t$% DEMONSTRATIO 



partem altitudinis multiplicetur , of.endam, quem ad mo~ 

 dum, (i latera pyramidis fuerint data , ex iis foliditas dcfiniri 

 queat ; perinde ac area trianguli ex datis tribus lafceribus 

 determinari folet. 



PROPOSITIO V. PROBLEMA. 



20. Datis fex hteribus feu aciebus fyramidis tri- 

 ^nguhris , eius joliditatem inuenire. 



SOLVTIO. 

 ^S- *• Sit A B C D pyramidis triangnlaris , cnius bafis tri- 

 angdum A B C , et \ertex D ; ac pcnamur tius latcra : 

 AB=:^,ACzr^,BCrr^, AD=</ , BDrz:^ CDzr/. 

 lam in hedris ADB, et ADC ex D ad bafes oppofi- 

 tas demittantur perpendicula D P , et D Q , et in bali 

 A B C ex punctis P , et Q educantur ad latera A B , et 

 A C normales P O , et Q O fe mutuo fecantes in O , 

 erit re&a D O perpendicularis ex vertice D in bafin 

 A B C , vnde foliditas pyramidis erit r |DOx aream 

 ABC; at duda AO, erit DO~ V(AD , -AO , j == 

 V(AD*~ AP*— PO*). T am ex elementis Geometriae con- 

 flat, cflc, A P = tl±J±=zl£. et AQ- tytfflT^ 

 Hinc producta Q O in S , fi angulus B A C vocetur 

 ±z a , erit QS zzz A Qtang. a , et ASr c -^~ , hinc 

 PS~~^ -AP. AtcumfitQS:AQ;AS~PS:PO:OS, 

 fcrit P O — ^^ — — -^ - -^- feu P O — 



ACL-APcof. a . r\'c A S . P S P S 



~ JtnTa "> tum WO O S = -^" = J^ — 



]i£kr« ~$r*> ide0( F e QO=QS-0 S = A Q tang* 



-A(i 



