6i INDEX FIGURAE PRO PRIET ATUM. 



Co.oll. F"E" X E"D" X D"F" = 2/-V : R. 



Tlieor. XXXV. Fig. 8. / : ^" = 2Ä : r. 

 Theor. XXXVl. Fig. lo. OP» = R^ — 2Rr; 



OQ2 = R'+ 2Rec , 0R2 = 7?» + 27?/3 , OS« = Ä* + 2Äy. 



Coroll. I. Ä = r±V/(OP^ + r^) 



-_«±V/(OQ=+«j=)=-/3±V'(OR=+/3*)=-7±V/(OSH5''). 

 Coroll. 2. ■ ^r = {R' - OP^) : R ; 



2x = (OQ^— 7?2):Ä, 2/3=COR»— Ä=):;i, 27 = {OS'—R^):R.. 

 Coroll. 3. Ä:Ä-)-OP = Ä- OP:2r, Ä:OQ+Ä=rOQ— Ä:2«,etc. 



Coroll. 4. OP- + OQ- + 0R= + 0S= = 12Ä». 



Tlieor. XXXVII. Fig. 5. {a + l>){a + c)(l> + c) :abc = {l + m ■\- n — r) : r. 

 Coroll. (n+6)(a + c)(6 4-c) = 4Ä/(/4-'" +« — r) : r. 



Theor.XXXVIII. Fig.xx. AD"'= i^-,, BD'"=^,, BE'"= ^-^^. CE"'=^, 



CP" = -il^, AF'" - ^^" 



a + c a -J- t 



Coroll. AD"'xBE'"xCF"'=BD"'xGE"'xAF"'=4M/-(Z4--«+/2— r). 



Theor. XXXIX. CD = , r^ » "^ — ; — ; — s"^? AL. = -7—; — r- • 



{a + b)ry {a + c)rß {b + c)n)i 



Coroll. CD'" X CF'" x AE'" = 8/- : (Z + m + « — r). 



Problema II. Fig. 11. F"'D"'= 



et HD'" = , . '^'! . ,, „ - V/ [ lR'+2Rr)ßj'+2aIR]ßr ] t ( 



Tbeor. XL. Fig. 10. AP : AE"' = /(i + c) : 2I. 



Coroll. 1. AP = , BP = - — ■—■ , LP = . 



« p y 



Coroll. 2. AP X BP X CP = 4Ä/-^ 



Theor. XLI. Fig. 11. All : HP = AE -. r. 



Coroll. I. AH = "iVh^-, BI = P^t . CK = ^i^':^. 



Coroll. 2. PH = Ü^i^^, PI = rVa^Li , PK = ^ff^. 



Theor, XLII. Fig. 11. Heda AE"' in punctis H et P harmonice düw'sa est. 



Coroll. 1. PE'" = iVi-^Zf , PF'" = ^1}^'4 , PD'" = P^-4?- 



CorolJ. 



