PRO 



2. Of the quantities , r, w, s, any three being given, the other may be 

 .found by the equation 



a r n a 



S =-T= 



3. Of the quantities a, /, r, s t any three being given, the other may be 

 found by the equation 



Ir a 



TTCT- 



4. When n, or the number of terms is infinite, then of the quantities 

 a, /, s, any t\vo being given, the other may be found by the equation 



III. Harmonical Progression. 



1. Let a, b t c be in Harmonical Progression; then a I c I", a 6 I 

 *. c. 



2. Let a, b, c, &c. be as before, then 



, y, , &c. are in arithmetical progression. 



3. Let a and b be the two first terms of an Harmonical Progression, to 

 ^continue the series. 



ab ab 



4. To find an harmonic mea n (x) between two quantities a and b. 



x= 2 ab 

 a+b 



5. If between two quantities a and b t an harmonic mean .r, and aa 

 .arithmetical mean y, be inserted, 



a : x ;: y : b. 



G. If between two quantities a and b an arithmetic mean x t a geome- 

 tric mean y> and an harmonical % } be inserted 

 x \ y \\ y \ z. 



7. If a fourth proportional be found to three quantities in Arithmetical 

 progression, the three last terms are in Harmonical progression. 



PROJECTILES in a vacuum. ( Whewell.) 



Formulae for finding the range, altitude, and time of flight, of bodies 

 projected along planes inclined to the horizon. 



J. Let r range, A = greatest altitude, t time of flight, v yelc* 

 213 



