D ' H ("as being equal to a Part of it^ will be further than It 
from AF. IxxAB ( which I put = \ ) let JB ^ be fuch a 
Part thereof, as is BSotDH Now becaule (^s is well 
known j all the infcribed Parellelograms, in the exteriour 
Hyperbola, ASyAHy &c, are equal ; and therefore their 
fides reciprocal ; Therefore as ^ ^ = i — w ( fuppofing 
B ^ to be taken, from B toward Ay) to J B = i, f or as 
m — I to ml ) ibis BvS 
I.I . I 
-"^m D H, to d hy which ^ ^ + 
is therefore equal to i 
»^ ^ I of Di? rth at is (^as ^ 
will appear by dividing 
I, by;» I J to m'\' mm 
i ,1 _i 
+ '^ ^^-?f^^ , m'^ m. 
OrifB ^ be taken be- — 
yondB; then as J -| — I 
I 4- ^w, to^B=i,oras 
' m 
m m 
m-^- I to m J To is m DH ^ mm mmm 
todk which is therefore t 
i. &CC. 4- — — 
equalto«^-pi D//;that * ?^mm 
Isf as will appear by like dividing of i by -f ^ 0 = to 
. ^ X 1. JL ^^c. o?DH. 
m mm m 
1 2 . Let fuch . ordinate dh^or f equal to it in the Afy mp- 
totej^ F, be fb divided in L, N &c. ( by perpendiculars 
cutting the Hyperbola in /, &c. ) as that FL, L M 
JL JL JL 
M N hQdiS my mm^m^ S^c. That is, fo continually de- 
crcafing, as that each antecedent be to its confequenr, as 
J. 
1 to w , or as to i. See Fig. IV 
I ^ This is done by taking A F^ALyA &c» in fuch 
proportion. For, of contmual proportionals the diffe- 
rences are alfo continually propOi tional, and in the fame 
pro- 
