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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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Cap. XVIII. DE NDLTTELECATIONE.
Sic in numerum 230040; sepotiris cribus ciptiris Finalibus (mulcipticandi nemp
duabus de mulciplicatoris una) habebitur 939736404 = 4085FX 23004; cni nu
mero l’acto si relticuancur rres illa ciphrae lepoliu, Prodibic 939736404000 =
4085100x230040. tic paricer in aliis.
Racio opcrationis lacis elt evidens. Si enim, verbi sracia, 300 per 20 multi
plicare oporieat; et, sepolicis ciphris, ducuncur 3 in Z habebicur 6 -= 3X2. P1
Teltieueis ciphris, 6000 = 300x 20. NTam, ( bis 3, Sint6; crune bis
30 dccies 6, hoc ct, 60; e bis 300 dccies 60, hoc clt, 600; ee deni-
que si bis 300 fint 600, crune vicies 300 (sire bis decies 300) decies
300
20
500, hoc cL, 5000. Ouxlibet enim adjecta ciptra numerum cui ad - 6000
jieitur decuplum tacit. Ec pariter in aliis ejutmodi mulciplicationibus
quibuleunque
Acque hinc liquet, cancundem prortus valere
Sive 2 ducancur in 3000, live 20 in 300, sive 3000 300, 30
200 in 30, lire denique 2000 in 3; quippe in 2
20111 200 2000
linguliS CMErGIE HUIErUS 60OO. CUt PatCL. LF 6000 6000 6000 6000
Paricer in limilibus.
Aique hactenus quidem de numeris incextis invicem mulciplicandis dixille sut
Fieiat.
Siquando numeris inceeris annecti contiserit parces aliquor decimales, live Parrium
(quod idem est) loci aliquot intra unicacis locum descendentes; eadem ommine decima
exic operarionis mechodus acque in numeris inteoris: cum hoc Tolo discrimine, lium mul
quod pollquam numerus productus eodem platie modo invenitur aeli cMene nu. tiplicatio.
meri omnino inceori, candem cor loci in numeto facto linea separacrice lunt ab
seincendi, ut parces decimales, quor crane in ursque simul F’actore sc abscitti.
Exempli sracia, Si numerus 36525 ducendus esset in 35
Polequam (quali ettene plane ICCBFI) invenerim productum
T278375 =36525X35; candem, quia in tactoribus rideo cres lo-
cos parcium decimatium (duos nempe in mulciplicando, ee unum
in mulciplicacore,) cres ulcimas producti tiguras linea separatrice
abscindo ut parres dccimales: adeoque habeo 1278 (375 = 365 (25
315. Acque idem in aliis parcium decimalium mulcplicationibus
oblerrandum cru.
365 125
B
182,625
2095,75
1278(375
Lacio hujus operarionis haec est. Ouoniam, uc numerus quilibet adjectione
ciphra in tine, decuplo ausetur; promora nempe qualibet tigura in locum proxi
me Superiorem, uc quae prius unicaces cigniticabar, jam signiticer decactes, e sic
de reliquis: ita tigura tinalis abscistione linca separarrice, numerus decuplo mi-
nuitur; derrusa nempe tigura qualibet in locum proxime inseriorem, ut qua
prius decades signiticabat, jam signiticet unitates, e sic de religuis. Puta si nu-
mero 35 adjiciatur ciphra, fiet 350 decuplo major; Iin ab eodem 35 abscindatur
linea leparairice tigura ultima, eric 315 decuplo minor. Ec similicer judicandum
erir ubi dua, tres, aue Dlures adjciuncur ciphea, aut cocidem abscinduntur loci
decimales; nempe numerus cencuplo, millecuplo, ecc. adjectione augetur, vel ab-
lacione minuitur. Adeoque in exemplo proposito cum 365 (25 lic cencuplo pi
nOr quam 36525, erit etiam 365(25 X 35 centuplo minor quam 36525 X35; cum
que etiam 315 sic decuplo minor quam 35, eric 36525 X 3(5 decuplo minor quam
365(25 X 35, adeoque decies centuplo, hoc est millecuplo, minor quam 36525x35.
Cum initur sic 2278375 = 36525X35, abscindendae sunt linea separarrice cres
ulcimae s Ma i numerus tiac millecuplo minor, nempe +278(375 5365(25X35:
adeogne loura 8 quae prius lisicabat coc millia, jam signiticac non nihi coridem
Pandem de hanc libet (ex Ougheredo) regulam generalem proponere, quae Denait
in cuos altionando numeris mulciplicatione Factis locos, sire in numeris intesris, numeri
live eriam partibus decimalibus, dirigat. Cum luos cuique loco indices assignari facti.
THIS, Ita nempe ne Onicatis locus indicent MaMatO (ue qui neque ascendit neque
ace) loci aurem supra su acceemes Pus, secundus. Tercius, ec. In-
dus, cerrius, _c. indices habeant negatiroS = Z, = 2, -3, dec. Index cujusque
Parcieularis Facti in mulciplicatione, aequatur indicibus utriusque Factoris simul
sumptis.
Onitaces, e lic de reliquIS. O
Acque haec eriam Sulticiant de partibus decimalibus mulciplicandis.
dices habeane attirmatiros, 1, 2, 3, ec. ec concra loci descendences primus, secun-