Tractatus mathematicus de figurarum curvilinearum quadraturis et locis geometricis / Autore Johanne Craig.

  • John Craig
Date:
1693
Catalogue details

Licence: Public Domain Mark

Credit: Tractatus mathematicus de figurarum curvilinearum quadraturis et locis geometricis / Autore Johanne Craig. Source: Wellcome Collection.

    47/96 page 31
    § 8: Sit tjzza4, unde u^sz^paz^Wqz^a eft aquatio definiens Curvas DK.M; ex qua cum aflumpta z~xm invenietur per Prob. 2, r ________ * l-\-mpax^mlxV'cjxm aquatio definiens omnes fimi- les Gurvas OFN, in quibus DHKr=BCFO per Lem. 2. Sed r ’DW£L~hz,'-\-caz?-\^laz‘zi-\-etilz?~yfa‘'z,-\-ga'y. V qz-\-a: Ergo ; Theor, VIiL U- e — — r2x on *. WEO—bxm-Y-caxim-\-ila‘x^A-e<i,x^-\-fa‘x”'-\-g!i'^ Vqxm-fa : ' -«-» . • * In auo b= ----- • Wq+Pq-A-n , ^ sr4,i’*4Hh**Sr ’ 5r+t’<4r4'!X?r+I><rs nm-ywq—n.rs _: _ 5r-J-1 x4r~j-1 * 3r~}~I X2r-~]-1 * e — r, x jo»^+6w—14« __ 5 I *4f>j-I x 3 I * 1 xr -j-1 x^4 5 > _ __ r4K lorp<r*-6pq-~14 rj_ Jni -' y V‘ V ii — *’ ' Sr+iMH'I*?H_IXW‘!xr+i*?s ’ *J a IU «« j , ; » Ex hispatet, non modo aequationum Curvas OFN, fed etiam Theorematum, earum Areas BCFO determinantium progreflus in infinitum; Sc facile eft innumeras alias Theorematum feries for¬ mare. Pro hujufmodi Figuris, quarum Valor Analyticus ordina- tim applicatarum ita reduci potiunt, ut duobus tantum exiftentibus terminis fub Vinculo, duo etiam in illos multiplicati, extra vincu¬ lum exiftant. Ex Methodo mea generali Exemplis 8 & 10 illu- ftrata, inveni Aream DHK pofle Quadrari quando in aquatione u^szri~\~pa: z?~c\V qz-\-~a Naturam Curvas DKM definiente, ex¬ ponentes n3 c funt numeri integri Sc pofitivi, pofito n cr- c. Prae¬ cedens Theorematum feries, quatuor ultimis Sectionibus inventa, eft Cafiis omnium primus, in quo nempe c—i ; Cafum fecundum (in quo c~i) adjiciam; cuique vifum fuerit reliquos eodem Itiodo proiequatur. < - ■ | x \. 5 • _J_ t -■ ■ ‘ 'r ’■ ,*T r » . , * | . r ; . Exiftenteitaque c=2, eritu=Jzn-l-paazn-2Wqz-t~ai undeper Methodum noftram generalem invenietur
    digitised image 1
    digitised image 2
    digitised image 3