I s o 



s o 



V U-y" - i': + "}'}'] 



If, inftead of the area, the length of the curve had been 

 ivcn, then we fhould have had 



of Linn. Soc. v. lo. 71. Prodr. Nov. H'"' 

 Clafs and order, Tetramlria Monogynia. N . 



ftii ^Jk = fx ^ [i +/»') ; and u 

 Therefore V = z-ry ^/ (i + />') — 

 and confequently, by formula [A], 



whence, again, by formula [</] , we have 



V (I +/■■) 



ihcr.ce, by rcduflion, 



('■~y -«) v/(i +f) 



/ (1 +/), 



+ < 



and 



Brown Tr 

 V. I. 36,'. 

 Ord. Pro.Y 



EfT. Ch. PerlBBth (rather corolla) four-cleft, with . 

 llender permanent tube. No fcales under the genn -. 

 Style entirely decidnous. Stigma tapering or cyhndriL.;. 

 Not feihle, iwelling, hairy all over. Brozvii. 



Mr. Brown, in the places above quoted, defnies 12 fpe- 

 cics of this genus, all natives of New HoJJand, fiich of 

 which as have come under the notice of other botaniii? 

 have been confounded with the Linnxan Pro/.a. They are 

 rigid flirubs, with fmooth /er.vcs, which are either flat or 

 tliread-Aaped, divided or entire. HeaAs tormina',, rarely- 

 axillary. Fhivcrs either very denfely imbricated '\n the 

 form of a ^ohoie JlrolUus, or fatligiate on a flattifli com- 

 mon receptnde, furnilhed with more or lefs of an invohu 

 frum, and befet with crowded deciduous fcales. — Exam- 

 ples of this genus are 



I. anetlj/folrus. (Protea anethifolia ; Sahfb. Prodr. 48. 

 P. acufera ; Cavan. Ic. v. 6. 33. t. 549.) — Leaves once or 

 twice pinnatifid, thread fliaped, fHrrowed above : their feg- 

 ments nearly erefl. Branches fmooth. Tube of the fiower 

 dowsy; fegments fmooth, bearded at the tip.— Native of 

 heathy ground on the eait coaft of New Holland, near Port 

 Jaekfon. 



I. arientotn/c/iiis. (Protea anemcnifolia ; Salifb. Pro^r. 4S. 



Sims in Curt. Mag. t. 697. Andr. Repof. t. 332. P. tri- 



daClylides ; Cavan. Ic. v. 6. 33. t. 548.) — Leaves once or 



twice three-cleft ; fegments hnear, !lat, r»lhcr fpreading, 



. fmooth beneath. Scales of the cone fponcjv. — Found ore- 



Of all ifoperimetrical curves, drawn between B and N, ftony heaths near Port Jackfon. The fcrw/v are yellow. 



We conlels this genus feems too nearly related to Mr, 

 Brown's Pctrophihi, with which it agrees altogether in. 

 habit, differing chiefly in the fruit of Petrophila being only 

 partially hairy. To this latter belongs Protea pulchelta^ 

 figured by Dr. Sims in Curt. Mag. t. 796. 



ISOPSEPHUS, lTo4-'!?5'f, in ylnliquily, an appellation, 

 given to judges, who had equal jurifdidion and authority j 

 •. iM r i:_j.._ __r i — '' votes were equal 



■ .^{z^y-a-Y-c'r 



t-he fluents of which expreflion being taken, gives 



- ■ .r = — hvp. log. 



and therefore the required curve is the catenary. 

 Prob. X. 



(f,g. 15.) to find B F N fuch, that B Z N (hall contain the 

 grcatell area, P Z being a fuadion of P F. See the fore^ 

 going hillorical flcetch. 



Let P F = y, and P Z a funflion of ^ = Y ; then/ V .> 

 correfpondsto/Y.v ; und/uxtof y' (i +p'j x. 



Hence V + ,7 «, or V^ = Y + « ,/ (i + p'). 



V = 



ipp 



hence we have, by comparifon of formula [A] 



^ P ^. 



V (I +/- )' 

 and hence, again, by form [«] is deduced 



P = 



Y + «./{! +/■■) 



ud confequently. 



likewife applied to a cafe where thi 

 on both fides. Another fenfe is given to it,, •viz. when the 

 letters of different words make up the fame fum, they were 

 faid to be imlr.^y. fr,,.:y.''iy, ; for the Greeks had no other cy- 

 phers to number with but the letters of tlidir alphabet ; 10 

 that a, iignified one, (3 two, y three, &c. But befide words, 

 the ancients had likewife whole verfes of this kind ; and it 

 is pretended that there are feveral fuch verfes in Homer. 

 Hilf. Acnd. Infcript. vol. iii. p. 311, feq. 



ISOPYRUM, in Botany, from .m-r, equal or nie, and 

 TVfo:, wheat, a name adopted from Diofcorides, whofe 

 ta-oTTUfoy, however, is very difficult to afcertain. He defcribes 

 it as having the leaf terminated by a tendril. Vaiions plants 

 have been taken for it by different botanifts, amongft others, 

 furely with httle probability, the ^qullegia, or Columbine, 

 •which we mention here becaufe it appears to have induced 

 Linnaeus to choofe the name for the prefent genus, very 

 much akin to ^qmlegia, and dill more diilinguiOied for de- 

 licacy and ek>gance. — Linn. Gen. 282. Schreb. 378. 

 Willd. Sp. PI. v. 2. 1334. Mart. Mill. Dia. V. 2. Ait. 

 Hort. Kew. V. 2. 271. Salifh. Tr. of Linn. Soc. v. 8. 



306. Jufl". 233. Gzertn. t. 65 Clafs and order, Poly- 



amlria Polygynia. Nat. Ord. Multifdiquje, Linn. Ranuncu- 



the equation of the curve. 



In the equation, as it ftands, there are two arbitrary 



jletermined quantities a and c. The integration of the cqua- laceie, JulT.'' 



tion would introduce a third ; and to determine thefe three. Gen. Ch. Cal. none. Cor. Petals five, ovate, equal, 



we have given the two points B and N, and the length of fpreading, deciduous. Neftaries five, equal, tubular,, very 

 "Tc'r^T3r->/-./-MwT • fhort, inferted into the receptacle within the petals, three- 

 ISO POGON, in Botany, {vom im-, equal, and rayi,», a lobed at their orifice, the outer lobe largelL Stam. Fila- 



heard, btcftufe the feeds are every where equally bearded, ments numerous, capillary, fliwter than tiie corcllaj anthers 



S fimple. 



