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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. XXXIII.  GEROMETRTCA. L
AV = _1 B, erit MN = Y, e M
A
V
. vel etiam  = - : hOC Mt HL. A: 
V. NI. _c NV. A:: V. M. Nam Singulis his modis proporcio concluditur.
29. Finc sequitur; Si quacuor termini tinc proportionales, sune de inverse
(aranan) proportionales. Puca si A. M:: N. V. ENIE (PEr. Pr. 38) AV =NVI:
ideoque, (ut ottentum clt, PCOp. praeccd. ) M. A:: V. V.
40. Icem; si quacuor termini linc proportionales, lunc es alterne (permutarim,
viciltim, cramras,) proporcionales. Puca si A. M:: N. V. adeoque AV =NN
CFIE A N:: M. V. uc clt octentum pr. 38. TcEM, NV. A: : V. MI. uVibId. d PF. 30.
4T. POrrO, Si quacuor proporcionatium vel primus de certius, vel secundus de
quareus, aequalicer rel mulciplicentur vel dividaneur manene adtue provorciona-
Les. Puca si A. M:: N. V, hoc elt A. AR:: N. NR; (ubi communis ratio est
R;) eru ee A. MB. : N. VB, hoc est A. A RB: : H. NR B. (ubi communis ratio
CM R B) Trem A. B) M:: N. B) V. hoc cAt A. B) R A:: NV. B) R N. ebI COm-
nis ratIO esFB) L. Simititr H A. M:: N. V. hoc estR) M. M:: R) V. V. eric
B) A. M:: B) N. Y. hoc est BR) M. HI:: BR) V. V dec. Vel Sic. Si  - cum
A
B = B. _B)  = B) . Sire (quod cancumdem eA) L -
BY. Vel eciam C)
CY. dc.
r
n =c, 10
AB NB
M
D
ee
BM
42. Tiem, Si proportionales Fuerine cum A. M: : N. V. TM a. N: : r. v. eum
a. m:: n. u. (cum li placet quarerni, plures quorlibec;) erunc iem cum tacti,
eum dividendo orei (Terminis respectire tumpeis) cermun proportionales. Elto
enim in primis ratio R, in secundis e in cereiis r. Adcoque A. NI = A K:: V. V
= NR. ITe a. N = a8: : v. u = VC REa. m = a r: : n. W = nr. KCBO (per PFOV.
4F.) AaA. MUm = A Rapar:: NVn. V VA = NRrSNr. HOC est Aaa.
AaaRBr:: Nrn. Non Rer. ubi communis racio est RPr. Pariter _ A a. M~
A a RP N, V0
NVRS
. Eire a) A a. a1) Aa R5: : n) Nv. nr) NV RP. ubi
communis uirobique racio cA C vel r) RP. Vet SC
A.
M = AR::
M = ar
Aa4. MP. m = Aaa Rer:: Won. VvV = LV nR
Aa NIV. AaRB ND VV NVRS
M
ar
n
43. Sed de idem obrinet in continue proporcionalibus. Quod similiter pro.
bandum erit. Puta,
Si A. B. C. D. L =: vel A. AR. AR ~. A R3. AR a:
EF
a. B. y. 5. E = vel a. a
:.
Erunt Aa. BB. Cr. DS. BE:: vet Ac. ACKP. A∞R5. AaKP. AaR5t..
EF
B C D H
B
 ve
AR A R A R A B
15 ac ast
44. Tx quidem, licet altera progrestio crescens tuerit, allera decrescens. VE B
Cum A. AR. A R 2. AR3. AR 4. :. tM a. 5) a. P=)8. 83) a. P2) a. . exIt CtiaM
Aa. 5) a AR. P2) a AR2. 53) a AR3. P2) a AR ~. :: uE patet; quixpe communis ra.
ti0 elt s) R
Arque hujusmodi complures proporcionalium immutationes de comparationes
Facile