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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 445, page id 851387705:0465
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eet
LHL LALEOR UN
e
rium: e Media proPOrtONaleS V2, V 6, V (2, V 20, _c. ellenE Ordinatim. a
plicata in EIyperbola, cujus tam lacus rectum quam lacus tranlversum sIC T. Ut
ex dietis, contideranci parebic. Ouod aluis rarionhus Lateris Recti ad Diametrum
Lcumtrectam, tacile accommodaBIEIII.
PROP. CLX LV
Theorema.
Fries numerorum Priancularium, in praemista tabella, commode
 interpolari poterit, s ipsorum numeris lateralibus tor interponan-
tur media Arichmetica, quoE opus est, et ex iis formentur numeri
FriangulaTeS, JuXIA PFOP. 172.
Puca si in serie numerorum criangularium F, 3, 6, 20, 15, dcc. unus ubique
interponendus est numerus; eorum latera 1, 2, 3, 4,5, ec. mediis Arichmericis
debite incerpolara, erune 3, F, 23, 27 2. 4, 3, 3234 427 5, c. quibus laceribus
(DEF PrOP. 172.) respondenc numeri criangulares, 8, L, 18, 5
4876, 78, 1C
1287 25, 176, 2. Fy c. Vel 83 E, 87 3, 8,6, 8, 10, 8, 25, 8, 24, _c.
denique 8, 8,
rentice lunt Arichmerice proportionales
Ve
8, 18, 150, 8c. quorum quidem disse.
Pari modo, li incerponendi sinc in lingulis interrallis duo loci; prodirent nu-
Meri, 3, 3, 1, 3,3, 3
5367 3, 13, 20, ec. Vel 3, 37373357 3, c. quo
rum iem ditterene luue Aciclumerice proporcionales.
Bo s: P R O P. CFZXVI
Lemma.
DRoposium sic inguirere quam habeane rationem numeri Prrami-
dâles, ad latus suum.
Liceret de hanc proxolicionem pari propreltu inrestisare, quo in prop. L7F.
utus Cum: (obserrato incerim diserimine quo disterr debua numeri Pyramidalis
dispOL
Verum cum non ita facile elter lectori concipere debicum punctorum licum in py-
ramide, (ue quae non omnia supponenda tunc in eodem plano,) et ansulorum (o-
licorum ad ea puncta politionem: Cacius ridetur illud hac qua sequitur methodo
praeltare. (Oux quidem, nisi mallem urrumque modum oltendisse, adhiberi Do-
ruisseo etiam ad DEOP. L7F. )
F. Numerus Pyramidalis aequatur asgregato numerorum Friangularium (uE p2
rec ex dietis ad prop. 130. es 132.) nempe ab Onitace ad numerum Triangularem
sibi collaceralem inclusire: (heut et numeri Priansulares hunc aggresarione L. a-
reralium; et Lacerales, Monadicorum; ur e Friansuli eriansulares, Pyramida-
lium; et sic deinceps.)
2. Est aurem lateris h numerus quiliber Friangularis
3. Ergo, sumpris lateribus F, 2, 3, 4, ec. Yel (corum l0c0)
ag b, C, due dec. summa horum a  an b = B, 6 + 6, d2 + a
Scc. erit duplum acoregati Friangularium; (quorum numerus
exit aequalis lateri maximi;) e hujus proprerea lemissis, erit
numerus eramidalis, cujus lacus aeguatus laceri maximi Pri.
angularium.
C.
4. PIE ivicur numerus egramidalis, semiltis aBerexaci dua Num Pyramid.
rum serierum; cousque ab unitare continuatarum, donec numerus locorum xove
cur laceri numeri Pyramidalis quaesiti, quod supponatur l: Onibus Si praeponatur
locus alter 0 f O, (ur series incelligantur ab 0 inchioacae,) Het HaruM nuMeTUS
FF. Ec ucriusque seriei summa scorlim innoteleet Per pFOP. 2 C 20.
5. Nempe, summa seriei Peimanorum 0 f a + B. F C, dec. quorum ulcimum est
3 numerus locorum L F E; erie  =L. per proP. 2.
PEF DEOP. 271.