HYP
i. The common black Henbane. 2. The common white Henbane. 3. The fmaller white Henbane. 4. The fmall yellow Henbane of Crete. 5. The red flowered Henbane. 6. The white flowered Egyptian Henbane. 7. The little golden Henbane of America, with fmooth narrow leaves. 8. The fmall yellow flowered annual exotic Henbane, lournef. Inft. p. 117.
There are two kinds of Henbane feed ufed in medicine, which poffefs the fame narcotic virtues, but in a different degree ; the white isthemilderof the two, and therefore generally prefcribed ; many, however, look upon them as poifonous, while others recommend them in many cafes, particularly in fpitting of blood.
Hyosciamus Peruvianas, Henbane of Peru, a name by which Dodoraeus and many other authors have called the tobacco plants, more ufually known by the name nicotiana. See the article Nicotiana.
HYOSYRIS, in botany, a name given by Pliny and fome other authors to the common knapweed, or jacea nigra.
HYPACTIC medicines, a term ufed by fome authors for cathar- tic medicines.
HYP ATE, in the antient mufic, an appellation given to the lowelt chord or found of a tetrachord.
The word is Greek, vte«rv t which fome Latin interpreters tranflate by fuprema ; as they tranflate mit»s by ultima or ima a . Dr. Wallis b fays, that the firft contrivers of thefe names, took, contrary to our cuftom, the grave for the higheft place, and the acute for the lowed: of their fchemes. This was the practice of Bcethius ; and Nichomachus, in the heptachord lyre, afcribes the Hypate to Saturn, and the neate, or nete, to the Moon. Some however interpret »V*tos as if it were viroccroi, but erroneoufly, according to the learned docfor juft quoted, who obferves, that Homer calls Jove Ckutq v xfuwrtav, as if dV^toi' were derived from ifr^TcnM. After- Wards it is faid, the grave was taken for the loweft, and the acute for the higheft place, agreeably to our notions. Some think that the Hypate might obtain its name from being pla- ced higheft in the lyre c . Martianus Capella and Bcethius tranflate Hypate, principalis ; and parypate, fubprincipalis. Alio Ariftides Quintilianus chufes to call the Hypate firft, rather than fupreme or higheft, and calls the nete, laft, inftead of loweft a . Perhaps the truth of the matter is, that the Hy- pate was called higheft or loweft, according as muficians confidered the defcending or the afcending feale c . The move- able chord next the Hypate, was called parypate ; and that next the nete was called paranete f . [■' Hen. Stepb. Thef. in voc. mm, ap. Wallis, append, ad Ptolem. Harm. p. 159. b Wallis, ibid. c Malcolm's Treat, of Mufic, p. 519. <* Wal- lis, ubi fupra. e Vid. Phil. Tranf. N 3 481. p. 269. f Wallis, ibid.] See the articles Tetrachord and Interval.
Hypate Hypaton, in the antient Greek fcale, was the note next to the proflambanomenos, and anfwers to the loweft nit of Guido's fcale. Wallis, Append, ad Ptolem. Harmon, p. 157. See the articles Diagram and Interval.
Hypate Mefou, in the Greek fcale of mufic, was the firft note of the mefon, and the laft of the hypaton tetrachord. It anfwers to Elami of the Guidonian Scale. Id. ibid.. See the articles Diagram and Interval.
HYPECOUM, in the Linnsean fyftem of botany, the name of a genus of plants, the characters of which are thefe : The cup is a fmall perianthium compofed of two leaves, placed oppofite to one another, of an oval figure* pointed, and ftand- ing ereel, and falling with the flower. The flower is com- pofed of four petals, the two outer of which are placed oppo- fite to one another, and are broad, divided into three lobes, and obtufe. The two interior petals are placed alternately with the outer, and are flightly trifid, the middle fegment be- ing flatted, but fomewhat hollow, end placed erecf. The {la- mina are four eredf, tapering filaments, arifing from the jaggs or fegments of the inner petals ; the antherae are ere£f. and oblong ; the germen of the piftillum is oblong, and of a cy- lindric form ; the ftyles are two in number, and are very fhort ; the ftigmata are acute. The fruit is a' long, crooked, flatted, and jointed pod ; the feeds arc of a roundifh compref- fed form, and placed fingly one in each joint of the pod. Linnai Gen. Plan. p. 54.
The characters of Hypecoum, according to Tournefort, are thefe : The flower confifts of four leaves, difpofed in form of a crofs, and each of them is ufually trifid at the edge ; the piftil arifes from the cup, and finally becomes a flatted and jointed pod, containing in every joint or knot one reni- form feed.
The fpecies of Hypecoum enumerated by Mr. Tournefort, are two : 1. The broader leaved Hypecoum. And, 2. The narrower leaved kind.
Thefe have been ufed to be called cuminum fdiquofum, or podded cummin, by the old writers in botany. Tournefort 's Inft. p. 230.
HYPENEMIUS, an epithet applied by authors to barren eggs, or fuch as a hen lays before fhe has been trod by the cock. They are alfo called zepbyria ova, and had both thefe names from the winds being fuppofed to generate them.
HYPERBIBASMUS, , T S r«§&&«r f wc, in rhetoric, a figure which inverts the order of conftruttion. Cornelius Nepos gives an inftance of it in his life of Chabrias : Atbcnienfcs diem ccrtsm
HYP
Chabrifs prajlltuerunt, quam ante domum tiiji rediffet, &c. for ante quam. Vojf. Rhet. 1. 4. p. 36. HYPERBOLA (£>/.)— Hyperbolas of all degrees may be ex- prefTcd by the equation x m y n ~ a m -\- n where « is a given quantity, x an abfcifla taken on the afymptote, and y an or- dinate to the afymptote.
If from any point B of fuch an Hyperbola, a line B C be drawn parallel to one afymptote, and terminated by the other and the parallelogram BCAD be compleated : Then will this parallelogram be to the hyperbolic fpace B C EO infinitely produced, as m — n to n. UHop'ital. Seel. Coniq. Art. 240. Hence, i°. When m — n is pofitive ; that is, when m is greater than n, we may always find the quadrature of fuch hyperbolic fpaces.
2°. When m—n, then m — ns^o, and the ratio of the paral- lelogram is to the hyperbolic area as to n. In which cafe this area becomes infinite.
3 . When m is lefs than n, m — n is negative ; and in this cafe the parallelogram is to the hyperbolic fpace as a negative number is to a pofitive ; which led Dr. Wallis and others to fay, that thefe byperkolic areas were more than infinite. See UHop'ital. Seel. Coniq. Art. 242.
But the truth is, this ratio of a negative number to a pofitive only fhews, that the fpace bounded by DB (the other fide of the parallelogram) by the curve and afymptote infinitely pro- duced, is to CBDA as m to n — m. UHop'ital, ibid. See alfo M.aclaurin'% Fluxions, Art. 294. Although the area comprehended between the Apollonian Hyperbola and its afymptote, be infinite, yet any fegment, or fector of this curve, may be fquared by means of logarithms. For inftance :
A B
Suppofe it required to find the area of the hyperbolic fegment EBCF, comprized between the arch of the curve ERF, the lines EB, F C parallel to the afymptote A D, and B C, the portion of the other afymptote intercepted between them. Then if ABED, the parallelogram of the Hyperbola, be taken as unity, the fpace EBCF will be Napier's logarithm of the ratio of A C to AB, or ofBEto FC. Hence if we had tables of fuch logarithms, we might find the area of EBCF by fubdu&ing the logarithm of FC from that of BE, and the difference would exprefs the ratio of the fegment to the parallelogram ABED or 1 . But as fuch tables are not extant, fome farther trouble is requifite to convert the com- mon or Briggs's logarithm into Napier's. Take therefore from the common tables the logarithm of the ratio of B E to FC, that is, the difference of their logarithms, and multiply this difference by 2.3025851, the hyperbolic logarithm of 10, the product will give the ratio of the fegment to the paral- lelogram ABED or 1. Thus fuppofmg BE:=36, and CF"=5, and the parallelogram ABED=i. From 1 . 5563025 = log. of 36. Subduit o . 6989700 = log. of 5. Difference o . 8573325 = log. of-,.--
Then o. 8573325 x 2.3025851 =1 -9740810 for the area of the fegment BEFC. This multiplication may be per- formed in Oughtred's contracted way.
Huygens, to avoid the multiplication by 2 . 302, fcff. finds its logarithm — o . 3622156887, and always adds this to the logarithm of the difference before found, and then finds the number correfponding to this fum. See Horol. Ofcillat. and Grandi, Dem. Theor. Huygen. in fine.
If it were propofed to find the area of the feflor A ERF; as this is equal to the fegment EBCF, the fame method may ferve. But it may alfo he done by feveral other analogies ; for which fee Cotes, Harm. Menfur. p. 12, 13. See alfo p. 25, 26, of the fame book. HYPERBOLIC (Qv/.J— Hyperbolic Logarithm. See the article Logarithm,
Hyper-
