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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. AAIIL. GEOMEFRTCA.
60. Daris cermino maximo, numero terminorum, ee communi ratione; V, T, R.
dacur rectangulorum aBBrCSatIM. Z. NaM Per PrOP. 20. A = Ra) V. ErGO Per
PrOP. 47. LV A == Z = Rd) TV.
62. Daris cermino maximo, numero cerminorum, de rectangulorum aGGreGatO;
V, E, Z; dacur communis ratio R. Nam, Per DEOP. 53. X = Z) V, L. Br8O
DeT PrOB. 17. R = 1+
62. Daris numero cerminorum, ratione communi, et rectangulorum aggresato;
T, R, Z; dacue cerminus minimuS. A. NaM per pF. 76. Y = Rd. EL PeF pF. 49.
L) 7. = H. EIBO Des PI. 54. FR4) Z = ) H = A2. Ideoque A =
FB
63. Daris iisdem; datur cerminus maximus. V. Nam per pr. 26 d 49. haben
cur X Et H, uE priIB. L1BO per BE. 55. V = Y: I - Y: = 1:
64. Daris cermino minimo, ratione communi, ee rectangulorum agGrCGAIO;
A, R, Z; INVENICUE CerMINOTUM NumerUS T. NaM Per PE. 45, vel 47.
adeoque 
= TM
IV. Icem per pr. 19. V = A Rd. adeoque (cum lcD F L =L)
CTIE RV = A R Rd = A RE EI RV Y = T A R. = A) ZR. (quia nempC
V. ) Ideoque FR = A2) Z R. Ouaerendum igitur, quoca poteltas
datae rarionis communis R, ducta in linum indicem sire exponentem poreltacis.
aequabicur quancicari dacae A) L. R. quippe poreltacis iltius index sive exponens
Cl T, numerus cerminorum.
65. Tildtem dacis; repericur cerminus maximus. V. nam per praeced. habetur Y.
acteoque V Per PF. 19.
66. Datis cermino maximo, ratione communis de rectangulorum aGgregatO;
V, R, Z; INVENITIE MUMErUS CENMIOTIMI F. EIL enim per pF. 45 vel 47
E = TH adeoque V) Z = FA. TTeM peT pr. 20. A = Rd) V. adcoque R) A
=RI
V. EC R) AT = RC) V F =RV) Z, nempe, quia V) L = L A
Et R) T = RV=) Z. Ouaerendum isitur quoca poceltas ipstus H, exponen-
tem luum dividens, extribebit quancicarem datam RVZ) Z. quippe poceltatis
ictius exponens sire index est Y, nuerUS terminorum quXLITIS. Vel etiam (nam
eodem recidic) mutacis sedibus, Z) RF == Z) RV2. O quaerendum (E, quoca
Doceltas ipsius R per suum indicem Tire exponentem dirila, exhibebit quancica-
rem cosnitam Z.) RV.. quippe pocellatis illius exponens est P, qualicus nume
TUS TETMINOTUM.
67. Datis iisdem, rePeTItE cerminUS minimUS, A. nam per pExced. habetur T.
adeoque A, PeF DF. 20.
Acque hae quidem propositiones omnes tactenus tradica, respondent cocidem
propolicionibus Cap. XAVII. de Progrectione Rrichmerica; linguli lingulis co-
dem ordine.
Seguitur Theorema, quo, in Geomerricx proerestionis Tumma investisanda,
ucuneur tere omnes Arichinerici. Nempe,
68. Si terminus maximus in communem mulciplicatorem ducatur, et ex produ-
eto auteratur cerminus minimus, reliduumque per mulciplicatorem communem
unitace minutum dividatur; quociens exhibet progrettionis cocius Tummam. HOc
est,
R - 1
Ouis hanc primus invenerit regulam, aut quibus mediis, exo plane ienoro; e
quidem, uenc ea plerique utantur, non memini tamen e illam uspiam demonstra-
eam vidilte; cum tamen rel maxime demonstracione indiseat. Nobis itaque hanc
libuic demonstrationem comminilei
Cum (IC, Per PY. 19. V = ARd, adeOQUE (DTOPIEF Y = D F L,) V R = ARC, de
PrOPIerem VR = A
ARC = A
e -
Facta divitione quanciratis A R. = A, per quan-
titatem R - Z, (eo modo quo supra octendimus dum divisionem Symbolicam do-
cuimus,) quociencis loco prodibir series exposica A F A R f A R. _c. hoc est,
quaneicas S, Eire cerminorum omnium lumma.
EremplI