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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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Primo, ducendo 24 in 8 habetur area 1OI 192 = 24 X8. Deinde aream totam
292 per 6 lacicudinem panni diridendo, habetur lonsicudo qua (Ita, 32 = 187. FF
similicer alibi.
Acque hactenus cum Mulciplicacionis cum Divitionis exercicium, in menturan
dis Parallelogrammis Rectansulis quancum opus est, oltendimus.
Cap. XXIII. _. I CIS.
C A P. XXIII.
Duclidis Flementum Secundum Arithmetice
demonstratur.
adem qua supra methodo; ex Tolo parallelosrammi rectanguli caleulo, 10-
P cum tere Elemencum sccundum Duclidis tacile demonstracur Arichmerice.
Exempli gracia,
LC2. Si sint duae rectae (puta R, B,) quarum altera (B) secetur in quol-
cunque partes (PUTa M, N, O,) rectanculum duabus illis rectis comprehensum
(RXB = RB,) aequale est iis rectaneulis quae recta insecta (R) e sineulis sectae
sermentis comprebenduntur. Hloc est, Si B = M F N FO, elt RB = KM F RN
FRO. Ouod ex mulciplicarionis caleulo patet. Vel, Si PONAnEUIE R, B, MI, N, O.
aequales numeris 4, 10, 5, 3, 2. Cric 4 X 10 == 4 X5 F 4 X 3 F 4X 2. ut ex calculo
item patet.
N
X
RsRnIRNII
B = M F. N. +. 0
e R
20 = 5 + 3+2
RB = RM 7 AH + RC 40= 20+ 12+8
2C2. Di recta linea (L.) secetur utcunque (in A _ F,) rectaneula quae 101a
e utroque seemento comprehenduntur (Z. A + Z. F.) aequantur quadrato torius,
(Z9.) Hoc est, Si Z = A f F, cst Z9 = Z A F L. P. Vet E TOt SIC 5, (C8
enta 3, 2: exIC 5X5 =-5X3 + 5X2.
25 = 25 + 10
4 LIL YZF.
2C2. Si recta (L.) secetur utcunque (in A, F,) Rectangulum tota e uno
seementorum comprehensum (Z. A,) aequatur rectaneulo sesmentis comprehenso
(AE) una cum praedicti seementi quadrato (A 9.) HOc CA, Si Z = A + F;
erit Z. A = AF + Ag: vel (i nUMeriS) E 5 = 3 = 2, Cxit 5X3 = 323
2. X 3.
(5 = 0 + 6
L
2. A = A4 F AF
4C2. Si recta (Z) Secetur utcunque (in A, E:) Quadratum totius (29)
comprehenso, bis s
X 2 = 3X2.
B
aequale est quadratis seementorun (A IL) unu cum rectaneule seementis
(2 A F. )  Ct st L = A FF; est Z9 = A9
FL9 + 2AF. vel (in M,) H 5 = 3 f 2. exit 5X5 = 3X3 + 2X2
29 = A9 F 2A R f F. 9
6. +
25 = 9 + 12+4