i6o DE LVNVLIS OVADRJBILIBVS. 



atque z : t~Vm : VI;. Hiiiiis autcm curuae , t ^ ~bVaa-uu 

 aequatio , vti quoquc reliqunrum , focile mutatur in aliam 

 ati coordinntas orthogoniiis ; vocenrur enim alfumto axe 

 AB, BPzz:a', PM — j, eritque ob triangula MPA et 

 BCAfimilia, AMC/j-.PMfj^^^ABC^^iCBfM), hinc 

 t^f\ porro AM(7^AP(^-£)=rAB(«):AC(y^ 

 — uu)\ vnde / —aa—ax. V aa—uu.^ qui valores aequati 



exhibent V ( «=-2ru'-f- X' -^y^ )=:t,et v(.r-.2°^.t-x'-+- F) 

 zzUy quorum ope aequatio propofita abit in hanc: 



2 3 



2 



{a — .v ~\-y- )^ —ab. a — x. Sed notandum eft, ta- 

 lem Lunulam fore Apertam A^erfiis B. Nam ab initio, 

 vbi u — Q, fit t^ ~ba ., et z^ zzma\ in fine vero , vbi 

 u — aj fit t — Oy zz:zOj vnde Lunula tcrminubitur in 

 pundo A. 



Fig. a. 5. 6. Interfecent fe duo circuli qnicunque , quo- 



modocunquc in B et A ; ducatur chorda communis 

 AB, cum arbitraria AI- et dcmilfi in eam perpcn- 

 diculari B C , pcr centra transeant reflae A E , AH , de- 

 miHis perpendicuhs in easdem BF, BG. Erit pofitis vt 

 ante ABrr^, ADzr^, Alrr^, BC=:«, BF :FErzi -.m^ 

 BG:GHr: I ;w,portio indcfinita curuihnea IBD— jLl=g^)-^_«. 



fed ob triangula funiha rectangula BDC et BEF, 

 nec non BCI ct BGH, lit C B , ^^ ) ■.CDj-Vaa-uu) 

 — BF:FE— i:;«; hinc tzzmu-\-V aa — uu. Deinde 

 C B ( tt ) : C I ( V aa-uu -::)=i;BG:GH-i:«, vnde 

 Z — Vaa — uu-nu-., fubditutis hisce valoribus in for- 

 mula diffcrcntiaU aUegata, nrodit portionis curuihneac 



BID 



