. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. DOCTRINE OF CHANCES. nor more rarely tlian â n â /times will be =. â But if x â * -4- i -j â, &c. + \- 2 2"% 12 36O 12 X 360St3 ' the probability of its happening to tlie probability ofjta fail- ing in any one tiial be as a to //, ltt L and lv be the two tenns equally diftant by the interval / from the greateft term of the binomial a + Z>\, and let S be the fum of the terms = 2/ 1S28 &c, the number whofe hyp. log. is â. included between L and R, together with the extre
. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. DOCTRINE OF CHANCES. nor more rarely tlian â n â /times will be =. â But if x â * -4- i -j â, &c. + \- 2 2"% 12 36O 12 X 360St3 ' the probability of its happening to tlie probability ofjta fail- ing in any one tiial be as a to //, ltt L and lv be the two tenns equally diftant by the interval / from the greateft term of the binomial a + Z>\, and let S be the fum of the terms = 2/ 1S28 &c, the number whofe hyp. log. is â. included between L and R, together with the extremes, ,2x then will the probability that the event happens neither more f 4. L f &c. Js , 4. _J |_ _J \ , , an , . 360 xJ in 51840*1 ficqucutly than + / times, nor more rarely than . â u r- . > u â T.,r r n t o l i ' \ â 1 ' u + b ' T> &e. (lee Cotes s Harm. Mem. Irop. I. Schol. 2 ), and ââ / times be rightly exprcficd by â -â. then: hyp. log. is 1 ^ â, &c. is a + b â «4-ij" -. '2 ibo Thefe are the rules given by forth? lb. eafily found to be ! Inch Mr. Stirling has proved lution of tins very difficult propofition, which hi '" b t!w "luare r?ot ot the "W^w of a circle, whofe arc founded 01. the common principles of the doclrine of '"'J"s ls """>'⢠J imfcrence be denoted bye, chances, and therefore require no demonftration. This is ,l,c feries 1 + ââ + ~ , &c. by d, and the num, certainly true, fo far as regards the general principles o( the 12 x 200* folution, but the method oi dcten mini: g the vi lues 1 I 1 and v» +} x/~ S are by no means fo obvious. In this, indeed, conlills the ber 2 JlSzS Sec. by m, then we (hall have ; x J whole difficulty of the folution; and as MI), = p Bn| ^ x ., , mmh fa omitted the procels by whtch he obtained thofe values ,t 1:utcJ b d bf inconfJerMe, and P m thiscafe will be will be necefTary to fupply the omiflion by inferting the
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Keywords: ., bookcentury1800, bookdecade1810, booksubjectencyclo, bookyear1819
