i5
��i3-i5. EXCERPTA MaTHEMATICA. J IÇ
AC ^ a, AE\^ a — y,
BC^ b, BE ^ b + cy,
r\Q ^ ccyy —yy + ^^r + ^^«^r
%a -\- T.b '
— c' 1 — 4"^^] — 4""' + 4' y — 9,aab •
+ 2c<:(r' - 4bc'l - Sabc { + -i' \yy - 8j** /
— I J + 4a (-^ + 4aicc(/-^ +4aacc) + 8ai*cK + ^bc 1 — 4<'fccc 4- 9,aabc
4aa -\-^ab +.4*^
��DE- V .
��5 Sitque F, in lineâ ACB inter A & C, centrum cir- culi tangentis curvam in pundo E, fit
r f^ abccy + "by -\- bby -\- aaccy — aab — abb -\- abbc -\- a abc accjr -\- bccy — ay — by -\- a a + a b -\- abc + bbc
Vnde clare demonftratur omnes radios à pundo B
refrados in curvâ EC tendere verfus A; vel contra,
10 tam in convexà quàm in concavâ figura, mode re-
fradio corporis verfus A ad corpus verfus B fit vt
vnitas ad c.
Fiat nunc AE^^a+j, Bï. ^ b ■{- cy,
CT) ex, rr — <:<:yy + ^"y — "^bcy ■
la — 2b '
— c' ] — 4,bc'\ -\^bbcc\ -\~ 4aacc\ -\r 9>aabc
+ 2cc|j +4jccf -\-%abc{yy — ^ibcJ — Sabbcl
-il +4bc{-^ —^aa ) - 4<'b i'^^ — Saab^-^
— 4a I — 4bb J + Sabb
4aa — 8jfc — 4bb
��DE- V ■
��I Et hîc neceffariô pundum D inter F & C vel B ca- dit, atque habeo :
��accy — by 4- abc — ab
��YC —
y — ccy + a — bc ' p p acc^ bccy 4- abc — bbc
��y — ccy -j- a — bc
��. p __ <j K — by + aa — ab
��y — ccy -\- a — bc '
quae duo funt inter fe vt ccy + bc ady -\- a.
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