( a il ) 
ritates / &r cogiiitcefunt (dantur enim fcmidiameter fpecuH^ 
ac punfti lucidi a vertice diftantia) 2: vero & / quselit^ ac in- 
cognita. "}2im in Triangulo DAB, erit ^ DAB : < ADB :: 
r : i. Item in Triangulo DBC, < BDC < ADB, ex 
naturaReflexionis, & < DBC = < DAB + < ADB, ex 
Elem. Eud. Ergo com < DBC fu ut r + & < BDC ut 
b5 eritetiam < DBC : < BDC : : r+ b : b, & (quod ex 
prindpio fiipra memorato confcquitur) DC : BC : : r + b : 
b. Sed quoniam punftum D ip(i E proximum eft, erit D C 
ipfi CE cqualis eftimanda, ergo CE : BC:: r + b; hoc 
eft f : z :: r +.b : b, Sr ( comparando Antecedentium & 
Confequsntium fummas ad Antecedences) f+z : f :; r +■ x 
b ; r + b ; fed f + z = r, ergo r : f : : r + 2 b : r -f- b, 
ergof=i^^. Q^: E: I. 
Si ponatur r + b (= AE) =d, Theoreroa in formam 
contradiorem rcdigetur, & fic ftabit f ===^. Sed utrovis 
modo, focorum inventioni, qusecunq; tandem fit, velSpeculi 
forma, velradiorum conditio, aptum evadet. 
Coroll L El It z d = d f — r f, five AE x BC = AB x CE, 
vel quod idem eft, linea AE harmonice dividitur in'piindi^ 
A, B, C, E,- nam prsedit9:a Redangdlbrum eqaslitas, Jmrx' 
fecundum proportionem harmoiiicam fedse, propria bft. Patet 
haec Veritas 2 Eft enim f = & z = r — - f == r — 
undc valores hofcc fubftituendo, Equatio manifefta fiec. Adeo 
ut in omnt Speculo Spherico, linesepA^ DB, DE, liint 
Harmonicales * & Punftum radians; Cenrnihi, To^ 
tex (unt punda divifionen).Harmonidam effitibhrili^ 
CcrolL II i«« Pofitod^^^^l erit 0x 
Temper. Hoc eft, fi piiniai radiantis diftantia major fit Se- t 
midiametro Speculi, foci diftantia ftmper major erit quarta ; 
parte Diametri. . , ■ 
Item, erit < r femper. Hoceft, diftantia foci fem* 
per erit minor fpeculi femidiametro. 
x^^' Si ponatur d = r, erit — five f= r. Hoc eft, fi'. 
pun<9:um radians in centr6*rpieculi conftitu^t&r/Ihlago ejus 
ibi mm eo unietur. 
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