CO\i:aENT.\TIO AD QUAESTIONEM MATHEMATICAM. 47 



ex eodem illo anguli vertice in latus demittitur subjectum, ad radium circuli in- 

 scripti. Id est : AH : HP = AE : r. 



Demonstratio. Est, ut novimus ex primis elementis, in triang. AD"'F'", ' 

 c[uia dimiiliat AP angulum A: 



AH= = AF'" X AD"' — HF'" x HD"' 



= (^a + t)Z + c) ~ «P'" X HD'" CTheor. XXXVIH.) 

 at est HF"' = "''^/^ . x F'"D"' (Probl. II. Solut. Part II.) 

 et HD'" = "'''/ x F"'D"' 



2« -f- 6 + c 



ergo : HF"' x H D'" = ("+^)(^ + g) ^ f"'D'"» 



(2(1 -{- 6 + c)» 



~" (2a + 6 + cY {a + b){a + c) 



(Probl. II. Solut. Part. I. (A) ) 

 b^C bc{a+ b + c){b -\- c — a) 



■ AU, bc{a+b + c){b + c — a) ^Pxbc 



erU: AH' = j rr := , — 



(2a+6 + c)'^ (2a 4- 6 + c) V«- 



, , jj sli/bcra ll^/bcrx 



adeoque : AH := ;: ^ r — = ,—-^ 



^ (2a + 6 H- c)?-« (2/ + ar^x 



= 7-2-r X i^^^ (Theor. I. Coroll. 3.) 



Quod attinet ad alteram partem rectae AP, habebimus : 



HP = AP - AH = ^^^^ - 2^^ (Theor. XL. Coroll. ,.) 



n-\-r — n X/bcra r \/bcra 



n + r x (/z-j-/") « 



erU igitur : AH : HP = — -— x = • X = n : r 



Simili modo : BI t IP = m : r , et CK : KP = Z : r. 



o ATT n\/bcra t>t m\/acrß' _^ l\/abry 

 COROILARIUM 1. AH = ,— r-, BI = ,—^ r^, CK = -i^ -1. 



/-. X.TT r\/bcra „, rl/acrß „,, rv/abry 



GOROLLARIUM 2. PH = r^ r- , PI = r—T^n ' ^K = -^ /. 



THE- 



