I N D 



Synopfis of Indtterm'mate FormuU. 

 T'orm. 17. Equation m^ x' -\- b »'' f f .r 4- </ r= 5^ 

 b' — 27 dm'' 



{^- 



'articular val. of .v 



(.^^' 



b, c, &.C. being given quantities, as ; 



Form. 18. Equation m' x' + ir" + ex +/^ 

 Particular val. of .» = if-^lH-SL', 



i-3 m-f' 

 tvliere alfo m, I, c, &c. are known quantities. 



Form. 19. Equation *•'' -j- axy -f iji' = z^. 

 f General val. oi x = ~ b t u'' — abu^ 

 \ y = iPu + ^atu' + {a'-b), 



where I and :/ may be afFumed at pleafure. 



Form. 20. Equation .\- + by^ — 2'. 



rGen. val. of* = /' — btu^ 

 \ y = 3t'u-bu^ 



i z = t' + u\ 



t and u being indeterminates, as above. 



Form. 21. Equation .r- + by'' =z z*. 



r Gen, val. of x = t* — 6bt^u'' + b' u* 



< y = ^t'u- 4.btu' 

 L a = t' + bu\ 



i and a being indeterminates, as above. 



Form. 22. Equation*' + by' = s". 



rGen. val. of* = t" —f^t"-'' u' b + o t"'' uH' — Scc. 

 J _jr = ar-'u — y t" ■ 'uH + it-'-'- uH' ^c. 



L z = t' + bu', 



V'here t and a are indeterminates, and I, a, ft y, 5, &c. the 

 •o-efficients of {t + u)"'. 



Form. 23. Equation x'' + /-j^^ =: 3;^ 



rGen. val. of .r = 4/* — 4 c/ m' 

 -J y=Hru + cu- 



where / and u are indeterminates, 



Forvi. 24. Equation x'' + ax'' y -\- b xy'' + cy'' = z\ 



< Partic. val. of / = —^ . 



I 21i> 



( Geii. val. of>; = /' + 2 c u w + a c 'ui^ 

 \ y := 2 tu — 2 iww — {a b — c) 'w'', 



where o and iv are indeterminates, on which alfo depends 

 the value of /. 



Ikdetermin'ate Problem, is that in which there are 



more unknown quantities than there are equations ; and 



therefore from the principles of algebra the number of fo- 



Jutions is unlimited, unlefs fome other condition enter, fuch 



Vol. XIX. 



1 N D 



a» requiring integral values of the unknown quantities, by 

 wliicli means the problem frequently admits of only a dcli- 

 nite number of anfwers ; as may be fcen in the preceding 

 article. In geometry a problem is always faid to be inde- 

 terminate, or unlimited, when there are not fufficient data to 

 Irmit its conllruction. 



INDEX, in Anatomy, the fore-finger. 

 Indi'.x, in Arithmetic, is the fame with what is otherwife 

 called the cliaractcrillic, or exponent of a logarithm. 



The index is that which fliews of how many places theabfo- 

 lute number belonging to the logaritlim confills, and of what 

 nature it i,i, whether an integer, or a fraction. 



Thus, in this logarithm 2.521293, the number (landing 

 on the left hand ot the point is called the index ; and be- 

 caufe it is 2, it (hews you that the abfolute number anfwer- 

 ing to it confifts of three places ; for it is always one 

 more than the index, becaufe the index of I is o ; of lo 

 is I ; and of 100 is 2, &c. And, therefore, in thofe 

 itnall tables of Biiggs's Logarithms, where the index is 

 omitted, it muft be always i'upplied before you can work 

 by them. If the abfolute number be a fraftion, the index 

 of the logarithm has a negative fign, and is marked thus, 

 2.562293 : which fliews the correfponding number to be a 

 decimiJ fraftion of three places ; -..•;s. 1.365. 



Mr. Townly has a peculiar way of noting thefe indices, 

 when they exprefs fraftions, now mucli in ufe, ws. by taking, 

 inllead of the true index, its arithmetical complement to 10; 

 fo that he would write the logarithm now mentioned thus : 

 S.562293. 



Hort- indices are to be added and fubtrafted, fee under the 

 article Logarith.m. 



Inde.v, in Mufic, a charaftcr ufually placed at the end of 

 each hne to indicate the firll note of the next line. The 

 following is the charafter W, wliich the Italians term a 

 mojlra, the Englifh call it a direa. 



Index of a Bool:, is that part annexed to a book, referring 

 to the particular matters or paffages therein contained. 



Index of a Globe, is a little flyle fitted on to the north- 

 pole, and turning round with it, pointing to certain divi- 

 lions in the hour-circle. 



It is fometimes alfo called gnomon. See Globe. 

 Index of Relation, in Algebra, the fame with fcale of re- 

 lation. See Scale. 



Index, or Indice, is alfo the denomination of a congre- 

 gation at Rome, whofe hufinefs is to examine book?, and to 

 put fuch as they think fit to prohibit the reading and fclli.ng 

 of, into an index. See Conguegation. 



Indices, or Expurgatory Indices, denote the name by wliicli 

 the catalogues ot prohibited books are called ; among which, 

 however, tliere is this difference, that feme are tjondemned 

 purely and abfolutely, and others only donee corrigantur, till 

 they be corrected. 



Father Paul fays, that Philip of S))ain was the firft who, 

 by a la>v made in 1558, procured an index to be pubbdied 

 of the books condenmed by the inquifition of Spain. Pope- 

 Paul IV. took the hint, and ordered the congregatio: of 

 the holy office at Rome to print a fecond in 1559. But Grtt- 

 fer, (De Jure Prohib. lib. li. cap. 19.) fays, that the index of 

 prohibited books was printed in Italy, by the papal autho- 

 rity, in 1548; and a larger one in 1552 ; and another larger 

 in 1554. Pius IV. recommended the matter to the council 

 of Trent ; the fathers at Trent, after feveral debates not 

 being able to agree, thouglit ht to refer the whole affair to 

 the pope, who, with the advice of certain leai'ued prelates, 

 H pubhihc* 



