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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 747, page id 851387705:0767
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Pcop. LVL. cunm cinadidatis.
cujus balis Priangulum BV a (aue huie aequale;) altiudo, perpendicularis (Pra Bis. 159
a punetum aequalis ipsi V,a =h; Adeoque (propter BV a = Z sB) Pyramidis, 100
magnicudo SSB2 = 35 R 2 = 35VR + 65V = 35 R = 35V R - Es: RL, (prOP
ter Cencer gravicaris batis B V a, 2 r a diltanciam, Zh; Prramidisque Cencrum ora
ricatis in recta inde ad verricem ipsi a puncto supereminenrem ducta, abseilla inde
vertus vercicem, Z ipliuis;) dictantia Ceneri graricaris prramidis d ra planos erit
Ex = B = Eh: e propierea prramidis momentum relpectu ra, = 5B3
=5V R 2 + = F 2= R = 52 = 35 R3 = 3 sV R 2 = 3 5 R F ,E SV. PrIlIaLIS Ve
r0, cidem B Va incumbentis magnicudo (propier balem BV a = Z sh; et alciru-
dinem V A = 2) cM 35B0 =Zs: Ejulque Cencri gravitacis a r a distancia (quiB.
De cadem qux basis Friangularis) Zh; adeoque Pritmatis respectu ra momencum
2SWB = 5S B= 2s R = =53v. Acque hoc addicum Prramidis momento  Sh 
extribet Ongula (ip(i B V a intistentis, aciem habentis T A,) momentum respectu
7 aq 3 SB = Z5Vh = Z SB = ZS B = 25 R3 = = 5 ∞ R 2 + = S R -  L B3~. (IdCM
acque aciem habentis ra momencum relpectu Y A. ) Acque hoc addItUM, MO-
mento Ongulae Semilesmento B V A insistentis, aciem irem habeners Y A, respectu
a 3a R3 = 85 R (= 3C R3) + 3 5~ R2 = + 5 R + a sV; exhibet, Ongila
Sectori Ba A insiltentis aciem habentis T A, momentum respectu Za, 8 a X
245  f 25D R f 2S R = 8FR3 - =sBR  + S R. (Idem plane acque
Onoulae aeiem habentisr a momentum relpectu F A: Ouippe quae illie elt AIEI
iudo, hic est Distancia; et vice verla.) Aeque hoc nomentum per Ungulae mas.
diritum, hoc clt, Per Z fR2 - EsB R = Z a R F ES R  F SSV R (UES NI. prOP.
Deaced.) exhiber da _ 2HC7 5R2 + 5v R + 25 9fR = sb R + 2 5. .
12a R + 45 R + 450
B
Rtanciam Cencri craricatis (Ongulae seclori B a A insiltencis, aciem habentis FA,)
2r a. Adeoque ejuldem Centri d T A distancia est  a R. F 5 X + 7 5u R = 2. 5
5fR. 2 SB R =
12 a R + 45R + 450
125R = 45B a e Ongulx respectu iptius T A (aciei Sux) mo.
mencum Ba R. + i SR =+ L S R= = 2 S R = 3s A L 2 5bR. = + s R
COnd
in L
habene= a Factum clt. )
Vel oiam; vrovier Ongulae; triangulo DV a intiltentis (aciem habontis P A,
ex Prramide et Prismare constancis) magnicudinem (modo exhibitam) ESh F Z Sh2
SA2- 35V R f 3 5o = sBR= Eh; Momencum ejus respectu r a (modo
ostentum) Es R3 = 5sV. RE + 5 s R - = 52, per magnicudinem illam dividendo:
habebicur istius Cencri praricaris a r a Distancia 85 R. - 452 R2 + 4 s R = 35 V
D
8 R2 = 4vR f 4 52
85 R= = 45V R F 4. 5.
L AI 8R = 4 0 XC + 45i Cadeoque d
spectu T A mOmenCum, 3,S R 3 = 3 su RZ -f 553 R. f 3 s V. Atque hoc addicum
Momenco Onsulae Semilesmento BV a intiltencis (acrem iem habentis Y A) re.
spectu ipSIuS FA, 3aR3 = 35 R3 (= SC R3) = 35VR 2 = 3 S R = = 53 V, (UI
S F;) exhibet momencum Onsulae lectori Ba A insistencis, aciem habentis T A,
respectu iptus Y A, 3a R3 + 35 R2. f  5V RE = FE S R. Ut priud.
Deinde .l ex his momentis Ongularum sectori. Ba. A insistencium, subductis Vn. X
gularum Priangulo BCa insistencium momentis respectiris, habentur mometita
Ongularum iccoe BC A Imeum respectira.
Oua autem. Frianeuto BCa insiltie Ongula Temiquadrantalis, aciem habens
a elt Pyramis: Cujus vertexa; Balis, Praperium rectae, BC, intistens, duabus
rectis, plano, circuli perpendicularibus es inricem parallelis incerjectum; quarum
altera, puncto C intiltens, aequalis est rectae C4== R; alcera, insistens puncto B,
aequalis rectae V a =b; quas itaque, in planum replicatas, repraesentent recta
Ca Ba. Ouod quidem Praxorium, (quo Centrum graritaris habeatur,) dirime
incellisatur in duo Priangula aBC, aB a. Ouae (propter communem alcicudi-
BbbBB 2
nem
8R = q u R + 45 12X - 4b + R. + q vi d et proprerea ejuldem re