H\T 



HYP 



HYOBANCHE, in botany, a genus of 

 the DidynamiaAngiospermia class and or- 

 der. Natural order of Personals. Pedi- 

 culares, Jussieu. Essential character : ca-, 

 lyx, seven-leaved ; corolla ringent, with- 

 out any lower lip ; capsule two-celled, 

 many-seeded. There is but one species, 

 viz. H. san.^uinea, a native ofthe Cape of 

 Good Hope, and is parasitical at the roots 

 of shrubs. 



HYOSCYAMUS, in botany, henbane, a 

 genus of the Penlandria Monogynia class 

 and order. Natural order ot Luridx. So- 

 lancx, Jussieu. Essential character : co- 

 rolla funnel-form, obtuse; stamina inclin- 

 ed; capsule two-celled, covered with a 

 lid. There are eight species. 



HYOSERIS, in botany, swine's lettuce or 

 succory, a genus of the Syngenesia Poly- 

 gamia ./Equalis class and order. Natural 

 order of Composite Semiflosculosx. Ci- 

 choracev, Jussieu, Essential character: 

 calyx almost equal ; down hairy and caly- 

 cled ; receptacle naked. There are ten 

 species. 



HYPECOUM, in botany, a genus ofthe 

 Tetrandria Digynia class and order. Na- 

 tural order of Corydales. Papaveraceae, 

 Jussieu. Essential character : calyx two- 

 leaved ; petals four, the two outer broad- 

 er, and trifid ; fruit a silique. There are 

 three species. 



HYPEL ATE, in botany, a genus of the 

 Polygamia Monoecia class and order. Es- 

 sential character : calyx five-leaved ; co- 

 rolla fivie-petalled ; stigma bent down, 

 three-cornered : drupe one seeded. There 

 , is but one species, viz. H. trifoliata, a na- 

 tive of Jamaica, where it is common in the 

 low lands. 



HYPERBOLA, in geometry, the sec- 

 tion, GEH, (Plate VII. Miscel. fig. 5 ) of 

 a cone, ABC, made by a plane, so that the 

 axis, EF, of the section inclines to the op- 

 posite leg ofthe cone, BC, which, in the 

 parabola, is parallel to it, and in the ellip- 

 sis intersects it. The axis ofthe hyper- 

 bolical section will meet also with the op- 

 posite side of the cone, when produced 

 above the vertex at D. 



Definitions. 1. If at the point E (fig. 6.) 

 in any plane, the end ofthe rule EH be 

 so fixed, that it may be freely carried 

 round, as about a centre ; and at the other 

 end of the rule H there is fixed the 

 end of a thread shorter than the rule, and 

 let the other end of the thread be fixed 

 at the point F, in the same plane ; but 

 the distance of the points EF must be 

 j greater than the excess of the rule above 

 the length of the thread ; then let the 

 thread be applied to the side ofthe rule 

 EIJ, by the help of a pin G, and be stretch. 



ed along it ; afterwards let the rule be 

 carried round, and in the mean time let 

 the thread, kept stretched by the pin, be 

 constantly applied to the rule: a certain 

 line will be described by the motion of 

 the pin, which is called the hyperbola. 

 But if the extremity of the same rule, 

 which was fixed in the point E, is fixed 

 in the point F, and the end ofthe thread . 

 is fixed in the point E, and the same 

 things performed as before, there will be 

 described another line opposite to the 

 former, which is likewise called an hy- 

 perbola ; and both together are called 

 opposite hyperbolas. These lines may 

 be extended to any greater distance from 

 the points EF, viz. if a thread is taken of 

 a length greater than that distance. 2. 

 The points E and F are called the foci. 

 3. And the point C, which bisects the 

 right line between the two focus's, is 

 called the centre ofthe hyperbola, or of 

 the opposite hyperbolas. 4. Any right 

 line passing through the centre, and 

 meeting the hyperbolas, is called a trans- 

 verse diameter ; and the points in which 

 it meets them, their vertices; but the right 

 line, which passes through the centre, 

 and bisects any right line terminated by 

 the opposite hyperbolas, but not pass- 

 ing through the centre, is called a right 

 diameter. 5. The diameter which passes 

 through the foci is called the transverse 

 axis. 6. If from A or a, the extremities 

 ofthe transverse axis, there is put aright 

 line AD, equal to the distance ofthe cen- 

 tre C from either focus, and with A, as a 

 centre, and the distance AD, there is a 

 circle described, meeting the right line 

 which is drawn through the centre ofthe 

 hyperbola, at right angles to the trans- 

 verse axis, in B b ; the line B b is called 

 the second axis. f. Two diameters, ei- 

 ther of which bisects all the right lines 

 parallel to the other, and which are ter- 

 minated both ways by the hyperbola, or 

 opposite hyperbolas, are called conjugate 

 diameters. 8. Any right line, not passing 

 through the centre, but terminated both 

 ways by the hyperbola, or opposite hy- 

 perbolas, and bisected by a diameter, is 

 called an ordinate applied, or simply an 

 ordinate to that diameter : the diameter, 

 likewise, which is parallel to that other 

 right line ordinately applied to the other 

 diameter, is said to be ordinately applied 

 to it. 9. The right line which meets the 

 hyperbola in one point only, but produc- 

 ed both ways falls without the opposite 

 hyperbolas, is said to touch it in that 

 point, or is a tangent to it. 10. If through 

 the vertex ofthe transverse axis a right 

 line is drawn, equal and parallel to the se- 



