(1+8); 



Hinc ergo colligitur FM — FN :NM = /(C O^ — CH^) : CO 

 __ ^ C F' — D F^ : C O , ob C O^ -H D F= z= C F^ -h C H' 

 = CA^. 



§. 8. Qiiia vt ex Elementis Gcometriae conftat, eft 

 MN' — FM^-f-FN^ — 2FM .FN cof.MFN et MN":MF' 

 _:|_PN^— 2FM. FN =r CO^: CO^— CH%- fit MN^: MN^ 

 _(FM — FN)^ = MN':FM. FN (i— cof.MFN) = CO^: HC%- 

 hincque ob i — cof. M F N — 2 fin. § M F N% erit 



M N': 4F M . F N . fin. ' M F N= = C O^- H C^ vel 



M G^ : F M . F N . fin. ^ M F N' — C O' : H C\ 

 AtQui fupra demonftr:iuimus efle duplam aream trianguli 

 ~\ N F M = 2 G M . E F fin. N E F, 



et quum dupla haec area quoque fit 



F M . F N fin. N F M z;: 2F M . F N/in. 'Mf M cof.-: N F M , 

 colligitur omnino 

 FM .FN . fin.l NFM . cof.lNFM: GM.EF=fin.NEF:i-CH: CO. 



Hinc fi ifta analogia 



F M . F N . fm. 1 N F M^ : G M' =z: C H» : C 0% 

 p!&r hanc modo allatam diuidatur, prodit 



tang.'NFMr:r^^; . '^; 



hinc autem porro colligitur 



,,F M . F N cof. ■ M F N' 1= E F* et 

 F M . F N =r G M= . ^g -h E F% 



quapropter erit (FM -k FN)^ — (FM — FN)' -F 4FM . FN 

 ^ 4.G M^ . '^ P'^-""" -4- 4G M" . ^ -f- 4E F^ =: 4G M^-H 4EF» 

 — 4F»2% ideoque FM-^FNr=2Fw, quod fupra iam alia 

 quoque ratione euidum dedimus. Tum denique habetur 



F M 



