. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. CALCULUS. râa A âB »7 B If . 'â¢"^g i? 37 B- + &c. .-1 _ A^' 2 ' B -â¦- 8cc, fin«c has to B fcch a ratio, as has to the ratio of B + A â B to B, or of A to B, the ntio of r to q, be ratio of r to j what it may, by taking any multiple} whatfocver of thefe ratio* and the lame mutllplci of r an! q. l"o- the fake of pcrfpi- cuity let thcfc mignitudci, and their multiplci, ftand in tlic following manner: are then refpcftively lefs than , or than nr nr tir â n T . -⢠-
. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. CALCULUS. râa A âB »7 B If . 'â¢"^g i? 37 B- + &c. .-1 _ A^' 2 ' B -â¦- 8cc, fin«c has to B fcch a ratio, as has to the ratio of B + A â B to B, or of A to B, the ntio of r to q, be ratio of r to j what it may, by taking any multiple} whatfocver of thefe ratio* and the lame mutllplci of r an! q. l"o- the fake of pcrfpi- cuity let thcfc mignitudci, and their multiplci, ftand in tlic following manner: are then refpcftively lefs than , or than nr nr tir â n T . -⢠- ⢠?⢠&C. / . !lf. 'HI. ZlZl, &c. > 7 7 27 m m mâ I â I I 1 Sec. fir nr â c id. Id. The magnitudes. ;d. B + B-B + r-7 A-B* *7 + &c. : B :*h. B + A-B: B Their multiplei. Oftheitt nr Of the 2d mq and the ratio B +â -A âB + â âuâ -â¦- Sec. ; B is then, of courfe, a lefs ratio of greater â if jd. B+ â-A-B + -⢠7 7 nr â i A âB'" â '-⢠- li' +&c.:B 27 B inequality than the ratio B + â 1 âjr- + &c. : B is. -B+ - i m â1 â i 4th. B + -- A-B + - I I i B Now it is evident, that if nr be equal to mj, by fuhftitut- ?"7f' >rg no for nr, the ratio B+ â ⢠A âB+ â ⢠7 7 27 B + S:c. : B t5 equal to, or becomes the ratio B + A-b + - I It is equally eridrnt, that if nr be greater than my, the an- lecedcnt B+ââ¢A-B+â â L â ^ " B + &c. VI greater than B + O}' + & >^-»^ B'"-' m â â m - ⢠A-B + - ⢠1 1 mâ 1 1 r-^q fince . .. 27 A-Bl' nr tir â q &c. B' 19 ^1 A ~B~ Here then are four magnitudes, and atiy equimultiples be- ing taken of the ill and jd, and alfo a ly iquimultiplcs be- in^ taken of the id and 4th, it is proved that, if the multiple of the III be equal to the multiple of the 2d, the multiple of the 3d is alfo equal to the multiple of the 4th; if greater, greater; and if 1 fs, Icfs. Wherefore (j. Dcf. E. J.) the magnitudes thtmfcUes are proportional
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Keywords: ., bookcentury1800, bookdecade1810, booksubjectencyclo, bookyear1819
