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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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ARITHMETICA PFOD. CLXXII.
Denique, s timul addantur puncta siC InVEnL; nemBe 3 P et 3 = 18 p
e
61. = 1514 1
rum omnium: Hoc est, numerus criangularis cujus latus L. Tdeoque.
ROP. CLZXII
Theorema.
Acus numeri cujutris Priangularis ad ipsum numerum, est ut
1 ad
VE oltentum est in praecec.
Adcoque, daco lacere l dabitur numerus Priangulacis illi lateri conreniens,
puca n -
Et Contra, Daco numero Triangulari, invenietur iptius latus.
Nempe, resolvendo hanc Aquationem 2u = 1 + 1, erie Y: + + 2n: -
P R O P. CLXXITI.
Corollarium.
T Fyperbolae Diameter cransversa sit L, e Lacus rectum :: sumpois
diametris (puncto applicationis es vertice interceptis) 2, 29 3,4 5, 0c.
Ordinatim. applicatarum quadrata erunt 1, 3, 6, 10, +5, C5c. nempe numera
Trianculares, cujus latera sunt 29 27 3,4, 5, Bc.
Probatue per 17 vel 33 prop. Con. Sect. nolE. Hyperbolam iptam exhribebie F.
pura prop. leq.
EtsitE
eROP. CLXXIVI
Torodarium.
ADB; Sique ut X ad V = sa AD ad DB, C a D ad DB; es suman-
tur aequales Aa = + = a D = DD e0c.
Rectangula BDB, BDB, Cec. erunt
ad invicem ut 2, 3, 6, 20, edc. numeri
Trianculares, quorum latera sunt a D,
a D, 530. Mediae vero proportionales in-
ter BD, DB; BD, DB, CC. sunt or-
dinatim applicatae in Fyperbola e, DF;
cujus diamerer transversa Ao- e3 latus
rectum aB, vel ipsi aequale.
Lercium 3V = (4V 2- 6. Quareum 4 V 3X5V
10.
Et lic deinceB. Suae lunc quadrata ordinatim applicatarum in Fyperbola, per
praced. Ideoque Medixe proporionales pura Y Z, Y 3, Y 6, Y 10, _c. ipsae ordi.
nacim applicatae.
Tem, Si fiant ad eandem rectam A a D dua Triangula similia, a DB,
Patet ex calculo. Nam rectangulorum BDB, primum erit V Z XZ V 3 = +
BecunduM Z V 3X3Y3 =3
dC. cbL. +VM
Si aelem sumpta tuistent AD = DB, _ a D== DB, cum rectangula Fuistent
XX2 = 2. 243  b. 34 = d 2. 4x5 = 20, _C. Cupla Mumerorit LHansula-
ruul: