 MNCF N99.
N9 - NA f A9 = RG, in 5Rg: = N g9 - NCA + N9A9 NAC + A99.
L. 9 - L. F = F. 9 = R9 in 5R9: = L. 99 = L CF + L. gF 9 L. FC + F99.
52. ErGO, In Trianeulo Rectilineo, cujus Crura continent Angulum graduum
36, (uE L, A; vet N E; vel M, L; vel M, N;) aut 108, (ut H, A; vel
nE; Si Ouadrata Crurum, Dempris corundem Rectansulo e Duadrato Ra-
du circuli circum soriori: Dusantur in Dcintuplum Duadran ejusdem Radii: Quod
prodit, aequabitur Diguadratis Crurum, Ona cum Medio proportionali inter ea-
dem L2
porcionatium.
CCC2
253. Tamgue
8
A.
F. 5