»4 



DIDERICI r, AX 



DODECAeDRI CAPACITAS. 



Liueae e ceiitro Dodecaedri spliacrae inscripti ad singulos angulos ductae formant 

 duodecim pyramides pentagonaks , vel quarum basis est pentagonum rcgulare, cujus 



radu quadratum, seu r- ~ - (lo). 



Perpendiculura e baseos centro ad latus ductum 





-Vs 



Rr 



4 



V5 



- K 4 *^ 5 — i/< ^ 



- 2 f^ 5-VS 



Vi 



Aiea pentagom igitur = — X -^ 5 ^^^5 

 _ 5R=^ / ^ 3 + V S 



- T^ 5 ~ Vs 



Quadratum diagonalis in pentagono (ii) = 5/-- — R- 



_ 5 X ^R-" _ R2 

 5 — 1/5 



= -(5-^-0 



^5 - VS^ 



_ pz V s (.V5 + O 

 ~ Vs (1/5- O 



V5 — i^ 



Er. 



^IB) Vid. supta p. 8. 



(11 ) Vid. Cl, »*» SvHtiim, L. VL Prop. il« Coroll. s. p. 857. 



