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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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ARLTAHETICA PFOP CLXV.
nis explicationem quam omnes sisillatim repetendo; rato enim dux vel plures
Occurrunt commenturabiles quae in unam addirione colligi possint.
Verbi gracia, s ponatur circuli Raclius aequalium parcium 6, Sinus recti seu Or-
dinatim applicata in Ouadrance lingulis parcium iltarum rerminis inliltentes, crunt,
V: 36 - 0:  V: 36 -= E: + V: 36 - 4: + V: 30 - - 9: + V: 36 -- 26: + V: 30
25: f V: 36 -= 36: (Der ea qua dicta TunE ad pr. X2F.) vel quod eodem reci
dic, V 36 F V 35 F V 32 + V27 = V20 f VEF -F Vo; rel, ue irrationalitas
ad minumos terminos reducatur, 5 f V 35 F 4 V 2 f 3 V 3- f 2V5 f V IT F0:
Racio igicur quam habet illud radieum aggresarum ad radicem maximam tocies
Poticam, puta 7 V: 36 = 0: rel 2V 36 vel 7X6 hoc elt 42; non explicatius ef
ferri porelt quam  F Y 35 + 4Y2 + 3Y3 + 2Y5 F Y1 +c
arque ea
eA rario quam habene illi sinus recti scu Ordinacim appliearx in Ouadrante ad
rocidem rectas Ractio aequales d parallelas in Ouadrato circum seripco.
Pariter, si ponatur radius parcium 20; erunc linus recti V: 100 =0: L V:
100 = 1: = V: 200 - 4: f V: 200 - 9: f V: 100 = 16: + V: 100=25: +V:
100. - 36: f V: 100 - 49: f V: 100- 64:  V: 100 - 8F: f V: 100 = 100:
Hloc elE V 100 F V 90 F V 06 -= V or F Y84 = V75 f V64 = V5I + Y 26
FY ∞9 Y V0. Vel cciam 20 + 3V 11 + 4V6 F VOC L 2 V 21 + 5 Y
8 f V5F F 6 = Y 2O + 0. Ouod agerceatum non alicer abbreviari porelt
quam pro 10 + 8 + 6 f0 substimendo 24; ut rario iltius aseresati ad radicem
maximam cocies policam, pura act 12 V 100 vel 2L x 10 vet 110, non explicatius
elterri poltic quam 24 + 3 Y 2c + + V6 F V or + 2 Y21 +513 + 151 + Yr0
O
quae minus adhuc videtur incellisibilis quam ubi ponitur radius partium paucio.
rUIM, Puta 6.
prove eodem modo quo plures supponuntur radii partes eo incricacior neceste
est ut fiat rationis explicatio; qua quidem fere omnium radieum repetirionem po-
Culet, cum pauex admodum, raro quidem, ec non nisi Forcuito qualiu OccurrunE,
qua vel rationales sint vel quidem invicem commenturabiles. lic propierea li
lupponatur Racius partium numero intinitarum, racio proveniens eriam minus ad.
huc videatur explicabilis.
Idem contingeret, Ei, juXta tenOrem prOP. F3G. ponatur circuli Diameter par-
inim F2. Tta enim ellent Sinus recti correspondentes in Semicirculo, V: OX F2
- 0: LF V: FKF2 - 7:  V: 2X T2 = +: F V: 3 x FZ = 0: L V: 4X +2 = 16:
+Y: 5X +2 - 25: f V: 6x12 -36: F V: 7XF2= 40: + V: 8x +2 64:  V:
9r12 = 82: = Y: 2Ox12= 100: + V: FFX12 -121: + V: 12X12 - 244. HOC
clt V: 0 - 0: L V: T2 = c: + V: 24 - 4:  V: 36 -- 9: F V: 48 - 26: = V.
60 = 25: + V: , 2 - 36: + V: 84 49. + V: 96 - 64: + V: 208 = 8L: + V:
120 - 100: + Y: 232 = 221: + V: 14.7 - 244. HIoc ct Vo = V 22. = V 2C
F.Y 27 = Y 32 f Y 35 F V 36 + V35 = Y32 + V27 + 120 F VIT + V0. Vet
propcer caldem radices bis poticas, 2V0 F 2V FF F 2V 20 + 2 V 27 + 2V 32
=2V35 f V36. Vel reducendo irracionalitarem ad minimos terminos, O = 2 VLF
= +V 5 F 6Y 3 F8Y2 f 2V 35 +6. Ratio iBITX quam habet hOC agGrCSA-
tum ad cocidem radices maximae aequales, Duta ad 23 V 36 vel 23X6, hoc Ctt, ad
2V12 + 4V5 F 6V3 + 8V2+2V35 +6
28, non explicacius esterri poreric quam,  
vel
8
Ye + 2Y5. +3Y3. + 4 Y2 + Y35 + 3. Aeque ea eAt rario quam habet
aepregaum illorum sinuum rectorum in semicireulo, ad rotidem reclas Radio
aquales ex parallelas in Parallelosrammo huic semicirculo circum leripio. Si au-
cem Cinus maximus Y 36 = 6 supponatur bis poni (pro utroque leilicet qua-
drance Lemet) atque Capropter prO 13 aqualibus, ponantur 24; (puta, pro
13X6 =78 PONACUE 14+6 = 84;) eadem erie haec racio cum ea quam lupra pro-
venire diximus potico racio parcium sex.
Pariter, S Drameter Ponatur pareium 20; Sinus, relti in semieireuso crunt
V: 0x20 - 0: = V: 1+20 - 5: + Y: 2 220 - 4: + V: 3220 = 9:  1: 4. + 2c
16: = Y: 5x20425: + Y: 6x20-36: 4 1: 7420 = 49: + V: 8720 64:
+ Y.