TRACTATUS DE REFRACT. ET TELESC. LIBER. I. APPENDICE II. 1652. 140 



Poft alternas multiplicationes per denominatorem utrumque omnia dividenda 



per^;; quo faélo ege quantitates quibus adhuc y aderit 

 omnes delendae funt, féd quae deleri dcbcre conftat 

 non opus eft fcribere ut hic erunt omnia prseterquam 

 quibus fimplex^^ inerit ^). 



Ergo ^p^x'^y — ^pprrx'^y + Sppr^x^y -h 



+ /\.p^rrx^y oo ôp^x^y — 6pprrx^y -|- 

 + I ippr^x^y H- ôp^r^'x^y — 6ppr^xxy 



ppx^ — rrx'^ — ^r^xx — pprrxx + 

 + 3r'^ 00 o 



dividitur ^^xxx — rr et ^ippxx — rrxx — ^f"^ oo 

 00 non tamen xx oo rr propofito convenit fed 



XX 00 



3^4 



pp — rr 



Ergo/>/>co^ — ; /> oo —]/ 3 rr + xx 



JvJy 



X 



n «•4 I ffXX 



Verùm ut q.AB (rr') adpp hoc eft — — -^^ 



ita eft q.AC (xx) ad q.CF 



XX 



Ergo q.CF 00 3rr 

 Subtr. q.AC 

 + q.AF 



reliq. 2rr 00 2 □ CAG s), div. peu 2 CA (2x) 



3^4 



rr r^ 



Ergo AG 00 — . Ergo q.AG 00 — . Sed xx 00 



X XX 



pp — rr 



fyfy f*f* * 



Ergo q.AG 00 ^^ — . Itaque cognitis p Qtr facile cognofcitur AG, et hinc 



angulus NKO. Nam ex finu AG datur angulus AFG, cujus complementum angulus 

 GAF. ergo datur et finus GF ^). Habet autem GF ad AQ perpend. in FD pro- 

 port, refraâiionis eandem fcilicet quam FC ad CA quse data eft. Ergo hinc datur 

 AQ finus anguli AFQ; cujus complementum angulus QAF. Hic autem bis sump- 



4) Comparez la note 1 1 , p. 48 du Tome XL 



5) Huygens ajoute en marge ,,13. i. Elem."; mais consultez la note 9 de la page 147. 



<^) Huygens ajoute encore en marge: „Vel subtrahendo q.AG à q.AF invenitur 

 ^^ 4 rr — pp" 



