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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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ap. C
lL G F B R A.
42. IIlique Areus (in parribus infinite extB) habendi lunc quasi coinciden-
18
tes cum portionibus Fangentium incer ealdem Ordinatas interccpeis. Or in
43 Hloc est; cum portionibus Pansentium Lacicudinis.
cudinum Pansentes, ad Sinus Tucs.
45. Quo itaque habeatur interceptorum Patallelosrammorum (seu SCsmen.
torum Fipurx) vera magnitudo: Vel proctanenda funt aequalia baliS Segments
aequalia trant illis in Fis. 8.
irahenda erune Secantes in eadlem ratione; (Nam, urrovis modo, intercepta Rect.
tam; quae (loco Sccantis) Basi intistal aqualiter dirita.
Fig. 7 (in ea ratione quam habent Lespectirae Tangenres ad Juum Sinum,) ue
44. Sunique lx Fansencium portiones, ad aqualia batis Segmenta, uc Laci
46. Vet (quod tantundem Vatel) LClCHCS aegutalibus interraliS FiGIER Z, PrO-
angula seu Parallelogramma aequaliter ausebuntur: ) VE L. M Fi8. 9.
47. Nempe; Or Sinus (lacicuuuss) au l’ansentem Tuam; sic Secans ad Ouar.
 = S. , L.8. 5
+.
e F ec
48. Oux ieaque TuHE, ut OrdinatX
 Llguta, quam roco (Arithmet. In
fin. PrOD. 104,) ex Reciprocis Secun-
danorum. Sumpris nimirum quadratis
2 In ordine Secusidanorum; seu ue lune
49. Hloc allem (Propter 23 = R
Sinulque S’in progrectione
ArichmLCa) reducitur (diridendo
in hanc Seriem Intinitam.
Arichmetice procedentium Ouadrara
52:
2
50. HIoc est (DOlItO R = F)
F = 52 f 54 f 5 dc
SF. Tunque (secundum Arictmericam Intinitorum) incerprecandus est S Tuc.
celtire per F5, 2 5, 3 s, erc. donec perrenitur ad s’maximum; qui itaque re-
peasencar numerum omnium
52. Jam vero; Duoniam primum membrum repraesentat seriem Aqualium;
secundum, Secundanorum; terrium, Ouartanorum; de sic deinceps: Primum ita-
que membrum mulciplicandum cst per S; secundum, per 3 S; cerrium, Pet Z ai
quartum, per Z Si et lic deinceps
53. Fritque omnium Ascresatum,
5. +5 5. +5 51 + ; 5 +5 5 _C. = F CLA, FiBD. = F RsL. P1E6.
54. Arque haec Series (Propter S semper minorem quam R = L,) cousque
concinuari poterit, donec poreltas aliqua iptius S tam tueric exisua; ut tum
ipta cum quae hanc sequuntur, cuto poltine neplioi
55. Jam tandem, quo tixec (ad Wriehri mencem) accommodentur, ad Char-
tam Nauricam: Data Paralleli propotiri Latitudine; quaerendus est (in Canone
Prigonometrico) Lacicudinis illius Sinus rectus; de huic equalis sumenda C L. =. S
Et hujus ope quarenda magnicudo iptius E. C. P. MI F18. 9. FTOC cst, ipsUS RF L
F18. 8. Hoc est, RFLS PI8. 6. AIque cum; DE RRL F (seu Radius cories
Cumprus) ad R E Ls (ABGregatum Secantium cousque;) lc crit AreuS A qua
toris (aequalis areur Lacitudinis prODOLICX,) ad distanciam Paralleli (lacicudi
nem illam in Charta designantis) ab A: quacoris linca. Quod erat inquiren.
dum.
56. Idem similicer obrineri Doceric, sumpris sinibus Versis in progrectione
Arichmerica.
dc