__ cof. 9— aco/".( 



CAtCVtl SinVVM, ft03 



; * C O R O L L. 3. 



52. Sitwni, ct «—2, erit 

 .cof.Cp-l-^i-cor. 3 (p4-«'cor. 5 (p-|-a»cof. vCp+etc .-' 



'fui.(I)+^n.34>-i-^'fin.5Cp-h«'fin.7Cl)-hetc.-^i^g^5 

 'Qiiodfi efgo flt az±i, erit 

 cof. (P -4^ tof 3 (11) ^- cof 5 (p -h cof 7 (p -i- etc. = o 



.,fin.(p+fin.3(p+fin.s4^ + fin.7^ + etc.r7^J:j^=:^ 

 Sin autem fit «zr— i, erit 



cof (p-cof 3(pH-cof 54^-cof 7 (p -4- etc, =r ,-^^ r ^ 

 fin.(p-fm.3(p-i-fin-5(p-fin.7(p-i-etc, — o. " 



S C H O L I O N. 



53. Ope huius theorematis ergo , cuius vfus la« 

 tifllme patet , innumerabiks exhiberi poflTunt feries (e- 

 cundum, vel finus, vel cofinus, multiplorum cuiuspiam 

 anguli progredientes , quarum fumma conflat, Cafum 

 hic quidem tantum euolui , quo coefficientes A, B, C, D 

 etc. in geometrica progreflTione progrediuntur ,---veruin 

 pari modo calculus ad alias feries accommodatur. Prae- 

 terea autem hic notafle fufficiat, ex feriebus iam inuen- 

 tis, innumerabiles alias, tam per difFerentiationem, quam 

 integrationem , elici pofle. Veluti cum fit 



cof (p - cof 2 (p H- cof 3 (p -' cof 4 (p -^ cof 5 (p- etc. =i i 

 erit differentiando : 



fin.Cp- 2fin.j(p-i-3fin.3(p-4fin.4(p+5fiu.5(P-etc.-o 

 denuoque differentiando 



