PROJP RIETATFM SOLIDORFM. i$9 



A Q, , AP , A P — A Qcof. « u . •_ * /-\» * rj* 



- JE«g2H- /n^T — /^i • Hmc entAOz=AP 



. r> r^* A P* -+- A a c — 2 A P . A Q.co/. a . , t\ r\* 



-+- PO =1 7^3 ~"i ldeoque DO ~ 



A D" fin. a* — \ P= — A Q_* -+- 2 * P . A. Q,co/. a «r 



± — ! __ ^ 2 — . Verum area tnan- 



guli A B C eft zz \ ab. Iln. a , ex quo erit (biiditas py- 

 ramiciis — ^^(ADYinV-AP^AQ^* AP.AQ.cof.a)r 

 \V[aabbdd:m a-\bb (aa + dd-eef-\aa(bb+dd-fff 

 -T-lab(aa~T-dd-ee){bb-T-dd ~ff) cof. a ]. Deinde 



ex triangulo ABC eft cof. azz ac ~*~ 2a b ~~ - c - , ideoque 



fin.a*=r 1 - \ a \b b (aa-\-bb-ccf , quibus valoribus fub- 

 flitutis prodibit foliditas pyramidis : 



, ^ iaabbdd—dd(aa-i-bb— cc)* -bb(aa-i-dd-ee) 1 -aa (bb-+- dd-ff) 2 ) 

 ii M -4-[aa-+-bb — cc ) (aa-+-dd — ee) (£■&-+- dd— //)• ' 



quae terminis euolutis in fequentem abit formam : 



/aaccdd-+-aabbee-+-aabbff-4-aaddff-+-bbccdd-+-bbddee\ 



j\rl aaccff-i-aaeejf-i-bbccee-+-bbeeff-i- ccddee -^-ccddff J 



\ — aa&icc — aaddee — bbddff — cceeff J 



— a*ff—aaf*--b*ee — bbe*~c*dd—ccd* ' 



quae adhuc commodius ita exhiberi pofTe videtur : 



r_f- a aff (bb-i-cc-4-dd-i-ee) — a aff( aa-+-ff) — a ~a b b c cl 

 i -1/ j-+- b bee( a a-+-cc -4- <2d -+-//) — bb ee ( bb-+-ee) — a adde e 

 15 l-+-ccdd (aa -*-&&•+- t e-i-ff) — c c dd( cc -+-dd) — bbddff 

 C — c c * ?// > 



Sicque ex datis fex lateribus a> b> c, d, e,f pyrarnidis 

 triangularis eius foliditas definitur. Q. E. I. 

 SCHOLION I. 



a 1 . Q>io ratio , qua in hac expredione latera a , 

 £, c> d t e>J inter fe combinantur , clarius perfpiciatur , 

 notandum eft , ex iis quatuor formari triangula , fcilicet 



A A B C conftat lateribus a , b , c 



AABD - - - - * , d, e 



A A C D . - - - b, d 7 f 



aBCD 



