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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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M M F
e
 LV M
Demonstratio.
Disterencia rectarum _, Cy dieatur X = A = F. FLFac, W X ad F, hC A ad 5,
e F ad F. Erit S, alcieudo corius Pyramidis vel Coni: P, parcis ad verricem ab-
Scilla. Adeoque SA9, criplum corius eyramidis vel Coni; P P.g, criplum parris
abscissa; et S Ag- P F.q, retidui Fructi criplum.
Est aurem S =
criplum Fructi.
∞
E. E1BO SA- PE.q-
F.AC- FFe Nem tic
X = A F.
Sed est AC - F. C = A9 + AX. + X. 9 in A - F, F,∞O. 
= XC
AF L F g. FEPEOBUrCa A9 + AF + Fg in F, criplum Frusti.
L L
=19 +
Si aucem Formecur Friangulum uc dictum est; Ouadracum Balis Zg aequabitur
cribus 29 ) AF + Rq Simul Cumpeis. Sed de idem Z9, aequabieur 3 RG, cri
Dlo quadrato Radii circum seripei circuli, (quorum urumque llacim demonstrabi-
TuT.) Adeoque cum ZgF = 3 RG F MM criplum Fructi, cum RG L Fructo X
quale. Ouod crai proposieum.
Quod aucem probandum susceximus, A9 + AF. + F. g = Z9 = 3 Rg. Sic
Octendimus.
Si Friangulum vc dictum est cirento inscribatur; cum angulus cruribus A, K,
concencus sic angulus in Peripheria, Grac. 220, adeoque insiltat arcui graduum
240; recta Z complens criangulum eric chorda cum arcus gradtuum 240, cum et
arcus practuum 120, (retidui nempe ad incesrum cireulum: ) Adeoque latuS exIt
Frigoni regularis inseripei. FL propierea Z g == 3 RG.
Sed e A9 + AF + Xg = 3 Rg. Quod lic probatur.
Si recta Aponacur Subcenta arcus simpli, erie arcus cripli subten(a 3 A - 
RG
Sin ponatur P subrenta accus simpli, erie hujus arcus criplicati Tubren (a 3 F. - =
Est autem una eademque recta, puta C, cum Areus A criplicaci, cum criplicati ar-
cus  Tubrensa. (Cum enim arcus _ F, Timut Cumpei, compleane criencem cir-
culis ucrique criplicati complebun circulum incesrum. Adeoque quae ex una parre
Tubrendit eriplo areus  eadem recta ex altera parre Tubcendic triplo areus K,
quippe residuo ad inceerum circulum.) P. L prOpterea 3 A - - C = (C. = ) 3F.
Et ZR9A = AC = 3 RGK = RC, EL3 RG A = 3 RG F = AC = F.c. Adeo-
que 3Rg =
10 - LC
= Ag + AF + F. 9. Ouod demonstrandum sulceximus.
Vel sic brevius, (sine ope rectae Z, qua nulla necesticace sed per spieuicatis cau-
ta adcicur. )
Duoniam A - P.. F:: A.
plum vrusti.
e
et
2- 1
EN EA PEC M- EC
A F.
L X
Scd e (propter anguluum or. 120.) areus M s, Simul, complene crientem cir-
culi; eorumque cripli, circulum incesrum; qui (cripli) propcerea candem habe.
EC
bune cubrentam. Nempe 3 A -   = 3L . Aeoque 3Ag A - A0 =
3R
e
e