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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 530, page id 851387705:0550
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F
C Y CL O IDE.
(Per 583) 3X3 -2 R2 P, GivC 1 ~3 -5D 2D; Solidum seu Conus ex simili
convertione crianguli rectiliner elt 7 ∞3, (nam circulus radii R est Z R~; ergo
2. vel 2 ∞
qui circulus, cum sic coni batis, ductus in s D eriencem alticudinis, dat L5 F3 mag-
nicudinem coni: ) Florum Colidorum ditterentia, nempe excellus coni lupea reli-
quum solidum, ct = D2P = =, ~3. Sin urrobique, pro circulorum peripheriis
lubstirmamus radios, (facta divitione per P, et mulciplicatione per ZD,) habebi-
mus planorum momenta respectu rectae CF; nempeillic isD ~ = - = D3, hic vero
3D P2; adeoque momentorum ditterenciam; D= = is D D2. Hlaec vero ditteren.
eia per legmenei magnicudinem divisa, hoc clF per 12) 2 - = DP, (est enim cri
lincum multum BBC = = D= unde si auteracur eriangulum libi inseripeum, quod
est circumleripei parallelosrammi dimidium, adeoque JsDP, manebie 1∞:
=is DP magnicudo scgmenci BA vet BC recta e curra comprehensi;) dat
12∞ 2 - ∞
12D = 3t
menturam promocionis cenrri pravitacis, dicti sexmenei cranctocari,
vertuS FC rectam: cujus iraque (emistis 12D : - ∞2
E+ D =6~ est ejuldem cencri distancia a
recta cBe: Oux quidem distancia, in legmenei magnicudinem 1D 2 = =, D D du-
cta, dat + 23 - 36 D X2 ejuldem momencum relpectu cBP rectae. MOmentum
autem erianguli rectilinei BcC. respectu ejuldem cB rectae cst 192 D Z 2 =  DY
5. 10.
X P. Onde si auteratur scomenci dicti momentum ; D - = D PE: manebiis D ∞=
D3 momentum criliner milci BcC respectu rectae cB. FM aurem corius BC
Parallelogrammi, respectu ejuldem cB, momencum Z D∞2 =-5 D ∞ xtP. (Unde
obirer liguet, selidui BCb crilinei momentum esle 5D3; adeoque, propeer ipsius
magnicudinem = D2, diltantiam sui centri graricatis d eB esles D; et consequen-
ter, d BC Crir Z P = ZD, uE Tupra 599.) Ratio igur momenu crilinei misti
BCC, ad momentum circum (eripes Parallelosrammi, ( respectu ejuldem cB rectX,)
CstuES DP2 - 8D3 ad 6+ D P2; SIVe, Ut ~ = - 8 D 2 ad D 2: UE PrIUS.
62. Veldenique, sic eriam eadem racio inrestisabitur. Momentum crilinei misti
CZ AF Hg. 7. respectu rectae C. F cM (uc Tupra) is D P = = = D3. MOmentum
aurem aequalis parasselosrammi C B, respectu ejuldem C F, est Z, DP- +D P∞ Y
Ilorum momentorum ditterentia J D D2 ==D3 (cum ex lola crilinei B s A in EI
tum BCC tranctatione oriatur) si per SDP - = D? (trilinei BCC magnicudi-
8D
L L = 8∞ mentura promotionis centri gravicatis cri-
nem) diridatur; prodibit
P2 - 8∞ 2
linei BB A in Tirum BCC cranclari. Fujus igicur semistis p p = 16D erit ejus.
dem centri d cB distancia: OuXe in SD P == D magnicudinem ducta; dat
a D F 2 = SD ejuldem BC C trilinei momentum respectu cB rectae. Vel, quod
eodem recidic, ditterentia momentorum inventa ;, D ∞ 2 - = D3, TemictIS S D ∞.
SD3,. est trilinei cranslocari momentum guasicum. (Nam Ouocientis dimidi-
um, in Dirilorem, duetum, relticuir Diridui semillem.) Unde cadem quae prius
Oritur racio s D ~ = - s D3 ad sa D P, live ~ 2 - 8 D2 ad Z2: quae in6OguX.
rebatur.
63. Hlac iraque ratione InVenCA, SIC prOcCdimIS. Ouadracum AF ti8, 10. est
1∞2 quod ductum in C A = 2 D, dat Z D P= agreBacum omnium AF 9. Si tiat
itaque (propter rationem modo inventam) uc ~ 2 2d 8 2 - 8 D2, sic : DP2 ad
quarcum; exir illud Z D P. = 4. D3 ageregarum omnium Z. V 9.
A Suverelt ur inquiramus, quam ad eaciem omnia A F 4, rationem habeant.
omnia bina rectanxula 2 V Z. n L. vtig. 10. (i 58 memorata;) hoc est, omnes
V2 in 2Zo hoc CL (per in XY) omnes VZ in 2 ar
n
1: D
=: HOC Cst, omnes V Z
=: in 2 a. Quam rationem his paltibus investigamus.
65. Rectae Z. Y crilinei C. Z. A P tie. 20. sime rectis Y Z. vedlinei B V CC. ti8. 7
PTODOT.