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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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DE PROGRESSTONE Cap. XXHII
cadem; crit rectansulum Rd) V X A Rd = V A = H = a a = bB- =c7 = d5
Scc. Aeque haec Tunc illa rectansula quorum omnium aggregatum Symbolo Z de-
Tiondcum volumus; Ft qua limpliciter Rectaneulorum accrecatum deinceos ap
Dellabimus.
29. Sin terminus omnium medius ab nroque excremo equalirer distet, (quod
tum continset quum terminorum numerus eAimpar;) Ouadratum medii aequa-
EUF eXTremOTuM rectanuIO. NTam PrOPEer R d) V =M = A R a, (8 distancianx
D urrobique xegualem,) erit R d) V X A R d = NIXM = MI9. 4ci
30. Similiter, In quatuor terminis utut discontinue proxorrionalibus, Rectan-
sulum extremorum aguatur rectangulo mechiorum. Puta A. MI: : N. V. Cum
enim (propter aequalem utrobique rationem) sic A R = = NI, EF N R ==V, adeoque
R) V = N; CxIE NXM =R) VXA R =V A. Acquehine sequitur Regula qua
dicitur surea, live Resula Trium. Nempe
Datis. DatUF.
A) NIXN(V
VI MXNCA
MTA XVIN
N) A XV (M
32. Quaruor proportionalium, datis tribus qui-
bullibet, datur ec religuus. Cum enim lic, per praeced.
AXV == NIXNI, eric (aequalicer ucrinque diridendo)
MN
AN
3A = Y . N= N. N = pr. FAque hec
Recula infinici pene ulus per Locam Machelin, ideoque me.
riro Aurea dicta.
32. FX tribus autem continue proportionalibus, Rectangulum extremorum
aequatur quadraro medii. Puta A. MI. V. -.. Nam, propier aequalem urobigne pa-
cionem, est AR = _, et M R = V; erBOR) V = M. Ldeoque R) V X AR = Y A
MIXM : NI9.
Datis DaLIE.
A) N9 (V
V) NG (A
VAV =M
33. Trium erso continue proporcionalium, datis duo-
bus quibulris, dacur e reliquus. Cum enim, per praeced.
AV = Mg. Eric A) M GCY, _ V) M4 (A, E Y AY =
VMg = MI.
34. Acque idem ralet de tribus quatuorre terminis pro-
grellionis concinux, utut non immediare proximis, modo x-
qualibus incerrallis distantibus. Puta La. B. C. d. c. f. 8. - : erit a C =02; nam
_ a. 6. e:: Per 14. TreMaf = cd; et de = b8; ec Be alibi. NaM a. 6:: d. f.
vel a. a: : c. f, _ b. d:: c. 2. vel b. e:: d. e. EC. per 42.
35. Sed e praecedencium aliquoc conversae pariter demonstrantur. Puta con-
verla prop. 28. In continue proportionalibus, (excepta tantum aequalium pro-
greltione, ut F. T. T. F. EC. , quae ee deinceps aliquoties excepia intelligatur;)
Ti duorum terminorum intermediorum rectansulum rectansulo extremorum xgue-
tur: Tunt illi ab extremis xequalirer urrinque remori, (hoc cst, quot pradibus eo-
rum alteruter ab alterurro extremorum distat, eot d religuus d religuo. ) Puta, EI
SInE a. b. C. d. C. f. 8. - :, GEgne Ce == a8; totidem gradibus distant an c, acque
cn 8; item an e, acque 5, 5. Cum enim duorum c, e, alter sic a L d, alter Rd) e
20
mulciplicatio se mucuo destruane,) adeoque d distaucia D uirobique aequalis per
PCOP, 13.
36. KE COnVerSa prop. 20. Si continue proportionalium, intermedii alicujus
quadracum aequecur rectangulo extremorum; aequalier ile ab urroque exiremo
diltar. Probacur ut praecedens.
27. Ttem COnrer(a PFOP. 32. Si unius termini quadratum aequetur duorum re
ctansulo, erit ille medius intex Hioo Ceometricus. Si enim AV = M 9 = M M, Erie
A
N
M
38. Similiter et Converta PrOP. 30. Si ex terminis quatuor, duorum rectangu.
dum, rectansulo reliquorum aequetur; sunt illi quauor proporrionales. Puca, Si
AV = M N, erit (aqualier urrinque dividendo) A =
N
N N
 e
M =  vel c.
tiam  = =; Hoc est A. M: : N. V. R. A. N: : M. V. tem, quia, ut prius,