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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 125, page id 851387705:0145
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Cap. XXIII. CL.  B15.
t
LDRDN =8 in E = S9uV 9 =NL. quMD4.
VS
Ubi nocandum est S _ V incerprecandum clte nunc per S -V, nunc per V - 5,
prouc S vel V major fuerit, (hoc clt prout D vel incra vel extra puneta L, N,
tuerie altignarum,) e proinde Squ Vq illic erit S9 - Vq hic V9- 59. OF
mulciplicando patebit.
5 - V
59 + 51
ML. q - DNC
V9+ VS
= ∞
NDg = NL 9.
7C2. Si recta (Z.) secetur mcunque (pura, in A, P:) quadrata torius (Z. 9) 
unius ex seementis (Dura A 9) simul sumpta, (Z. 9 + A 9,) aequanur rectansulo
bis comprehenso a rota e aucloscemento (2Z. A) una cum quadrato reliqui seementr
=2L. P. Y X. Dc limilicer in numeris, quod experienci patebit.
2.
E
29-
+ A9
+F
A F F
A + F = Z
EA 2 A
A9 F ZAE F E4 2A9 F 2AF = 2ZA
+ A9
FEg + E9
29 = A9 = 219. f 2AE L E 9 = 2A9 + ZAF + E9 = 2ZA + FG
L
E4
A Y F = Z
X2V. X2 F.
A9 + 2AL. F EQ 2AF f 2(9 = 2ZF
+ A9
+ A9
C4FL4 = A9 F 2AC +219 =A9+ 2AC F 2F9 = 271. + A9
8C2. Si recta (Z.) Secetur utcunque (in A, F.,) rectaneulum quater compre-
Bensum a tota e uno ex leementis (Puca 4 Z. A) una cum quadrato reliqui seementi
(F9) equatur quadrato compositae a tota e praedicto seemento (O: Z + A.) H0C
est, Si Z = A f F; erit 4 L A F F 9 = G: Z F A: = Z 9 + 2L A + A9 FF
(eadem ratione) 4Z F F A9 = O: Z. F F. Ec in numeris pariter.
Z = A f. F.
X 4 A
X4 A
4Z. A = 4 A9 + 4 A F
+L9
P. 9
2 A f F = Z L A
2 A F F =- Z L A
+A9 F 2AF
F 2AF + F. 9
+EA + Eg = 4d9. f 4AF F E9 = 4 A9 f 4AF. + C9 =9: Z. + A.
Z. = A f F.
A F 2F, = 7 + F
A  2F = Z L F
A9 F 2AF
+ 2AF. F gF9
(L. 9.) Hloc est, S Z = A + C, CrILL9 = A9 = 2 Z A + F. 9; IIEM L9 + FC
L
4Z F. = 4AL.  4C9
+14 + A9
A9 + 4C= a+ 4aC F 419 = A9 F 4AL. f AF9 = 9: Z + F.
DC2. Si recta (Z.) secetur rum in segmenta aequalia (S, S,) rum inaequalia
A = S ] V, F =S--Y;) quadrata inaequalium seementorum (A g + V. 9) sunt
dupla quadratorume dimidia e e recta inter puncta sectionum, (259 = 2 V 4.)
HIOC