/mpdtidictila^ in tiie triangle tviiose base is the product i^ awl 

 hypothenuse the product auk The equation of tbe ienMtecate i8> 

 fifA ][»ie ifijriUable,) 



DUQjib; itt Lemni is pepr^jd {ax bf), 

 and pep (co^ a ^bsi^) is r; i. e.^ 

 y" + a:* =z (a V — ^V)*, or, 

 i^coa.'^jft' '— 6*sin.^)* r^ r. 

 for Dl5^ vide 3^* 



(rf.) If ax — A* and by r= /», (ax — iy)* is (;&« — /'')* ; or 

 the perpendicular to base <!6y5* and hypothenuse (oa:)*, both 

 ^ven mean ■proportionals : cafl this per mea/i (aa; ^y), Grperean 

 {ax by). 

 (e.) Bi Cdng is p&rean (^ *«75), 



{/*.) or Cbsha Ckng of Hkrm. legs, 



(^.) and t'i. 4ih is the vl. «e;^ 



i. e., if d be the BiOang, of iiseetor of "C, the vertical angle of a 

 triangle, s taxA. »i being the two segments of c made^.by it, 



rfzrCosiCX-^ a) 



if.') Oosha in if) is Conine of &«lf : of is X) when betire^ 

 two quantities. 



Harm, is >iarmonic mean, of the legs a and ^'4 

 Harm oA is two 06 fey Sab. 

 (ff.) t;e in ^r is a contraction iox qusie of (di*Me)^ the-qootto 

 of a and b is the quote of the segments of the base c. 



For an example of the use Qipoth^ take one from Alg. Geom. 

 ^(^,) lorJs the con. by poth f ics-; 



with which may be given the corresponding 

 (i.) plor^s the -con. by dig fics. 



In the line ax •■\- by -z c, referred to right «xes, if we Call 

 lor the^ortest distance p of the /ine from the orighi, 



