VRGBLEMATIS CEOMETRICl 233 



parflUelogrammiim CEDF. Tiim producatnr EC in f , 

 vt fit C(? — CE, et ad CF normaliter iiingatnr CGn: 

 CF. lundlis E G et eG producatur EG in H , \t fit 

 G H =1 G ^ , et duda e H bifecetur in I \ atque in reda C I 

 capiatur KLrrKI. Deinde ex centro C circmi apertura 

 C I defcribatur arcus M N redlas F D et E D fecans in 

 M et N , atqiie ad has redlas ex punftis iftis perpendi- 

 culares conftituatitur MO et NO fe mutuo in O fecantcs , 

 per quod pundum O ex centro C vsque ad arcum M N 

 ducatur reda COA , erit haec fcmiaxis transuerfus , in 

 eoque pundum O alter ellipfeos focus. Denique ad C A 

 normaliter flatuatur C B — C L , eritque C B femiaxis 

 coniugatus. 



Demonftratio. 



Ponantur femidiametri coniugatie C E r=: ? et CFzn/ 

 flngulus vero ECF — • erit ex conftrudlione Ce:rze, 

 CG"/, et angulus GC^rrpo" — 0, ideoque cof GC^ 

 — fin. 0. Porro vocetur femiaxis transuerfus CA=«, 

 ct femiaxis coniugatus C B ~. ^ ; erit per fupra inuenta 

 aa-^bbz=:ee~\-ff Qt abef{m.&. Hinc fiet : 



aa~{-2ab+bb:zee-\ff-\-2ef{\n.$etaa-2ab+bb~ee-\-ff--zef{\n.9 

 crgo a-\-b~V{ee~\-ff-\-!ief(\n.Q)Qta-b=.V{ee-hff~2.efCin $) 

 At ex triangulo ECG ab CE— e , CGrrf ct cof GC^— 

 fin. $ reperitur EGzziV[ee-{-ff-\-!ief(in.^) , ex triangu- 

 lo vero ^CG, vbi cft C^— £-, CGzr/ et cof. GC^— fin. ^ , 

 £t Ge^zzViee-^-ff—zeJdn. 0). Hanc ob rem habebitur: 



a-\-b—EG et a—b~eG 

 ideoque 2ff=zEG-\-eG et ib—EG-eG. 



Tom. III. Nov. Comment. G g ' Cum 



