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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)
# Folio 468, page id 851387705:0488
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AR ITAMETTCA
Arem.
minor c b
duarum 2
m
duarum 
Prop. CXCI.
minor qual r3 = Y 2=
ajor quam, 13 = Y +2
Ex propterea B n 7 = y = 3∞
Sminor quam 3 XV 2 .
Emajor quam ZX V L2.
HOC estus A minor quam 3  3 ~ Y L3. major quam:
3 + VF2.
(minor quam
n
XYX3
majoc quam 3 + 5 x Y 15
Hhoc elt, ominor quam  u a u a 26Y 25. majoc quam
2 X 4
PXG
2X 4. X + 26
Et (concinuata ejusmodi operatione juxta PabelIX leges) invenietur
Cminor quam3
Cmajor quano
e 
(5X5X7X7YGY OHELKZEXTZX12
2x4 X4 2676Y818L1OX 10+ 124 12 1 24
3X3X5XSX7 XZXOY OXTEXTEXT3XF3
Y2i.
ZKALAL6X6LBZBZLOLLOL22 LI2L24
2i
3
Et Sic deinceps quousque libet. Tra nempe ue tractionis Numerator Fat conti.
nue muluplicando numeros impares 3, 5, 7, ecc. his Politos; Denominator vero,
continue mulciplicando numeros pares, 2, 4, 6, c. bis item POHIIOS, exceptS
primo ec ulcimo, qui lemel ponuntur: Pt toca denique ratio sen tractio, sic facta,
ducatur in Radicem quadraticam Onitacis aliquota parre sui auctae; ea nempe quae
denominatorem habet cum qui cst ultimus numerorum, continue mysciplicatorum,
imparium, si quaeramus numerum justo majorem, vel parium, si julta minorem.
Acque hoc pacto cousque tandem pervenietur donee majoris ee minoris ditte-
rentia cractat quaris altignaca minor; (quae PropterCa, Si Sipponatur in infinitum
concinuanda operatio, randem cranicura CA.) Ouod quidem, E opuss, sic de
E
monstrabitur.
Numerorum, ita ut jam dictum est, concinue mulciplicatorum, parium maxi-
mus (nempe, ex Denominatoris factoribus ulrimus) dicacur 2; adeo que impariun
maximus (nempe, ulcimus ex Factoribus Numeratoris,) exit 2 = - L, (quippe qui
ab ilto unitate detieic.) Frit isitur (proxrer eundem ucrobique mulciplicato.
torem compoticum) numerus justo major ad numerum julto minorem ut
V2 = - ad Y 2 =, (nempe, uc terminalis numerus surdus in illo ad cerminalem
numerum turdum in hoC,) hoc est, ut V - - ad V =  = hoc ct, ut Y- 
2d V: 2. = T: Hoc cle, ut V 33 = ~ ad V: 2 - F. Fieri aurem porest (aucta nem.
pe, quantum opus est, quantirate 3) ut differencia radicum V ~ e V: 22 = +:
nempe Z = V: 2 = 2: minor cradat quaris assisnanda, (ut nocum clt, et alibi
etiam a nobis dictum ad prop. 29. Con. Sect.) Et Propterea numerus julto ma-
jor excedat numerum justo minorem, secundum cam rationem quae minor Lc qua-
vis altienata. Quod crar ostendendum.
Cum autem, ut ex dictis patee, aucto in infinitum numero Z, numerus julto
major numerum jutto minorem ea ratione TupeTCF quae minor sic quaris astienata:
exie
Ex (pari ratione) exit d = Cx