Philosophiae naturalis principia mathematica . majorem Bafin AB pertinente, 6c habebis fiBD^ Superfi-ciem differentiae Bafium infiftentem. Sic in hoc Exemplo. [FideFig. T*r<ecedentem.) Si AB = X, & A/3 = I ; Erit /3BD^ = 4: Etenim Superficies ad ABpertinens(—DF<4)eriti—j fivei; &fuperficies adA/3 pertinens (viz. A(p^ — ^ct) erit 1— i, five—I: & earum diflferentia (viz. ABF—DF* —A(p/3 -t- ^(p* = /3BD^)erit s -hf five J. Eodemmodo, fi A/3=i, AB^a-; Erit/3BD^=f-»-iAr^—;^-^ Sic fixA;—3Ar—Iat-*-j-x? ==), &A/3=i;Erit /3BD^=ix*—i^-l- lr-3 ^^ Denique notari poterit quod fi quantit
Philosophiae naturalis principia mathematica . majorem Bafin AB pertinente, 6c habebis fiBD^ Superfi-ciem differentiae Bafium infiftentem. Sic in hoc Exemplo. [FideFig. T*r<ecedentem.) Si AB = X, & A/3 = I ; Erit /3BD^ = 4: Etenim Superficies ad ABpertinens(—DF<4)eriti—j fivei; &fuperficies adA/3 pertinens (viz. A(p^ — ^ct) erit 1— i, five—I: & earum diflferentia (viz. ABF—DF* —A(p/3 -t- ^(p* = /3BD^)erit s -hf five J. Eodemmodo, fi A/3=i, AB^a-; Erit/3BD^=f-»-iAr^—;^-^ Sic fixA;—3Ar—Iat-*-j-x? ==), &A/3=i;Erit /3BD^=ix*—i^-l- lr-3 ^^ Denique notari poterit quod fi quantitas x- in valore ipfius ^ re-periatur, ifteTerminus (cumHyperbolicam ?fuperficiem generat 3 feorfim a reliquis con-fiderandus eft. Ut fi A + A- -»- a;- = y ; Sit a;- = BF,& a; + X- = FD, ac A/3 = I; Et erit ^(pFD= i -<- iA; — iA;^, utpote quae ex Terminis«•* + x~^ generatur. A a Quare, fi reliqua Superficies iS(pFB, quse Hyperbolica eft, ex Cal-eulo aliquo fit data, dabitur tota /3BD< PER ^QUATIONES INFINITAS. fAltarum Ommum ^adratura^R E G U L A III. Sm valor ipfius y, vel aUqms ejus Termtnusfttpracedentthusmagts compofttus, in Termmos Simplictores reducendus ejf;operando in Ltterts ad eundem Modum quo Arithmeticiin Numerts Dectmaltbus divtdunt ^ Radtces extrabuntyvel affeEias ^quationes folvunt j ©* ex ijlis Terminisquafitam Curva Superficiem . per pracedentes Regulasdeinceps elictes. Exempla Dividendo. Sit^^ —y; Curva nempe exiftente ut -^quatio ifta a Denominatore fuo liberetur, Divifionemfic inftituo. ^ + ^)rf^ + o(-—jr+TT —77 &C. o _^ + o ?—T — *. o o+^ + aaXi 4«» o — + 0 — a/ixi17 4ltX*
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