PAR 
Parabola, fig. 10), and the curve of the in- 
cumbent parabola. 
The parabolic space is to the rectangle 
of the semi-ordinate into the absciss, as S! to 
3 ; to a triangle inscribed on the ordinate 
as a base, it is as 4 to 3. 
Every parabolical and paraboloidical space 
is to the rectangle of the semi-ordinate into 
the absciss, as r x y r) to x y ; that 
is, as r to -|- r. 
Parabolic spindle, in guaging ; a cask 
of the second variety is called the middle 
frustrera of a parabolic spindle. The para- 
bolic spindle is eight fifteenths of its circum- 
scribing cylinder, 
PARADE, in war, is a place where the 
troops meet to go upon guard, or any other 
service. In a garrison where there are 
two, three, or more regiments, each have 
their parade appointed, where they are to 
meet upon all occasions, especially upon 
any alarm. And in a camp, all parties, 
convoys, and detachments have a parading 
place appointed them at the head of some 
regiment. 
PARADISEA, the bird Paradise, in 
natural history, a genus of birds of the order 
Picae. Generic character : bill covered at 
the base with downy feathers ; nostrils co- 
vered by the feathers ; tail of ten feathers 
two of them in some species, very long ; 
legs and feet very large and strong. These 
birds chiefly inhabit North Guinea, from 
which they migrate in the dry season into 
the neighbouring islands. They are used in 
these countries as ornaments for the head- 
dress, and the Japanese, Chinese, and Per- 
sians, import them for the same purpose. 
The rich and great among the latter attach 
these brilliant collections of plumage, not 
only to their own turbans, but to the housings 
and harnesses of their Iwrses. They are 
found only within a few degrees of the 
equator. Gmelin enumerates twelve spe- 
cies, and Latham eight. P. apoda, or the 
greater Paradise bird, is about as large as a 
thrush. These birds are supposed to breed 
in North Guinea, whence they migrate into 
Aroo, returning to North Guinea with 
the wet monsoon. They pass in flights of 
thirty or forty, headed by one whose flight 
is higher than that of the rest. They are 
often distressed by means of their long fea- 
thers in sudden shiftings of the wind, and 
unable to proceed in their flight ; are easily 
taken by the natives who also catch them 
with birdlime, and shoot them with blunted 
arrows. They are sold at Aroo for an iron 
pail each, and at Banda for half a rix-dollar. 
PAR 
Their food is not ascertained, and tliey can- 
not be kept alive in confinement. The 
smaller bird of Paradise is supposed by 
Latham to be a mere variety of the above. 
It is found only in the Papuan islands, 
where it is caught by the natives often by 
the hand, and exenterated and seared with 
a hot iron in the inside, and then p\it into the 
hollow of a bamboo to secure its plumage 
from injury. 
PARADOX, in philosophy, a proposi- 
tion seemingly absurd, as being contrary to 
some received opinion ; but yet true in 
fact. No science abounds more with pa- 
radoxes than geometry ; thus, that a right 
line should continually approach to the hy- 
perbola, and yet never reach it, is a true pa- 
radox ; and in the same manner, a spiral 
may continually approach to a point, and 
yet not reach it, in any number of revolu- 
tions, however great. 
PARAGOGE, in grammar, a figure 
whereby a letter or syllable is added to the 
end of a word ; as med, for me ; dicier, for 
did, &c. 
PARALLACTIC, in general, something 
relating to the parallax of heavenly bodies. 
See Parallax. 
The parallactic angle, of a star, &c. is the 
difference of the angles C E A (Plate Para- 
bola, &c. fig. 11) BTA, under which its 
true and apparent distance from the zenith 
is seen ; or, which is the same thing, it is 
the angle TSE. The sines of the paral- 
lactic angle ALT, AST (fig. 12) at the 
same or equal distances, Z S, from the 
zenith, are in the reciprocal ratio of the 
distances T L, and T S, from the centre of 
the earth. 
PARALLAX, in astronomy, denotes a 
change of the apparent place of any hea- 
venly body, caused by being seen from 
different points of view ; or it is the difference 
between the true and apparent distance of 
any heavenly body from the zenith. Thus 
let AB (Plate XII. Miscell. fig. 1) be a 
quadrant of a great circle on the earth’s 
surface, A the place of the spectator, and 
the point V, in the heavens, the vertex and 
zenith. Let V N H represent the starry 
firmament, AD the sensible horizon, in 
which suppose the star C to be seen, whose 
distance from the centre of the earth is 
T C. If this star were observed from the 
centre T, it would appear in the firmament 
in E, ami elevated above the horizon by the 
arch D E ; this point E is called the true 
place of the phenomenon or star. But 
an observer viewing it from the surface of 
