Cow
CRE
If the factors of the binomial a 1 " ± x x be required, the index A being any integer : letthecircumference ABCD,thecenter of which is O, be divided into as many equal parts as there are units in 2 A ; and from all the divifions let there be drawn to any point P In the radius OA, produced if neceflary, the rightlines AP, BP, CP, DP, EP, FP, &c, then fuppof- ingOA = (j,OP-jf, the produd of all the lines A P, C P, EP, caV. taken from the alternate divifions throughout the whole circumference, will be equal to a* — #\ or x X — «*, according as the point P is within or without the circle ; and the product of the reft of the lines BP, DP, FP, in the re- maining alternate places will be equal to a* -J-**.
For inftance, if A =5, let the circumference be divided in to 10 equal parts, and the point P be within the circle, then will AP X CP X EP X GP X IP be equal toUA 5 ~0? and BPXDP XFPXHPxKP = aA s +UT' 5 . In like manner if A be r= 6, having divided the circumference into twelve equal parts, A P_X CP X EP X GP X IP X LP will be equal to O A 6 — O f \ and BPXDPXFPXHP XKP X MP = OA & -f-Op 6 .
The demonftration of this theorem may be feen in Dr^Pem berton's Epift. de Cotefii inventis.
By means of this theorem the acute and elegant author was enabled to make a farther progrefs in the inverie method of fluxions, than had been done before. But in the application of his difcovery there ftill remained a limitation, which was re- moved by Mr. de Moivre. See Dr. Smith's Theoremata lo- gometrica & trigonomctrica, added to Cotes's Harmonia men- furarum, p. 114, 115. De Moivre, Mifcel. Anah/t. p. 17, fit
COTTON (Cyd.) — Lavender-QoT-voK, a name fometimes given to a genus of plants, called by authors jantolina. See the article Santolina, Suppl.
Cott ok -tree, in botany, the Englifh name of a genus of plants, called by authors gojfypiwu. See the article Gossy- fium, Append.
Sttt-CoTTOK, a name ufed by fome for a genus of plants. called by authors xybn. See the article Xylon, Append.
Cot t on -weed, a name ufed for the gnaphalium of authors, See the article Gnaphalium, Sutpl.
COUCH-grafs, or dogVgrafs, in botany. See the article Grass, Append.
COVENTRY-/*//*, a name fometimes given to the campanula. See the article Campanula, Suppl.
COUGHS (Cycl.) — See the articles Cold and Consump- tion, Append, and Tussis, Suppl.
COULTER neb, in zoology, a name given to the anas arSlica. See the article Duck, Suppl.
COW, in zoology, the female of the ox-kind. See the articles
Bos and Ox, Suppl. Sea-Cow, the Englifh name of a genus of fea-animals, called
by zoologifts manatl. See the article Manati, Suppl Cow-itch, phafeolus hirfutis, in botany. See the article Pha-
seolus, Suppl. Vide guihe. Pharm. p. 230. Cow's-lip of Jerufalem^ in botany, a name fometimes given to
thepulmonaria of authors. See the articlePuLMoc^iuA, Suppl; French Cow's-Hp, a name by which fome call the auricula, or
bear's ears of botanical authors. See the article Auricula,
Suppl. COWL (Cycl.) — Friar's-CowL, in botany, a name fome- times ufed for the arifarum of authors. See the article Ari-
. SARUM, Suppl.
CRAB, in zoology, the Englifh name of a genus of fliell-fifh, of the fquilla kind. See the Article So^jilla, infra.
Crab-*>w, in botany, the Englifh name of the malm fylvejiris of authors. See the article Malus, Suppl. and Append.
CRABRO, the hornet, in zoology, the name of a genus of flies of the apis, or bee-kind. See the articles Bee and Hor- net, Suppl. and Apis, Append.
CRANE (Cyd.) — There are feveral improvements of this ufe- ful machine mentioned in Dcfagulier's Experim. Philof. p. ijS, feq. particularly how to prevent the inconveniencies arifing from fudden jerks, as well as to increafe its force by ufing a^ double axis in peritrochio, and two handles.
CRASPEDARIA, a genus of animalcules, without any vifible limbs or tails, but with an apparent mouth, and a feries of fimbria? round it in the manner of a fringe. Of this genus there are three fpecles : 1. The crafpedarium with a roundifh body. 2. The crafpedarium with an oval body. 3. The crafpedarium with a cylindric body. Hill's Hift. of Anim. p. 5.
CRASSULA, in botany, the name of a diftindt genus of plants called by fome bajlard-navel-wort.
The characters of this genus are thefe : the cup is a perian- thium, formed of five lanceolated, hollowed, acute, erect, and permanent leaves, which meet in fuch a manner as to form a kind of tube ; the corolla is fomewhat of an infundi- buliform fliapc, and is compofed of five petals, the ungues of which are very long, linear, frrait, connivent, and joined at their bafes ; and the bractea?, which form the limb, oval and reflexo- patent j the nectaria are five very fmall emarginated fquamas, annexed outwardly to the bafe of the germen ; the ftamina are five fubulated filaments, of the length of the tube, and inferted into the ungues of the corolla ; the antherae are fimple; the germina are five, oblong, acuminated, and ter- minated by fubulated ftyles, of the length of the ftamina - r the ftigmata are obtufe ; the fruit is compofed of five oblong, acuminated, ftrait, comprefl'ed capfules, opening longitudi- nally inwards ; the feeds are numerous and fmall. Linna' Gen. Plant, p. 133.
Vaillant makes it only a fpecies of fedum. See the article Sedum, Suppl.
CRAX, in zoology, a name given by the antients to the orty- gomeira, or daker hen, a bird larger than the quail, and com- mon in Ireland and fome of the northern counties of England. Ray's Ornithology, p. 122. See the article Ortygome,-
TRA, Suppl.
QJLKY-flfh. Thefe fifh are comprehended among the fpecies of fquilla. See the articles Cjr a X-fiJh, Suppl. andSqyiLLA, Append. CRAZE-m///, or Ckazikg -mill, a mill in all refpects like a grift-mill to grind corn, and is fo called by the tin- miners, who~ ufe it to grind their tin, which is yet too great, after trambling, and then it istrambled only. CREEPER, the Englifh name of a fpecies of ifpida, which, though very unlike the common king's-fifher both in colour and figure, yet is comprehended under that genus on account of the ftructure of its feet. Seethe article Ispida, Suppl. This fmall bird has likewife been called certhia and certhius, by authors, and in Englifh the ox-eye. See the article C&r- thia, Suppl. CREODIBA, in the cuftoms of the middle age, a robbery and murther committed in a wood, where the body of the perfon killed was burnt, in order to prevent any dilcovery of the crime. The word, fays Wendelihus, is compounded of gruy and diven, that is, wood-robbers. Tit. 74. of the Salic Law, edit. Hcroldi, relates to creodiba. Du Cange> GlolT. Lat. CRESSES (Suppl.) — Indian Cress, Najluriitmi hulicwn, in botany, the Englifh name of a genus of plants, called by au- thors cardamindum and trepesalum. See the articles Carda- mindum, Suppl. and Trgpjeolum, Append. Sciatica Cress, a name ufed by fome for a genus of plants, called by others ibcris and cardamine. See the article Cardamjne, Suppl. Sciatica Cress, or Babylonian Cr ess, are names fometimes alfo given to the kpidium, or Dittander, Seethe article Lepidium, Suppl Wdter-Cs.Ess, or w/'nter-CRJLSSf names given by fome writers to a genus of plants known among authors by that of Jifym- brium. See the article Sisymbrium, Suppl. CRESTED p'afsj in botanv, Seethe article Grass, Append.
CRIMSON
