 | Pierce Morton - Geometry - 1830 - 584 pages
...understand the ancle FGXandnotFGx. 34. In the equation у = « x + b, the quantities a and 6 may be either both positive, or both negative, or one positive and the other negative; lei us then examine the course of the line to which the equation belongs in each case. Now it is clear... | |
 | Mathematics - 1835 - 684 pages
...understand the angle FGX and not FG x. 34. In the equation y = ax + b, the quantities « and b may be either both positive, or both negative, or one positive and the other negative ; let us then examine the course of the line to which the equation belongs in each case. Now it is... | |
 | Joseph Ray - Algebra - 1848 - 252 pages
...complete equation of the second degree may be reduced, is x2-}-2px=q ; in which "2p and q may be either both positive or both negative, or one positive and the other negative. Completing the square, we have x>+2px+pi=q+p> Now, the first member is equal to (a;+p)', and if, for... | |
 | Joseph Ray - Algebra - 1848 - 250 pages
...complete equation of the second degree may be reduced, is z2+2pz=g ; in which 2p and q may be either both positive or both negative, or one positive and the other negative. Completing the square, we have Now, the first member is equal to (z+p)2, and if, for the sake of simplicity,... | |
 | Joseph Ray - Algebra - 1852 - 408 pages
...degree, containing one unknown quantity, may be reduced (Art. 231), is in which 2p and q may be either both positive or both negative, or one positive and the other negative. Completing the square, we have Now, x'*-\-2px-\-p''=(x-{-py. For the sake of simplicity, put jj-p5=m2,... | |
 | Edward Henry Courtenay - Calculus - 1855 - 526 pages
...dxdy 1 1 ^^(i,^ ^ dy* 1.2 ( ^ • • • • Wi in which series we must be at liberty to make h and A both positive, or both negative, or one positive and...equal to zero, the other remaining finite. Now when Ic = 0 the series (1) reduces to *«.(±A) ,£«. (± *)',*«. (± A? ^ ~T~ f <b* ~T2~ + ^"3 T^3"H... | |
 | Edward Henry Courtenay - Calculus - 1857 - 522 pages
...necessary to Lave du (±A) du (rfcfr) d?u (±A)» <PK (±A) (±*) d* f~ """dy' 1 rfF ' . 1 . 2 ~ " in which series we must be at liberty to make A and...one positive and the other negative : or, finally, cithor may be taken equal to zero, the other remaining finite. Now when k = 0 the series (1) reduces... | |
 | Joseph Ray - Algebra - 1857 - 408 pages
...degree, containing one unknown quantity, may be reduced (Art. 226), is in which 2p and q may be either both positive or both negative, or one positive and the other negative. Completing the square, we have Now, x*+2px-\-p*=(x+py. For the sake of simplicity, put =Tn2, that is,... | |
 | Edward Henry Courtenay - Calculus - 1860 - 516 pages
...十切ガ切ノ士め + &c ・く互 nWhichseriesTVemustbea 七 Ⅱber 七 Ⅹtoma ] ( e んれ nd ゐ bothpositive ， or both negative, or one positive and the other negative : or, finally, Now when k = 0 the series (1) reduces to ぴ一劣ぱ切 (2); in which h may be taken so small that... | |
 | Joseph Ray - Algebra - 1866 - 250 pages
...be proved directly, as follows : Take the general form, x2-\-2px=q, in which 2p and q may be cither both positive or both negative, or one positive and the other negative. Completing the square, We have x!+2px+p2=q-\-p2. Assume q-\-p2^=mt . That is, Then, Transposing, (x+p)2—m?=Q.... | |
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The general form to which every complete equation of the second degree may be reduced, is z2+2pz=g ; in which 2p and q may be either both positive or both negative, or one positive and the other negative. Completing the square, we have Now, the first... 
