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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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DE NIULTTPETCAPIONE Cap. XX
cunda, certia, quarta, ec. Ita nempe ut cujusque poteltatis index aequalis sic nu-
mero dimentionum.
Solent aurem Radix, Quacracum, Cubus, Biquadracum, (reliquaeque deinceps
Poreltates,) Sic notari, 28, 23, 2, 2373, erc. (ut olim,) ret R, , C, Q, dc.
vel eriam A, A9, AC, A9G, etc. vet an a a, at, ecc. (ur tulius diximus Cap. XI.)
nempe compendii causa pro an aa aaa aaca etc. Lx proprerea (notas illas in
tras, ubi opus exit, relolvendo) a = aa a = a a = aaa. at = a a = a a = aa
aaaa ec. TIem A9 = AA. AC = AgA == AA9 = = AAA. A99 =- ACA == A9A9
= AAC= AAAA, SC. Sic 2A9X3AC est 2 A A X 3 AAA. et 23 x ∞ =(8 seu
De XZe in 2 X ZCX2B. HC CONtra A) Ag9 (AC, hOC CA A) AAAA (AAA.
E5)B8 (E, hoc ett 2e n 2) 2e22ex2ex2 x2 (2e x 2 x 28. Sic a) a (a hoc
elt aaa) aaaaa (aa. F. L Tic in aliis.
De senis Duod aurem autinet ad signa + e -, in mulciplicacionis Producto, vel divi.
ex . Tonis Ouoriente, ponenda; hac obterranda cAt Regula.
In Mulciplicatione e Divisione, si datorum siena sint similia, Producti vet
Orri sienum erit  (affirmativum:) sin dissimilia, - (necativum.) Nempe
 per +, vel = per =, dac +, (live mulciplicando sire dividendo;) et 
Der -, vel  per F, dac -.
Vel etiam (quod cancundem ralet) Si multiplicatoris vel aivisoris signum sit
. Nulciplicandi vel Dividendi sienum retinetur; sin =, mutatur. Nempe
F per  dat F, ec = Der f dac =; item f ver = dat -, e - per - dac 
Racio sive demonstratio hujus, ab ipla Mulciplicationis et Diritionis natura pe.
cenda est. (Ouales c80 matim, ubi tieri potelt, alterre, quam demonstrationes)
Polteriori.) Quam isitur in lingulis casibus oltendam.
citat to. Mulciplicacione supponitur quanciras Muliplicanda cories poni quories mulei
plicator indicat, ut ex supra dictis cap. 18. Patet. Adeoque qui quancitatem
quamlibet (sire policiram sire ablaciciam) musriplicat per 3 vel f 3, ille eandem
quantitatem (sIgNIS NON mUTatIS) ter Ponit; qui per 2 rel = 2, bis ponit; qui
per F vel = L, lemel TaNCIM; qui vero per o, ne semel quidem, led pallies vo-
nit, (adeoque quanciras quaelihet, per o mulciplicata, cranescit:) qui aurem per
F, - 2, - 3, ecc. mulciplicat, toc ricibus paucius quam nullies ponit, (eum
=F, = 2, = 3, ecc. sine minus quam nihil, leu paucius quam nullum,) hoc elt
revera cories tollic, (per ea quae diximus Cap. XV. de signis  e- contrario
sensu exponendis;) qui vero collie, ille cancundem ponit mutato signo, (ut ex Jc-
sibus Subductionis Cap. XV. Patet:) Et propterea qui mulciplicat per L, 2, 3, ec
vel alium quemris mulciplicatorem attirmatirum, is quancitarem mulciplicandam
coties ponir serrato beno; qui vero mulciplicat per = 1, = 2 - 3, ecc. aut
alium quemris mulciplicatorem negatirum, ille quanciratem multiplicandam tocies
vel tollic vel (quod tantundem est) sub concrario signo ponic. Ouod erar oltenden-
dum. Adeoque AXZ == 2 A, Ax -
2A, = AX2 = - 2A, = AX= 2
 = 2 A (nempe = A bis. TOHitE:) Sic AX B = BA, A x - - B - - BA,
 A XB = == B A
sic in reliquis.
x. B = = BA (vet + AB quod cancundem cst.) F. L
In Diritione, quaeritur quoties divisor, seu quancitas dividens, in quancitate
Diridenda continetur; Vel (gusd cancundem est) in quam quancitatem ducendue
CA divisor ut tiac aequalio quanriraci Dividenda; ut paret ex iis quae de Diritione
cradica Tunc Cap. ZIZ. Fc propeerea, ubi quanciratis Diridenda tionum elt L
(attirmatirum,) sienum Ouocientis idem erii acque diriloris; sin quantitatis Di
videndx signum sc = (negacirum,) signum Ouocientis exic signo diritoris con-
crarium: cum enim diriloris in quocienrem ducti productum Futurum est aequale
quancitati dividendx; non porest illud attirmatum esse, nisi lactores ligna ha-
Beane similia; nec nesacirum, nisi dislimilia: uc ex modo probatis constat. Adeo-
que si diridacur + per +, vel - per -, quoriens erit +: sin + per =, aut
 per +, quotiens exic =. Ouod crat ostendendum. Adeoque 2)
104
Dach.
Dio-
Phant.
1. T. dc
nium
als.
art. 2
cap. 4. 1
i  die tetat ted
Sic a)YA IV.