$0 VARIAE DEMONSTRAT. GECM.~TR. 



Demonftratio. 



Cum fit AB— AS-j-ES, erit \trumqiie ducendo in RS, 

 AB.RS — AS.RSh-BS.RS 

 addatur A R . B S A R .BS vtrinque , et erit 



AB.RS-f-AR.BS=:AS7RSH-"BS.KS-|-AR.BS 

 AteftBS.RSH-AR.BS=BS(RS-|-AR)=:BS.AS, 

 Tnde fit AB.RS-}-AR.BSzzAS.RS-hBS.AS 

 VerumeftAS.RS-f-BS.AS=AS(RS-|-BS)— AS.BR 

 Confequenter habebitur : AB . RS -H A R . BS zz: AS . BR 



Q. E. D. 



Scholion. 



Fig. 2. §. 5. Hocce lemma etiam fequenti modo per Ib- 



lam figuram geometricam demonftrari poteft. Super da- 

 ta reda AB in pundis R et S vtcunque diuifa confti- 

 tuatur quadratum, ABab et latus Ba fimili modo fecetur 

 in pundlis r et j , vt fit Bjz^BS ; jtzzSR et ar— 

 AR : tum dudis redis Kh , Sg item sc^rd lateribus 

 quadrati parallelis , erunt partes S s , cg quadrata circa di- 

 ngonakm Bb fita , ideoque trk niAe—cnae. Addatur 

 vtrique redangulum cf^ fietque njAe-i-acf—cJae 

 -f-o^/feu c3Af—n2ae-\-acf, fed C3ae—oaf-{- 

 □ <?r , vnde c3Af—cjaf-{-c3er-\-C2cf—Daf-{~ 

 nner. At eft aA/=zAS . Brizi AS . BR ; et o 

 afz=zar.BS~AR .BS atque □rrir: AB.r.f m AB. 

 RS , quibus valoribus fubftitutis elicietur : AS . BR — 

 AR . BS -I- AB . RS feu AB . RS -4- AR . BS zzAS. 

 BR prorfus vti lemma habet. 



. Theorema 



