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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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Cap. XCV.
4.BF - F A B
A L G F B R A.
LX4. AD: FrrOre non majore existence quam  V a N, sC
560 aa
Oui semper minor erit quam r_ totius segmenti, etiamli Sesmentum illud Foret
Semicirculus.
Similicer, in Flipse vel Hyperbola B AB; cujus Vertex A, e illetvis axium
AK, et FacuS rectum AP: Sumatur prO F IIpH, PC = = AD J FDAR ZLAF
Sed, Dro Hyperbola, PC = = AP f 2DAK. f 2F AP p A P. Lcctase  BB
FOAK
abscindet Fansencem AF, proxime aequalem arcui Elliprico, vel Hyperbolico
AB; modo non Tu arcus valde magnus.
Tiem, pro Area segmenci Fyperbolici BD A.
TnDP, Sumatur DNT = 3ADC
+ AK
Frectisque in
D _M perpendicularibus, DB, NN, secanti
bus in B_ N Semicirculum diaetro AP de
seriprum. Sic exic F. A N F A B
Proxime. Vel actrue propius; Si sumatur DM =
SAD9
A F; acquerum 2FAN + 4 AB ,4AD = BBA,
DrOXIe.
Sine adhiic (in eisdem Schedis) multa alia contimilis natuTX. Ttem (aBuId
extCTOS) Libnitius _ Chirnhausius nonnihil hujusmodi praesticerune; (qui de
hac re scriplerant, uei audio, ad D. Oldenburcium Liceras aliquas, sed quas ego
non vidius) ec (apud nos) facobus Gresorius, et Nicolaus Mercator. Sed quae
Tune (ut plurimum) nonnisi Casus aliquot particulares, intra ambicum genera-
lium Regularum Veretom.
Fale est illud Zibninii, edicum in Actis Fruditorum Zipsiensium pro mense
Febraario, 2682. Obi ostenditur (inter alia) Quadratum Diametri ette ad A.
ream Ciireuli,
DC x ad F - 3 f 3 - 3 + 3 = et f 15- 5 + ri = is ec. in infinitum.
Oux quidem est Conversens Series (sed tarde conrersens) quae tandem perdu-
cet ad Difterentiam data minorem.
Veretonus (in dicta E pistola Oetob. 24. +676.) tantundem extibet in simili
ferie. sed cum aliis signis. Ouippe in Leibniti serie Tigna L = alternantuF
cingulis locis, sed in Vereroni serie in binis quibusque. Sic Scilicet: POnatuE
Chorda Arcus quactrantalis in Circulo = Z, adeoque Circuli diameter = Y2. LOn.
vicudo quactrancalis arcus exit,
= 5 + 5 = 5 - 3 + 5 f  = 1n = 1 + ec.
Arcusque dimidii = = f 15 - 53 + ias _c.
Oux non minus simplices sune quam illa Leibnitii, _ magis COnrerBUnI.
An aucem harum omnium ulla porior sic pro Ouactratura Cliculi Approximatio,
quam ea quam eso primus extribui, Lectoris elto judicium. Nempe; ut r ad
3Z3Y5YSY7XZXOX OXTEXLTXL3X23
2 X 4. X 4. X6XBXBXBX IOX IOX T2. X I2 X T4.
EC
HIoc Cl, 2d F X 8 X 32 X ad X 3b X Yio X 76B _C.
Seu 1 + 3A f= B F ao C F os D. = iio L + 1oo F _C.
Dum haec sub prelo crant (in Fdirione Anglicana) prodiit eodem anno 1684,
Fdinburei; Fractatus consimilis naturae, Davidis Gresorii (qui et Facobi Cre-
eorii NePOS ex Fratre; et Macheleos tunc Protestor Kainburei; nunc Collesa
meus meritistimus Oronia, Protestor ACtronomix;) cui Piculus Pvereitatio nova
de Dimensione Ficurarum. Vbi plura suppecune fexempla hujusmodi procestium.
E90 aurem hic Specimina tancum exhibui iltius Doctrinae, quam speraverim Nere.
CC3
tonum
TO AK
AP.