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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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ADDETIONE
vel deleris 2 manebune 3. Demonstratio dependet ex illo axiomate, Si aequalia
aequalibus auserantur, reliqua erunt aequalia. Ideoque Si Line
deleris utringi 3
manebune
Sisitur, ub ex Additionis summa additorum al-
terum auteratur, quod reltat aequatur additorum
reliquo, operario rite peracta cMt; S autem Resi
duum subductionis, reliquo addendorum non
consruat; indicium elt erroris. Aeque idem in
Sranctoribus numetis accidit. Or in apposito ex.
emplo.
Si aureur plures numeri addantur; Subdu-
ctionis opus lapius eric iterandum. VC in ex-
Cmpso appolico.
Verum cum hoc pacto examinandi labor eva-
dat ipsa primaria operatione major: Satius For-
casse videbitur iptam pocius Additionis opcratio.
nem repetere: praelerrim Ci ordine retrosrado vel
aliquo alo modo inverto procedatur: verbi gra-
tia, st prius gulas series a nota suprema deor-
Tum plocenus (ue in exemplo ulcimo, 5 + 4
-9. 9. F 3 = 12. 12 76 ==+8) in repetita
operatione ad intima nota incipientes procedamus
Turtum, (uc 6 F 3 = 9. 9 f 4 == 23. [+3 f5 = 18,
ue eo minus sit vericuli in eundem errorem, li.
quis prius commillus tueru, denuo incidendi.
Ouod aurem de Addirionis probatione in addendis numeris absolutis dictum
est pariter etiam in addirione Algebrica e Speciola locum habet; ut de in ad
dendis quantitacibus plurium denominationum. Iam ec hic eadem ommino ratio
obtiner quae superius, ur non sic opus alia demonstracione. F. xempla (UNCO.
Ho. unc. drach. sCr. er.
3785692
4825865 aldetiat.
86TT55 Summa.
482586 Subducendus.
378569 ResiduuS.
38925
79634
82703
98516
addendi.
230778 Summa.
38925 Subducendus.
200853 RelidurS.
29634 Subducendus.
2812F0 Retiduns.
82703 Subducendus.
98526 Residuus.
AdC
Summa 1C
Subduc. 2
ReltaL. 73
Adeliio Z
ted
3B F C F
+2C
dubalic. 33
A F 3B- C. F 2D
D
D
erobatio,
Subducti
onis.
2b3
=+ TR +
2
38
L. F TR -f
363 = 2b
AcuIO.
Subeet.
46 O∞ adaII.
263 = b f 40 F oC Cubduc.
3 + 3b -5b = 13
In Subduetionis probatione, Cactem fere methodo incedendum elt, qua in pro.
batione addirionis: sed vice verta. Ur enim subducendo examinatur additio, ita
addendo examinanda eAt subduetio. Nempe, Si quancitas ABlaca e RClidua Limut
addira constieuant quantiratem primo Proposiram (unde nempe altera auterenda
erat) indicium eltoperationem rite procestisse; Iin secus, crracum clt. Nam Ab-
latum e Residuum Simul aequantur Inteoro (quippe Pocum Fuis Partibus Cimul
Tumpris;) ideoque si Residuo restituatur Aolatum, redibit
Inteoerum. Fxempli oratia. Si ex numero quinario, autera-
cur binarius, e ternarius superesse dicatur, Patet operatio.
nem probe peractam esse, quia numeri binarius et ternarius
Cablacus d reliduns) limul addiri consticuune quinarium.
Quod icidem in cocidem piinctis oltendetur; nam (I pun-
ctorum quinque deletis duobus, tria dicantur superesle;
rerum illud esse liquee, Guoa  etsbs s relidius relticuantur duo ablata,
redibic punctorum numerus quinarius primo posicus. Vet denique si sint