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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 806933011:0500
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A A Z
rent trom thar wrtrich was deduced by e for- that when anY Line, 25 FC, F6, (9c. is coin-
2y u = 0, arid here rIS ly u = d Zn =0
buc chat thele F.quations are exaetls che lame, il
cidene ich P F, which Limagine c0 BC a Nor
mal ro the Curre in che Poine B, From che lame
Poine F; chac chen che intercepred Line, F B.
F FI, (90. is coincident wich the Subnormal FD.
hus casilys discovered. Because i = -, and) and consegueneix upon che decerminins ol an
= Zi, ereo u: 2: : 7; trom whence
1: n: : 2u: uZ, bue (by whar wene betore
i = 272 F d27 - 299u erxo 1: n:
dy22 = 4227 - 2712: v J. Tiom hence
Extremum, che Invencion OF a Pangent natu-
FaIIY FOIIOWS.
Totorm che General Equation chat is to serre
in this Bulimls, ve hare, trom che Rectangular
Lriansle EBC, ZZ = = n n = 2 n X .
X 3
L yy; Or on the ocher side P, trom he Prian-
Sle GHTF, 2Z = X X - = 2n X I n n - yy3
OF FOT AM EXtremum, 2 X X -= 2 n r F 2yy = 0:
In Whrich Eguation, iE in ThC rOOM OF 2 y y We
substiture ies Value from che Equation of the
in MII. NeimentiirS Fquation, viz. ly u = d Zn Curre, che Subnormal ill be discorered
o Substimmrine chese Ouantiries in the room Fx. er. Suppole the Curre Were an Pyper-
OF L’and n, ro vrhich ches are proporrional, ve
have  u Z2 a y -  u 27 7 Z = u u 22 y7y
bola, Mhen 27i = r x + 2 r X Z: Theresore
=du ZZ = 0, or diridins all by 1 Z, and mul- ( 2 X X = 2 n x F r  -- 2 Y X X = 0, and 2 n X
tiplrins by yy, and rejectins Contradictories,
we have d 27 y - 27yy u = 0, chac is, d Z = 2 X x -- r x  2 rX ~, andn = x ]
- 2y 2 = 0. d. F. D.
These Examples may serve 10 illustrate a Y g = FA, erBO FD (Ehe Subnormat)
a Rule wrhich is in ic setf rery plain and obri-
OuS.
AS For the Dse and Application oF the DO-
ctrine de Maximis C Minimis, perhaps ic may
Y 9. 8. F. L
Suppose the Curre a Circle, in which Cale
De a5 DTetul and Noble 2 one a5 any, 20 Men (2yy = 2r X = 2 x x; then proccedins as Be-
hon trom hence all Tors oF Curres may be cur
at Righe Angles, (and consequenty the Inven
tion ot che Langenrs isro be pertormed.
FOrC, We have 2n X = 2r x, and n = r, and
ergO F D = r = x; wrhich Mews chac P is
erer in chis Curre, the Cenere ic SelF. In chc
Common Parabola, rX = 2 y y, and Cheretore
n = = -  x, and (OFD = =. BuE Eis NOL
ontr in chese Conick Sections, buc in any otter
Curre whatsoerer, char trom chis General Equa-
tion by a due Substiturion of che Value OF 2 y y,
the Tangene, or (which is all one in eHect) the
Subnormal will De discover d.
MEAN Axis, in Opcicts. Sec Axis.
MFAN Diameter, in Causinz, is a Geometri-
cat Mean between the Diameters at HPead and
Buns in any close C ask.
MEAN and Extream Proportion. SeC EX-
tream and Mean Proportion.
MEAN, in Lam, Gonites the Midele Berween
EVO FxtreamS, and chat cither in Time Or in
Digniey. As in che First, Ilis Action Was Mean
berwixe the Disseism made eohim and his Re-
coreer, that is in the Interim, (OF, 25 we laY,
in the mean rime.) OF che Sccond, there iS
Lord mean Or mense, and Fenant mean. Sec
Mesne.
HIEAN Motion, Or Meam Loncirude of the
Sun, in che Prolomaicte Hypothesis, I5 an ArK OL
he Pcliprick, reckond from the Beginnine ot
Aries ro che Line oF che Suns Mean Morion,
decoumcins accordins ro cho Order OF the Signs.
Rod re alo res voulual 10 cal are
mer PrOcCIS: There the Equation WaS d Z
Tet A C C BC any Curre wtcre rertex is A
AXC A TT, iES Ordinates E D, C B, CFHI: Let
any FOMH, 25 P, be caken in che Axe ac liberes
att Lom chence che Lates LC, LL Le DC
atas Co che Curre.
TeE A F = n, A B, AD, AEI = X, TIF
F FD = n = X, ED, BC,
n =  X,
OFI = y, FC, F F, FC == Z. The POInEF
beines catien aus vohere ac Ubecer, io evident,
HE AN