TRIANGVLORVM. 69 



S O 1 U t i O, 



Angulo B per redam B D bifedo , erit tri- 

 tngulum ADB ifofceles , et triungulum BCD 

 toti ACB fimilc , 



fuae fit AC:BC — AB:BD=BOCD, 



- , ac a a 



leu 0: a — C'. -^ — a : -f. 



Ergo BD=V et CDr^x; hinc AD~£>-V- 

 At ob BD=:AD habebimus ac^bb -aa y qua ef- 

 go aequatione cowtioetur relatio quaefita inter latera 

 trianguli,quae eft vel ( AC+BC)(AC-BC)-AB.BC 

 ^l AC— BC(AB^-BC). 



C o r o 1 L u 



9» Vltima •equato' fecilem hanc fuppeditat 

 demoJiftrationem formulae inuentae ; produdo enim 

 latere AB in C, vt fit BEznBC , erit ant,ulus E 

 femiflj* ipfius ABC,. ideoque ipfi A aequalis , vnde 

 triangiila ifofcclia ACE et CBE erunt llmilia ^ 

 hmc AE:ACi:CE:BC,feu AB+BC:AC- ACBC. 



C o r o 1 L 2. 



3. ViciflTim ergo», quoties ititer latera trian- 

 guli A B C haec relatio deprehenditur , \t fit 

 AC*=iBC.(AB-4-BC) feu bb — aa-^ac , toties 

 concludi oportet , angulum ABC efle duplum aa- 

 guli BAC 



I 3 Scholion. 



