PAR 



PAR 



and absciss approaches, parabolic asymp- 

 totes of various kinds may be discovered. 



PARABOLIC conoid, in geometry, a solid 

 generated bv the rotation of a parabola 

 about its axis : its solidity is = ^ of that 

 of its circumscribing 1 cylinder. The cir- 

 cles, conceived to be the elements of this 

 figure, are in arithmetical proportion, de- 

 creasing towards the vertex. A parobo- 

 lic conoid is to a cylinder of the same 

 base and height, as 1 to 2, and to a cone 

 of the same base and height as 1% to 1. 

 See the article GCAGIXG. 



PARABOLIC cuneiis, a solid figure formed 

 by multiplying all the D B's (Plate Para- 

 bola, fig. 9) into the D S's ; or, which 

 amounts to the same, on the base A P B 

 erect a prism, whose altitude is A S ; this 

 will be a parabolical cuneus, which of ne- 

 cessity will be equal to the parabolical 

 pyramidoid, as the component rectangles 

 in one are severally equal to all the com- 

 ponent squares in the other. 



PAIIABOLIC pyramidoid, a solid figure 

 generated by supposing all the squares of 

 the ordinate applicates in the parabola so 

 placed, as that the axis shall pass through 

 all the centres at right angles ; in which 

 case, the aggregate of the planes will 

 form the parabolic pyramidoid. 



The solidity hereof is had by multiply- 

 ing the base by half the altitude, the rea- 

 son of which is obvious ; for the compo- 

 nent planes being a series of arithmetical 

 proportionals beginning from 0, their 

 sum will be equal to the extremes multi- 

 plied by half the number of terms. 



PARABOLIC space, the area contained 

 between any entire ordinate as V V (Plate 

 Parabola, fig. 10), and the curve of the 

 incumbent parabola. 



The parabolic space is to the rectangle 

 of the semi-ordinate into the absciss, as 2 

 to 3 ; to a triangle inscribed on the ordi- 

 nate as a base, it is as 4 to 3. 



Every parabolical and paraboloidical 

 space is to the rectangle of the semi-or- 

 dinate into the absciss, as rx y (m -j- r) to 

 x y ; that is, as r to in -}- r. 



PARABOLIC spindle, in guag'mg; a cask 

 of the second variety is called the middle 

 frustrum of a parabolic spindle The par- 

 abolic spindle is eight fifteenths of its cir- 

 cumscribing 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 par- 

 ties, convoys, and detachments, have a 



parading place appointed them at the head 

 of some regiment. 



PARADISEA, the bird of Paradise, in 

 natural history, a genus of birds of the 

 order Picse. Generic character : bill co- 

 vered at the base'with downy feathers ; 

 nostrils covered by the feathers ; tail of 

 ten feathers, two of them, in some spe- 

 cies, 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 coun- 

 tries as ornaments for the head-dress, and 

 the Japanese, Chinese, and Persians, im- 

 port 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 horses. 

 They are found only within a few de- 

 grees of the equator. Gmelin enume- 

 rates twelve species, 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, return- 

 ing to North Guinea with the wet mon- 

 soon. They pass in flights of thirty or 

 fort}', headed by one whose flight is high- 

 er than that of the rest. They are often 

 distressed by means of their long feathers 

 in sudden shiftings of the wind, and una- 

 ble to proceed in their flight ; are easily 

 taken by the natives, who also catch them 

 with birdlime, and shoot them with blunt- 

 ed arrows. They are sold at Aroo for au 

 iron nail each, and at Banda for half a rix- 

 dollar. Their food is not ascertained, 

 and they cannot be kept alive in confine- 

 ment. The smaller bird of Paradise is 

 supposed by Latham to be a mere va- 

 riety 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 put into the hol- 

 low 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 

 paradoxes than geometry; thus, that a 

 right line should continually approach 

 to the hyperbola, and yet never reach 

 it, is a true paradox ; and in the same 

 manner, a spiral may continually ap- 

 proach to a point, and yet not reach it, 

 in any number of revolutions, however 

 great. 



PARAGOGE, in grammar, a figure 



