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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 396, page id 851387705:0416
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ARTTAMELICA PFOPLXYI.
P R OP: FXVI.
Theorema.
LCenica quancitale seriei alicujus inteerae, cognolcitur quanci-
Tad Csce Oala.
.
C.  F
Duta, Si A B Friangutum sIC Z A B Paralleloprammi; et a6 Frianeulum,  ab
Parallelosrammi: cric reliduum Praperium, ZAB,  3 a 6. 17 Trem AB Parabola
EHB Paralleloorammi cemeripei; de a P parabola Z a B parallelogramini circum-
seripei: eric reliduum, E A B = 3 a B. Ex pariter in aliis. ti
P R O P. LXVIF. oidi  etriur 10
Corollarium.
Triangulum rectis quoclibet secetur basi parallelis e aequaliter ab in-
virem remotis, (portiones aeque altas abscindentibus;) abseissa Trian-
sula (verticem inter es rectas secantes,) sunt
ut 2, 4, 9, 26, c. numeri quadratr. Sparia
vero rectis illis interjecta, ut 27 3, 57 778c.
Ariihmetice proportionales.
Ouia Friangulorum abseittorum cam asticudi-
nes quam bales sune Arithmerice proportionales:
ergo plana in duplicata rarione Rrichmetice DrO-
porcionalium, tire ue numeri quadrati, F, 4, 9, 16,
ecc. FF Propterea, spacia incerjecta, 1, 3 A 2
5=(847= 16 - 9, eC.1
EROP. FXVFTY
Corollarium.
Tconus planis quorlibet secetur basi parallelis, c aequaliter ab nuncem re-
motis, portiones aeque altas abscindentibus;) abseisse coni (verticem in-
ter C3 plana secantia) sunt ut L, 8, 27, 64 C5c. numeri cubici. Portiones
vero interjectae, ut 2, 7, 29, 37, 80. disserentie numerorum cubicorum, (es si
lc
FIG. Pra
ed.
militer in Pgramide.)
erir ratio conorum (qua ex alcicudinum e balium ralis) in ra-
tione alcirudinum triplicata, sen ne X, 8, 27, 64, eec. EI proprerea portiones inter.
jectae ut F, 7 = B = 1, 29 = 27 - 8, 37 = 04 27, e.
Ouia cum conorum absciltorum alicudines sint Arichmetice proportionales, et
propierea etiam balium diametri; adeoque vales in carundem ratione duplicata;
PROF.