538 
QUA 
proposed position of that line, be denoted by 
bd\ then will in, the rectangle under bd, and the 
ordinate £R, express the corresponding fluxion 
of the generating area A/'R: which fluxion, if 
A b — x, and Z-R — y, will be yx. From whence, 
by substituting for y or x, according to the 
equation of the curve, and taking the fluent, 
the area itself AiR will become known. 
Eut in order to render this still more plain, 
we shall give some examples, wherein x, y,. z, 
and u, are all along put to denote the absciss, 
ordinate, curve line, and the area, respectively. 
Thus, if the area of a right-angled triangle is 
required, put the base AH (fig. 13,) = a, the 
perpendicular HjM = b, and let AB = -v.be 
any portion of the base considered as a flowing 
quantity; and let BR = y, be the ordinate, or 
perpendicular corresponding. Then, because of 
the similar triangles ARM and ABR, we shall 
have a * b * * x * y — — -. Whence, y x, the 
fluxion of the area ABR, is, in this case, equal 
to — * ; and consequently the fluent thereof, or 
a 
b> 
the area itself, : 
— ; which, therefore, when 
2a 
x = a, and BR coincides with HM, will become 
aa __ a » X liM _ — t j ie area G f t h e w hole tri- 
2 2 
angle AHM ; as is also demonstrable from the 
principles of common geometry. 
Again, let the curve ARMH (fig. 14,) whose 
area you would find, be the common parabola ; 
in which case, if AB = x, and BR = y, and 
the parameter = a, we shall havey = ax, and 
y — a* x' 1 : and therefore u (= yx) = a 1 x 2 x ; 
whence u = 3 X a 2 A ' 2 = 3 " 2 * 2 X x ~ f- 
yx — 1 x AB X BR. Hence a parabola is two- 
thirds of a rectangle of the same base and alti- 
tude. 
The same conclusion might have been found 
y 2 
more easily in terms of y : for x = , and x 
~ ; and consequently u (= jri) = - — — — ; 
a a 
Cy 1 2y y 2 2 y 
whence « = — = -— X — - = — - X * — f 
a 3 n o 
X AB X BR, as before. 
Quadrature, in astronomy, that aspect 
of the moon when she is 90 1 distant from the 
sun; or when she is in a middle point of her 
orbit, between the points of conjunction and 
opposition, namely, in the first and third 
quarters. 
Quadrature-lines are two lines placed 
on Gunters sector: they are marked with 
Q. and 5, 6, 7, 8, 9, 10: of which Q. signifies 
the side of the square, and the other figures 
the side of the polygons of 5, 6, 7, &c. sides. 
S, on the same instrument, stands for the se- 
midiameter of a circle, and 90 for aline equal 
to 90 ’ in circumference. 
QUAD RAT US, in anatomy, a name 
given to several muscles on account of their 
square figures. 
QUADRIGA, in antiquity, a car or cha- 
riot drawn by four horses. On the reverse 
of medals we frequently see the emperor or 
Victory in a quadriga, holding the reins of 
the horses ; whence these coins are, among the 
curious, called numtni quadrigati, and Victo- 
riati. 
QUADRILATERAL, in geometry, a 
frmre whose perimeter consists of four right 
lines, making four angles ; whence it is also 
QUA 
called a quadrangular figure. The quadrila- 
teral figures are either a parallelogram, tra- 
pezium, rectangle, square, rhombus, or rhom- 
beides. 
QUADRILLE, a game at cards, some- 
times called ombre by four ; which chiefly dif- 
fers from ombre by three, in being played by- 
four persons; and having all the forty cards 
dealt out, to each person, at ten each. 
The general laws of this game are, 1. It is 
not permitted to deal the cards any otherwise 
than four by three, the dealer being at liberty 
to begin with which of those numbers he 
pleases. 2. If he who plays either sans prendre, 
or calling a king, names a trump cf a dif- 
ferent suit from that his game is in, Dr names 
two several suits, that which he first named 
must be the trump. 3. He who plays must 
name the trump by its proper name, as he 
likewise must the king he calls. 4. He who 
has said I pass, must not be again admitted to 
play, except he plays by force, upon account 
of his having spadille. 5. He who has asked 
the question, and has leave given him to 
play, is obliged to do it ; but he must not play 
sans prendre except he is forced to do it. 6. 
He who has the four kings may call the queen 
of either of his kings. 7. Neither the king 
nor queen of the suit which is trumps must 
be called. 8. He who has one or several 
kings, may call any king he has in his hand ; 
in such case, if he wins, he- alone must make 
six tricks ; if he wins, it is all his own; and if 
he loses lie pays all by himself. 9. Every- 
one ought to play in his turn, but for having 
done otherwise no one must be beasted. 10. 
He, however, whose turn it is not to play, 
having in his hand the king the ombre has 
called, and who shall trump about with either 
spadille, manille, or basto, or shall even play 
down the king that was called, to give notice 
of his being the friend, must not pretend to 
undertake the vole ; nay, he must be con- 
demned to be beasted if it appears that he 
did it with any fraudulent design. 11. He 
who has drawn a card from his game, and 
presented it openly in order to play it, is 
obliged so to do, if his retaining it may be 
either prejudicial to the game, or give any 
intimation ic the friend, especially if the card 
is a matadore ; but he who plays sans pren- 
dre, or calls his own king, is not subject to 
this law. 12. None ought to look upon the 
tricks, nor to count aloud what lias been play- 
ed, except when it is his turn to play, but to 
let every one reckon for himself. 13. He 
who, instead of turning up the tricks before 
any one of his players, shall turn up and dis- 
cover Iris game, must be equally beasted with 
him whose cards he had so discovered, the 
one paying one half and the other the like. 
14. He who renounces must be beasted as 
many times as he has so done, but if the 
cards are mixed he is to pay but one beast. 
15. If the renounce prejudices the game, and 
the deal is not played out, every one may 
take up his cards, beginning at the trick 
where the renounce was made, and play them 
over again. 10. He who shews the game 
before the deal is out must be beasted, ex- 
cept he plays sans prendre. 17. None of the 
three matadores can be commanded down 
by an inferior trump. 18. If he who plays 
sans prendre with the matadores in his hand, 
demands only one of them, he must receive 
only that he mentioned. 19. lie who, instead 
of sans prendre, shall demand matadores, not 
6 
QUA 
having them ; or he who shall demand sans 
prendre instead of matadores ; cannot compel 
the players to pay him what is really his due. 
20. Matadores are only paid when they are 
in the hands of the ombre, or ot the king his 
ally, whether all in one hand, or separately in 
both. 21. He who undertakes the vole and 
does not make it, must pay as much as he 
would have received had he won it. 22. He 
who plays and does not make three tricks is 
to be beasted alone, and must pay all that is 
to be paid; and if lie makes no tricks at all, 
he must also pay to his two adversaries the 
vole, but not to his friend. 
QUADRUPEDS, in zoology, a class of 
land animals, with hairy bodies, and four 
limbs or legs proceeding from the trunk of 
their bodies; add to this, that the females of 
this class are viviparous, or bring forth their 
young alive, and nourish them with milk 
from their teats. 
QUADRUPLE, a sum or number multi- 
plied by four, or taken four times. 
QUAKERS. By stat. 7 and 8 W. III. c. 27, 
and 8 G. I. c. 6. quakers making and sub- 
scribing the declaration of fidelity mentioned 
in 1 Y\ . and M. shall not be liable to the pe- 
nalty against others refusing to take such 
oaths: and not subscribing the d duration of 
fidelity, Ac. they are disabled to vote at the 
election oi members of parliament. 
By 7 and 8 W. TU. c. 34, made perpetual 
by 1 G. I. c. 6, quakers, where an oath is re- 
quired, are permitted to make a solemn affir- 
mation or declaration of the truth of any fact; 
but they are not capable of being witnesses in 
any criminal cause, serving on juries, or 
bearing any office or place of profit under 
government, unless they are sw orn like other 
protestants ; but this clause does not extend to 
the freedom of a corporation. 1 Lord Raym. 
337. 
By stat. 22 G. II. c. 46. an affirmation shall 
be allowed . in all cases (except criminal) 
\vhere by any act of parliament an oath is re- 
quired, though no provision is therein made 
lor admitting a quaker to make his affirma- 
tion. See Friends. 
QUALEA, a genus of the monandria mo- 
nogynia class and order. The calyx is four- 
parted; corolla two-petalled ; fruit a berry. 
There are two species, trees of Guiana. 
QUAMD1U SE BENE GESSERIT, a 
clause frequently to be found in letters patent 
of the grant of offices, as in those to the ba- 
rons of the exchequer, &c. where it intimates 
that they shall hold the same as long as they 
shall behave themselves well. It is said that 
these words intend what the law would imply 
if an office was granted during life. 
QUANTUM MERUIT, in law, is an ac- 
tion upon the case, founded on the necessity 
of paying a person for doing any thing as 
much as he deserves. 
QUARE, in law, a term affixed to the title 
of several writs: as, 1. Quare ejecit infra ter- 
minum, is a writ that lies for a lessee cast out 
of his farm before his term is expired. 2. 
Quare impedit, a writ that lies for a person 
that has purchased an advowson, against him 
who disturbs him in the right thereof by pre- 
senting a clerk to it when the church is va- 
cant. This writ differs from what is called a 
darrein presentment, because that is brought 
where a person or his ancestors formerly pre- 
sented ; but this lies for him that is purchaser 
himself. Y et in both these writs, the plain- 
