IN THE STUDY OF ANALYSIS. 31 



sides, and the external segment between the obtuse angle and the perpen- 

 dicular let fall from the opposite angle. 



" In any triangle the square of the side (6) subtending an acute angle, 

 is less than the sum of the squares of the sides (a and c) containing that 

 angle, by twice the rectangle under either of them, and the segment 

 between the acute angle and the perpendicular let fall from the opposite 

 angle." 



These enunciations, to say nothing of the proofs, are something 

 for a beginner to remember ; nor would it be easy to express 

 them in fewer words. Any teacher who will put a youth, even 

 of moderate capacity, in possession of the following mnemonic, 

 for both the proof and the properties, will be able to judge for 

 himself of its value: — 



Read ba, as well as ac, as one syllable, marking well the 

 accent and the rhythm. Pronounce Sq.'b squib : SUD and 

 DUQ are syllables, as are perc and Bang. 



(3.) Draw perc : SUDba is SUDsegs of 'c, 



and Sq.'b is DUQac mol seg. op. two 'c, (A.) 



as 'tiise or 'cute is Bang op. 'b 

 or Sq.'b is DUQac le coBang two ac. (B.) 



(a.) Here perc signifies the perpendicular Cp on c from C : 

 draw this ; then if * be the segment Bp of c, not adjacent to 6, 

 62 _ a^ — (c 4: 5)2 — **, or 



62 =r o2 ^ c^ + *. 2c ; (A), 



the upper or lower sign being taken as B is obttise or acute, 

 (b.) SUD is >S'Mm X -Difference of the two quantities in- 

 dicated. 

 SUDba is {b -f- a) (6 — a) or b^ — a^ i SUDab would 



be a2 — 62. 

 SUDsegs of c is Sum X I^iff* o£ the segments Ap and 

 Bp, or (c + sf — «2. 

 (c.) DUQ means duo ^uadrata of the indicated pair of 

 quantities ; 

 DUQac is the two squares a^ -|" ^^' 

 Sqb is squared 6: pronounce squib ; squab might mislead. 



{d.) mol is a contraction of wore or fess, + 



