OpuscutA 271 



Ex aeqnallonibus (i), (16) simul multiplicatis 

 babebimus a:t = t'^ 



ex muhiplicalione aequatlonum (2J , (6) xy=x"^ 

 ex niuliiplicalione aequationum (5), (10) y z-:=y'^ 

 ey mnhiplicatione aequalionum rii),(i6) ut^u'i- 

 ex muhiplicalione aeqiiaiionuin (9), ('3) uz-=.z'^ 

 Productum aulem omnium harum aequalionum 



6St 



^2^-2 z2„2f2 = ^'2^2 s'2„/2^/2 



ex quo elicitur 



xy zut^= x' y' z u' t' 

 Ergo 



THEOREM A XXXIII. 



79. Ductis e quovis puncto peripherlae circull rectis lineis 

 perpendicularibiis ad latera cujuscumqne peutagoni circumscri- 

 pli, necnon ad latera pentagoni inscripii relalivi productum 

 algebricum perpendicularium ad latera pentagoni inscripii ae- 

 quat productum algebricum perpendicularium ad latera penta- 

 goni circumscripli. 



80. Ex multiplicatione aequationnm (2), (7) §. 76. 

 habemus xz=x"^ 

 ex muhiplicalione aequationum (1), (11) nx=zz"'^ 

 €X multiplicatione aequationum (8), (12) zt-=u"^ 

 ex multiplicatione aequationum (3), 04) '/=^"* 

 €X muhiplicalione aequalionum (1), (12) ju=y"'^ 

 Productum aulem omnium harum aequalionum, 

 scilicet 



reducitur extractlone radicis secundae ad 



xjzut=x"y'' z'>u" t'' 

 Ergo 



THEOREMA XXXIV. 



81. Duclis e quovis punclo peripheriae cJrcnli perpendicu- 

 laribus ad lalera cujusque pentagoni circumscripli , necnon ad 

 diagonales pentagoni inscripti relalivi, algebricum productum 



