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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)
# Folio 387, page id 851708439:0411
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Cap. LIC
= + 26 1Y-
20
56 a
L G F B R A.
6
60
i
5a
160C9
3663 a a
5C~
76a
ec.
Eri mimerales Coefticientes terminorum in suprema linea (2, - =, - 10,
576, ec. in insinitum,) oriuntur a continua mulciplicatione primi 2, Dex termi
nostrujus progrectionis,
= THZ EX3 345 5X7 7 Y 9
2X 34 X 5 6X7 BKG FOXFF
_c
Pc numerales Coefficientes descendentium terminorum in quaque columna, in infi
nicum; oriuncur d continua mulciplicatione supremi; nimirum,
In prima columna, per candem progresionem.
XF 3X3 5X5 7X7
In Secuncam per hanei 2 n 3 4 n 5 6x 7, 829 dc.
XF 5X3 7X5. 0XZ
In terria, pex HanC, 2 X 3 4 X 5 6X 7 8Xg .
XF, ZX3 9X5 TTX7
In quarta, per haner 2 x 3 4 X5 6Z7 8XO
XF OKZ TEX5 Y3X7
In quinca, per hanen 2 x 3 4x 5 6n 7 8X9
Et sic porro in infinitum.
_c.
dec.
simili modo, postunt mulcorum aliorum Solidorum Segmenta detienari; eorum.
que ralores exprimi per hujusmodi series numerales, regulari ordine procedentes
In Problematis perplexioribus, in quibus haberi non poterunt hujusmodi se.
ries, sive per Diritionem, sire per P. xeractionem radicum A quarionum simplicium
aut aftectarum: alciores achue methodi procectuum actribenda Tunt. Ouales ha-
bere se duas ait: alteram Fxpediriorem, alieram magis Creneralem.
Sed e alias item methodos innuit obrinendi series Conrergentes; quarum de
nonnullas exhibet: Sed quasego, ne prolixior sim, omitto.
Per has methodos; Duando Problema reductum fuerit ad hujusmodi Seriem,
infinite continuandam; muliae approximationes, ului commoda, tacile obtineantur,
ec labore non magno, dua alias agre obcineantur, magno cemporis de laboris impendio.
Hlujus Specimen exhiber in exemplo subjecto, pro Circuli Ouadratura; cum illo
Clarist. Christiani FLugenii, super idem subjectum, comparando.
Exemplum Z. Data cujusvis Arcus chorda A, areusque dimidii chorda B; Lnve-
nire arous loneitudinem, proxime. Ponatur arcuS = Z; et circuli racius = r: tM
(per ea quae lupra ostenla lunc) habemuo ( duplum linum aecub 3. 2)
dc
_C.
FCB =
4X6rr 4X4 X T2O74
2 X16XOY anotLa
Pum