■^>'}=o( 



I) 



GEO 



Let the equation of any interfering plane be 



z — Ax + By + C. 

 The projeftion of the iuterfeftion of the curve with the 

 fill face on the plane xy will have this equation, 



x^.L +NA ) + v'(M + NB') + 2ABN 

 + 2 A C N .V + 2 B C N^' + NC - I 

 • If the interfeiflirg^ plane he fuppofed to change its pofi- 

 tion by moving parallel to ilfclf, A and B will remain con- 

 ftant, and C only will change its value ; hence it follows that 

 the co-efficients of x',y', v y, in the equation of projection, 

 will remain the fame, whatever be the value of C. But bv 

 the transformation of the co-ordinates this equation may 

 be reduced to this form ; 



/ u' + m' v' + n' II V -\- p' = o ; 

 in which equation the co-efficients I m n' only contain A and 

 B ; p' alone being forae funclion of C. If C be made to 

 var\-, the value of p' may be fuppoled to become p" , and the 

 preceding equation to become 



/ u" + m' 'd' + n nv -\-p'' == O 

 which as it only dilL'rs from the former in the conilant quan- 

 tity, evidently belongs to a fimilar curve ; hence it may be 

 demon (Irated that all parallel feclions are fimilar, and limi- 

 larlv fituated. Moreover, the locus of the centres of thefe 

 feftions is in a diameter of the furface. 



If in the equation L x' + M v' -+- N s' — i = o we 

 fubftitute for the co-efficients L, M, N, the conilant quan- 

 tities — , -r, — , a being greater than i, zndi > c ; it bc- 



i rx^ + c'a'y' + d' h^ z^ = a K c"- (E) 

 The advantage of this fubftitution is to render the fign of each 

 term of the equation independent of the particular values of 

 the co-efficients, and to introduce as conilant quantities 

 <in the equations of the fections of the furface by the planes 

 of the co-ordinates) only the principal axes of thefe feftions. 



From the dilTerent combinations of the fig;is three diftinci 

 cafes arife from equation E ; for a full inveftigation of which 

 we mud refer our reader to the original work from which this 

 article was principally extrafted. (Vide Application de 

 TAnalyfe a la Geometrie, par M. Monge.) 



The three equations are 

 I' c' x"^ -^^ c a v' + a"-i s;- = «-*'r-,or L.v' -(- M/ — N2'= i 

 h c' x^ -\- 1 a y' — a b "z.- t::^ a h e iOtIj X -1- M^' — Nz"-=i 

 lrcx~- — c'ay -a"^'s' = a'iV ,or L.v — Mjr -Nc==i 

 The former belongs to the elhpfoid and the two other? to 

 two different fpccies of hyperboloids. 



Geometry, CharaRers in. See Character. 



Geometry, Spherical. See Spjiehical. 



GEOMORI, fti'MOr'"' i" -/intiqiiity, the divifion or clafs 

 of the ancient Athenians employed in agriculture. 



GEONOMA, in BoCany, from •jtjjc^o:, z fuller out, or 

 diftributor of land, alluding to the mode of growth of the 

 firft fpecies of the genus in queftion, as hereafter defcribcd. 



Willd. Sp. PI. v. 4. 593. — Clafs and order, ALno.'cia Mo- 



nadtlpiia. Nat. Ord. Pa/nut. 



Gen. Ch 



EflT. Ch. General Spatha double, of two valve;. Male, 

 Calyx in three deep fegments. Petals three. Filaments 

 fix, united into a cylinder. 



- Female, Calyx and Corolla hke the male. Style one, 

 lateral. Sticcma of two lobes. Drupadry, with one feed. 



1. G. pinnatifrons. " Fronds pinnate ; the pinnae ab- 

 luptly jagged.'' — Native of the Caracas, in Ihady woods on 

 the lofty mountain of Buenavifta. B,\:'tm.yer.^T\\e trunk 

 is fimple and llender, an uich in diameter, fmoolh, riiing to 

 i. 3 



GEO 



the height of fifteen feet, when, by the power of the wind 

 on its ample foliage, it is blown down, but foon produces 

 new fhoots and roots from the top, whence a Hew trunk 

 fprings up to the fame height of about fifteen feet, and in 

 its turn is quickly laid proftnte like the former. The 

 fronds (rather leaves) are pinnate, their pinnas irregular, 

 fomewhat folded, jagged abruptly at the fummit. Spatha 

 double, of two valves, wcdge-fliaped, fomewhat comprcfTed, 

 acute, three inches long. Spndix fifteen inches in length, 

 branched at the top, the branches round, bearing each from 

 feven to nine alternate, cylindrical fpikes, of the length ot 

 three inches each. Floivers conilantly three, funk in a little 

 hollow of the fpike, two of which are male, one female. 

 Drupa dry and fibrous, the fize of a pea. Kut globofe, black. 



2. G. fimplieifrons. " Fronds fimple, wedge-fhapcd, 

 cloven.'' — Found at the Caracas with the fonmr. Brede- 

 meyer, — The trunk of this is permanently upright, ten feet 

 liigh, an inch thick. Fronds (or leaves) a foot long, fimple, 

 wedge-lhaped, taper at the bafe, cloven, and divaricated at 

 the fummit, fupported on very long ftalks. Spatha double, 

 of two valves. Spadix bearing at its extremity three or 

 four cylindrical fpikes. Floiuers inunerfed in little cavities, 

 like the former. Wdldenow. 



GEOPONIC, fometliing defcribing or relating to agri- 

 culture. Cato, Varro, Columella, Palladius, and Phny, 

 are fometimes called geoponic writers. 



GEORG, St., in Geography, a town of Germany, at the 

 conflux of the rivers Teya and March, formerly a royal 

 city, but now much reduced ; 24 miles N.N.E. of Pref- 

 burg. — Alfo, a town of Hungary ; 7 miles N.N.E. of 

 Prefturg. 



GEORGE, in Biography, furnamed the Cappadocian, 

 was made bilhop of Alexandria when Athanafius was driven 

 from that fee by the perfecutions of the emperor Conftan- 

 tius, about the year 355. (See Ath.-vxasius.) He was a 

 native of Epiphania, in Cilicia, where his father purfued the 

 bufinefs of a fuller. From this obfcure fituation the foa 

 raifed himfelf, it is faid, not by the moll honourable means, 

 to the flation of a prelate in the church. At firll he obtain- 

 ed a lucrative appointment as purveyor of bacon to the 

 army : not contented with the regular profits of his office, 

 he made ufe of every art, however bafe and corrupt, in the 

 accumulation of wealth ; fo as to render a mean employment 

 truly infamous. His depredations on the pubhc purfe be- 

 came fo notorious, that he felt it extremely dangerous to 

 wait the iffue of a fuit commenced againft him. He fled 

 from the purfuit of juftice, and contrived to take with hira 

 his ill-gotten wealth. The place of his retreat was Alex- 

 andria, where he profeffed great zeal for the Arian fyllem of 

 theology, and being a man of fuperior talents, he acquired 

 confiderable influence with his dileiples in that city. Here 

 he collcifted a large and very valuable colledlion of books, 

 which the emperor Julian afterwards made the foundation 

 of the noble library eftabliflied by him in the temple ereiled 

 in honour of the emperor Trajan, but which was burnt by 

 the connivance of the emperor Jovian. When Athanafius 

 was driven from Alexandria, George was elected bifhop by 

 tlie prevailing party. In this ilation his conduit was in the 

 highell degree cruel and oppreffive. He perfecuted the Ca- 

 tholics with an unrelenting hand, and the other inhabitrnts 

 of tliis vail diocele were objects of liis tyranny and avarice. 

 The merchants he impoverilhcd by unjuft monopolies and 

 cruel taxes ; the Pagans, who had been excited with the 

 hopes of freedom and toleration, did not efcape his rapacity, 

 and the rich temples of Alexandria were either pillaged or 

 infultcd by him, who exclaimed, in a liaughty and threaten, 

 jog. tone 01 voice, " How long will thcle fepulchres be per- 

 mitted 



