• ■ ( 6r24 } 
MemiimiU^ Htvid^s'^ cdculi noflrl fummm ad linemTy A fed f^tk 
dnimadvert^, non m^jori diffcultfite referri fotulffe ad i A 
Vld.eandem ^^^^ pariter data eft , ) dnUis fcil. lineis , qnas in Schemata 
Fi£,Vl\, pmlils ddmhr^vimm. Verum novo calculi latere non 
§fm, Sienim re^U d A, ejufque fartibm, eofdew ac prim termlnos ana- 
lytic os adhiheas, b, e flip [am d A facias dqudem x, D n = b. n A 
] r: a, i E = &c S pYodihlt eadem (iy£quatio qua prim s & infinitm 
dias Hyperbolas & Ellipfes ohinebps, qua cum Circnlo dato Fr$blmm (4- 
tisfacient, ^o{liKo^ effem, fi fingulos cafus profeqm vellem, cum illorum 
^qumlones je'la figmrum i varimione difcernantur. Unum tamen 
excipio^ mm. cu'^ angulns d A D ^/ re^m S ejus enim aqumo hahetur^ 
expunBis d prigri aqmtlone partibm^ in quibm n {qu<& in nlhilum abit) in- 
venitP^r : nempe , 2 x b a a - q q b a = b z q q - z q q e , vel (pro 
2 z b a a pofito ejpu valore) zbqq-qqba = 2zbec - zqqe. 
Sed mimadvertendum eH^quodJicet refer endo Analyfinad reSlam 0 A, 
ftatim fefe offer ant in aquatione du£ Hyperbola h & alia totidem k prioribm 
diver fa ^ ciiw refer tur ad re^iam d A eafdem tamen omnino Parabolas 
haberi^adutramvis reflarum d A vel Y) A referatur Analyfis : cujm rei 
ratio levi confideratione T'ibi occtdrret, 
Fatere nnnCy V, Cl, Pit fuperiorem Analyfin ommbHs^ qua circa SpeCH' 
^ lorum" Spharicorum reftexionem proponi folent^ Problematibus 
Fijy'll* apfticeWy novo faSio Schemdte, Sit igitur^ut prihs^Circulm], 
cn]u5 centrum A, pmB:umY> datum^ & ah eo radim incidens 
D Ej cujpu reflexus fit E JunU^ D A, ducatur ad itlam Tangens 
E C, & mrmalisE I ; & producatur ad eandem, reSla Q E B ^ deno- 
minentur partes ut prius. D A = z. C A=rX. A E = q. B A == 
A 1= a. I E ~ e. Igltur^ propter tres DA, C A, B A , Harmonice 
froportknales , & tres C A> A E, A I, Geometric} , femper habebitur 
^quatio.y = , i^ quo^cmque Circuli punHum cadat D E. Itaque^ 
ft qucsratur punEium'E^ in quod fi radius DE incidat^ refieciatur mfc&K^ 
hihos diametro LAV mrmali ad D A reflexm Q^E, produtlus tran- 
fibit per ly m patet S ^ I B .coincident, Igitur 2i=zy^ '^33 . 
five, aa — ^lii — ^qq, & Problemaper plana folvetur. 
Si quaratur punSium^ d quo radius refleFtatur parallelus alteri cuilibet 
iinea y m A K (dnEia ex centro A ) ducatur ad ill am , ex pun5lo 
Tangens KL==cl. Evl dens eft, Triangula AKL, E I B, fore fmi- 
a a J cum omnia later a unius parallela jint lateribus alterius, Itaque A L 
ad \,1L m E \ ad \ ^ ^ five q I d I e I a • v • & l^im-=v==:lll_ 
C?-zq,=2qzaa— zzdae-q^ai-qqdei five, pro a a pfiu q q - 
ce, zq3-zzq^~,2zqee — 2zda e — q'a + qqde. Vtraque 
autem^qmtio eft ad ^^yferhdm circa afjmptotos, qn^cum Circnlo dat^ 
Frobiema abfolvn, 
■ , Prol 
