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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0597
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A F
Proporrionals ill stand chus,
Wrhich Was ihC ThinS ac sirA proposed 10 bc
proved.
bedt 25 2, 3. an  rs  3
bra meved r0 be very brietts chus.
is clear; Becaule, From the ArIt ProPerEY oF the
And this is a erue and rery shorr Onacrarune
Parabola, P A =OO and P a == 00. WVhere
FOre PA La ==OO = 00, From the Na-
Fure OE EquariotIS. And thac last resolved inre
P. O-6: : O-0
OF the Parabola eF wotrich Archimedes Wvrore (0
lons 290, al MTaII) ScoaS Mare LMICC
expedired.Tis plain alto That CMIS LCIMONTEa
tion id habertali alle cavcrnio lo dtg. Parabo
licti dpaco.
The Ouadrature Dt the Parabola by chie 
hod oE Fluxions, L have formeriy in my Alsen
A PARABOLICK Space, iS ThaE ArCa COn
rained Declveen ile Curve of the Parabola anc
any Entire Ordinate CFI.
And ThIS Space IS EO a Parallelogram ciroumseri
c
Tec che Parameter be p = r, che Abscissa BC
Calsed x, and che Ordinare y.
Lhen by che srst Properis oF ctie Paraboles
-yy, Decause p
And consequenir by che Exrraction ot chc
20 ihe Paralletozram L. LL . . 2. 3. BIL IO THC ROOES OF cach, and ulins che nem Noration,
DEFH : : 25 4, 3.
FOF, L. EF, eF. 8F, ec. are in continual A.
rirhmerick Proportion trom the Nature oF Plain
Friangles.
2.3
SC
:eh, (DY Cor. L. PrOP: 2
OE che Parabora.) Buc he in che Axis F. F == b
and in che Arst Parallel ef must be equal to = in
the next ef, ic ill be equal to =; in chechire
10Z; and (o on in a duplicate Arithimerical PFO.
GrelTIOn. FOr a8 es
: (015 5e l
fecond
= 1
1). Ch l = =.) And as ehe
2) : : C5 2; t0
eh = 4, (9c. And thus vill ic be it the Lines
FS, ff, ecc. be 2gain bissected, (9c. ad Infini-
cum. 50 chac aHI chie Indirilibles oF the Tri
lincar Space P R II F will be in a duplicare
Rrichmerical Progrestion increasins. BUE
3. LC Su OE à Rark oF such Ferrris 15
suberiple ro a Rank oF as many equal ro rte
x = y. Then multiplvins X By X che F
xion oF etie Abscissa, ie will Rand chuS X X L
eo the Fluxion oF che Area. ACrer Wohich And the
Florine Ouantier ansverins eo chac Fluxion,
wetrich all sire the area in tenoon Terms.
Fodo which, cheFluxion being x x sirst Fate
aWar the x, and there will remain x Hextin:
creale che Index oF chac Pover by Oniiy, and
it will sand chus X X =. Ttien divide X x= bY
1. + : or by 3 (etus 2) = = (3 X ∞ ) ne
itie Ouorient You sec wist B 2 X X
LastIY, Instead oE x Tubsiture WHaE WaS BC.
Pore tound equal to ir, viz. y and ii will Be
2 X
Torhie Area oF etic Semi-parabola VM P.
grearest; (25 we proved in N. 7. OF arichme- And il rou double char, vou will fain the Area
tical Procression, Wvhich sec) Wheretore che ertiole
Trilinear SpaCC PK HIF is ro che Parallelo.
Fram : = 25 F 20 3. And consequenels che re-
ot che Wvhole Parabola M V O
Wheretore che Parabolicte Area i5 LWo chirds
oc a Rectansle under che abseissa and e Or-
mainins Pacabolick Space must bc 10 it 20 2103. dinate. 8. Li. D.
P. E. D.
ratelogram 25 F EO 27 IE MUIC DC WOCIC Lala
bola 25 1      3  4 8. F. D.
Lec FFI che Semi-oru D avided into
LarES, OF in108, 76, 69c. andt cntoushr thc
Dirisiono utaW Lines, 25 ef, ef, ecc. parallelto
the Axis L L. Suppose al(0 B F 10 bC 4.
Then L las, the Parabock SPA LILL, IS
And since the Friatiole F F EL is E0 the Pa.