ALOYSII CASINELLI 



OBSERVATTONES ANALITICAE 

 IN FORMULAM f,— . 



§. 1. 



Evolutio basis logarithmonim sistematis hjperbolici 

 in novas series. 



B= 



Tasini loi^arithmoriun, (\n\ hyperbolici nuncupanlur ,qtiani 

 comiiuio littera e designaljisnus, nolum est in seiiem 



evolvi posse . Scd et aliae alque inuumerae series, ilia cpio- 

 qiiecoiivergenliores, docUici possum ad hasim ipsam expriuieii- 

 dam, niethodo, qnain hie breviier exposiluriis sum. 



, io seriem evolula praebel banc ae- 



/og. X ' 



qnatioiiein , 



Ex hac aequalione, diflferenlialione, habenius 



d X d X d X d x log. X d X lo^.x d x log.xS 



liig-x X lug-x X l.x 2.3.x 2.3.1.x 



(/ xloe. X 



jL -§ — etc. 



^2. 3. 4. 5.x 



Ablato commiini faciore dx, et ducta aequalione in quanti- 

 talem x, babebimus 



X 1 loe-x /%'-x" log.x '"gx 



/og.x — /og.x^ ^ 2" ^ 2.3^ 2.3.1 ^2.3^4.5 



T. in. i3 



