237' 



AOB, BOC fiant aequales. Super lateribus igitur ABTab'. III. 

 et A-C trianguli dati conftruantur triangula aequilatera Fig- 3- 

 ADB AEC, iisque circumfcribantur circuli., et punftnm 

 interfe&ionis O horum circulorum erit pun&um qdaefitum. 

 Nam anguli 



AOC= i8o 9 — E~ i2o°, 



AOB= i8o° — D=i2o° 5 , 



confequenter anguli AOC,- AOB r BOC inter fe erunt 1, 

 aequales. . 



Scholion: 

 J." 25. Ifta puncti O pofitio memorabilis commodam 

 nobis aperit viam ad determinandas ipfas re&as OA,-OB, 

 OC, per fola latera data trianguli; Sit enim B C ~ fl , 

 AC = b 5 AB^c; tum vero OAzzx, OB = j, OC ~ % 9 

 et. quoniam anguliab his reclis in O formati funt quisque 

 120 graduum 5 ideoque eorum cofinus — — |, habebimus 



xx+jj + xji: c c^ 



x x + z z '.-+- x % —bh? 



y y -+- % % -f- y % — a a, 



Ponatur brevitatis gratia x -hy ■+■ %~ s, , atque" manifeftum 

 eft fore : : . 



a a — b b — s (y • — x) , 



bb — cc ~s (z'—y) 9 



c c — a a — s (x — z). 



At vero ex harum aequationum prima et tertia ' adipifcimut 



