rpr0pmur nme e^cere] ut rdlm njtexiu tranfeat per datum punohum 
N {ut in Pr&ble?mte Alhazeni,) vel m prodnEius verfmpunUum reflexio^ 
m E occur rat dmo punch N. £x N cadat in A L mrmalis N O = n 
Jltt^ue A. 0=h* Patet ejfe, ut K O ad differ enti am ipf arum AB* 
ita E I ^^i I B, b I n . y I e 1 a - y ^ velh I y • n | e | a - y. ^Imtlr 
^'=y= ~r^q-^^^^^ 2xb a a.22nae>qqba + qqn e^b'^z qq 
- z q q e . nim illa ipfa ^qmnio Frohkmatis Alhaz^emani quam fupra in- 
nmmm TW, fecmdocafu, *^Ji^==y— 2 z b a a + 2 z n a e 
-qqba-qqne=zbqqfzqqe. De qutbm ^quationibm pliira mn 
addo^cumvel nimiafint fortajfequjs fupra diximus. 
Atque h<zc fmt Prohiemata,qu£ circa Pm^fum reflexionij preponi folent 
in quibus tamen finitam punEhi D dati difianiiam fuppo' 
ffiimus. Sedfacilior erit Analyjis, Ji fuppommus lti&* V.eand.F/j.VlIL 
nit am. Se5}Ji enim CA Ufariamin G, con flat ex 
preprietate trium ^ DA, CA, B A, flarmonice fropemomiium; tres 
D G, C G, B G, fore Geometrici proportiomlesy fuppolttk qukcuniiP:e 
pmBi D difiantia, Itaque, f fupponatur Infinita, BG ahihit in m- 
hilum, & punEtum B cum pun5io G coincidet, Jgitur A B erit perpetuo 
aqualisBC erit itaque Ck=iy, & KeEiangulum CAl, aquale 
^luadratQ K E , dabit, in terminis Analyticis^ z a y:=^q y ~: 
. ^ : CUmque difiantia pm^i D fupponatur infinita , erit E D parai'ieia 
A C. Itaque, fi qu<zratur radius reflexus parallelus AL , qmniam ea 
cafu coincidunty erit a =:y=ra3, /z'^ a a -=iq q : J'^' qmratur ut 
parallelus fit AK j erit rurfus q | d ] e | a - y 5 & ^'f;~:=y —3^ , five 
2 q a a - 2 d a e=r:q^. Si petatur ut tranfeat per N, erit , ut fftpra, 
:y =i3, 2 b a a + 2 n a e =::b q q iq q e qu<e aquationes funt 
b a +n c 
b + e 
quoque ad Hyperbolas circa Af)mptotoSy fiifiN pun^lum ejfe fupponatur in 
A L 5 nam^ cum tunc n aheat in nihilum^ fublatis ab aquatione parti bus ^ 
in quibus n continetur^ refidu^ dant atquationem ad Parabolam , ut fuprd 
^uoque monuimus, 
Non exfpeUaSj V ^ Cl, ut cnm fpecula Con cava haBenus in exemplpim 
adduxerim, nunc agam de Convexis. Sets enim^eandem ejfe prorfus Ana* 
lyfin, ^ (t/Equationes fola fignorum + — variatiene diftingui, Scis^ 
Parabolamvei Ellipfin, qu^e uni fatisfacity fatisfacere alteri i & ^ fi Hj» 
perbgla in Convexo problema abfohat^ e']pts oppofitam pariafacere in Con- 
cave. His itaque omiffiSy addo tanthm^ eadem Analyfi haberi in Speculis 
Concavisfocos ^fpatia, qm radii occupant in ^ axe, data qualibet punEii 
lucentis difiantia • Sedmir a facilitate, cum radii fuppom 
mntur paralleli i quod tamen nonnullo circuit u a quibuf- V.71/i'#II.Fig.IX. 
dam demon firarlvidi. Nam in Speculo Concavo EE, 
cujus centrum A , / radipis extremus refiecii intelUgatur ad axem 
A R in B, du^k tangente E C, erit C B = B A, Bljeatur femi-axi^ 
S s s s s s 2. • A R 
