ET SOLFTIO PROBLEMJTIS. 149 



Jf;, vt. partium A/ et fg differentia fit geometrice 

 aflignabilis. 



Solutio. 



Pofitis femiaxibus CA — ^, CB — ^, et breuita. 



t3S gratm n— — ^^ — , m verticis A tangente AD fu- 

 mantur ablcifliie , ac ponatur abfcifla toti arcui A^ dato 

 refpondens A G ^g , quacfita autem , quae punclo / 

 refpondeat, fit Afzizf. Cum igitur diflferentia arcuum 

 A/ et fg debeat effe geometrice aflignabUis , quaeftio 

 continetur in Probl. I. fumendo ibi p~f et ponendo 

 ^:^:^, ynde obtinebimus has formulas : 



„, zbbjV{bb^ f f)ibb^ ^nff) 



■\/(h U «. ^^ — bHbb~ff) -bff{bb~nff) __ b(b*-2bbff-^.nf*) 



Y\pj-gg) — b*-nf* WZnf* 



-VlU h f,frn-\ — hHbb-n ff)—nbff {bb-ff) __ b{b*-~2 n bbff-^.nf*V 



Ex quibus combinatione oritur : 



y(H- ngg) - n V{bb-gg) -^—^^*$^ hincque: 



nf* -v^— n gg) — n v(&5— g g) — ( i_--Ti)_5_ 



i>*' — ^{bb—ns^) — n^/{bb — ss)~h{>—n)b 



quae formula reducitur ad 



nnj* {^{bb—n gg) — ny/{bb~g g) — {i-—n)b)'- 



b* 2bb—{'-t-n)sg — 2V{ob — sg){bb~ngsl 



vnde radice quadrata extrada fit : 



njf ^/(bb~^g)—^^/Jfib—gg)-^^ 



bb — y(66— «gg)— V-(66— gg) , • gg 



cx qna porro elicimus : 



^hrJ^ (i— n)(£— V(66— gg) (b—^lbh—gg)){y/{bh—ngg{-i-^/{bb-g g)) ' 



Ib ^[bb-ngg)-^/{hb-gg) gg 



"^JD {i— n){b—y/{b b—ngg)) { b~V{bb-ngg)){^/{bb-ngg )-i-^{bb-gg)\ 



bb — V{6&— ngg)— V[66-gg) — gg 



T 3, Pundum 



