. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. I s o I s o (c + ay) V V lA~y^- - (f + ay)'\' If, inftead of the area, tlie lengdi of the curve had been given, tlien we fliould have had =fi. = fx ^/ (I + ^') ; and « = V (I +/>')⢠Therefore V = 2vy ^/ (i +/>") â « v^ (i +/'), and confequently, by formula [AJ, z-^yp-ap ^ vO'+ />')' V. hence, again, by formula [rt], we have {i-^y-a) y (i +/.^-) â¢* hence, by reduftion. a)p- + ^; the fluents of which exprcflioii being taken, gives X = _- liyp. log. 1(2 Try â a) +
. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. I s o I s o (c + ay) V V lA~y^- - (f + ay)'\' If, inftead of the area, tlie lengdi of the curve had been given, tlien we fliould have had =fi. = fx ^/ (I + ^') ; and « = V (I +/>')⢠Therefore V = 2vy ^/ (i +/>") â « v^ (i +/'), and confequently, by formula [AJ, z-^yp-ap ^ vO'+ />')' V. hence, again, by formula [rt], we have {i-^y-a) y (i +/.^-) â¢* hence, by reduftion. a)p- + ^; the fluents of which exprcflioii being taken, gives X = _- liyp. log. 1(2 Try â a) + ^/ (2 tt v - n)' - c^] + c', therefore the required curve is the catenary. PllOB. X. Of J'll ifoperimetrical curves, drawn between "R and TI, hi?- ^5-) to ftnd B F N fuch, that B Z N fhall contain the greatelt area, FZ being a function of P F. See the fore- going hiicorical iketch. Let P F - y, aad P Z a funaion of _)- = Y ; then/V .v correfponds to/Wv ; nud/ujetof^/ (i +/>') x. Hence V + au,orY' ^Y + a ^/{i + p'), Yy Brown Tr. of Linn. Soc. v- 10. 71. Prodr Nov. HoJI, V. I. ^6^, Clais and order, Ti'irundria 3IonogyrJta. Nat- Ord. Proteaccd-. EfT. Ch. Perianth (rather corolla) four-cleft, with 9 flender permanent tube. No Icales under the gcrmen. Style entirely deciddous. Stigma tapering or cylindrical. Not feiliic, Iwelling, hairy all over. Broiuii. Mr. Brown, in the places above quoted, defines 12 fpe- cies of this genus, all natives of New Holland, fuch of which as have come under the notice of other botanills have been confounded with tlic Linirxan/'ro/ev?. are rigid (hrAibs, wuh fmooth leaves, which are either flat or thread-lhaped, divided or entire. Heads terminal, rarely axillary. Floivcrs either very denfely imbricated in tiie form of a ^lohofe /Irol/i/us, or fadigiate on a .flattiih com- mon receptacle, furnifiied with more or Icfs of an involu* erum, and befet with crowded deciduous fcales.âExam- ples of this genus are L anethifoltus. (P
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Keywords: ., bookcentury1800, bookdecade1810, booksubjectencyclo, bookyear1819
