c -8;)

cer aliis per Hyperbolam operosior videatur, Lineae tamen simplicitate, quaParabola inter reliquas Sectiones commendatur, operam compensat.

Iisdem igitur Datis, Jungatur AI, & producatur in S, donec AS fiat«equalis A H, junctaque H S, & bisexta IS in M, ducatur per M Rec-ta* R M Q_ normajos ad H S, in quam cadat ex A Nqrmalis A Q_, & cuiParallelus ducatur Radius AC. Tum factis tribus ProportionalibusI A, AC, A E,‘fiat ut S A ad A E, ita MQ. ad AD, & RS ad 4 P (iprecta AQ_ versus Q.;) & in eadem ab alia parte simatur D O squalisDC. Demum bisecta PD in X, inclinetur per X, Angulo §ema’-recfQ a$4 X, Recta V ^ L, occurrens Normali in D erectx in puppto & inquam ex O cadat Normalis O B. Ajo, si fiat ut V ^ pd $ B, ita $ B adBL, punctum L elfe Verticem, LV Axem» XV Latus Rectum Parabolae,quae Problemati satisfacit omni caso; Secans ninfrum Cjsculum datum jctpunctis K, quorum sipremum & ultimum ad Problem/ 1 Alba^enianum pertinent,reliqua ad aliud.

Datur, ut supra indicavi, alia quoque Parabola, qux cum bac paria fecit,’& cujus descriptio ex hac adeo facile deducitur, ut nova non sit opus. Suma-tur enim A/, in Directum D A, & ipsi aequalis, & in Directam O A. ipsiquoqup aequalis A «. Tum bifecta P <fi in .ducatur per £ Recta « £ ß, Nor-malis ad X B, concurrens cum cT», Normali ad O A, in », & in quam cadatNormalis a $; ac fiat ut » £ ad £ S, ita hxc ad 9 a : Erit a Vertex, a £ Axis,* £ Latus Rectum Parabolae, quae in iiflem cum priore punctis Circulum dji-tum secabit.

Fg. 9 *‘

X. Let B E ß be a double Convex Lens, C the Center of the Segment 7» fi»* *beE B, and K the Center of tsie Segment E fi, B ß the Thickne$ of the Lens,

D a Point in the Axis yf the Lens; and it ig required m find the Point F, universaUy ; byat which tsie Beams proceeding from the point D, are .collected the re i rj, the ^ r ' Edm -Ratio of Refraction being as m to n. Let the diftance of the Object D B pjjsö!’ 2 ° 5 '= DA = i (tjhe point A being sipposed the ferne with B, but taken at adiftance therefrom, to prevent the Coincideqce .os lo myny Linesj) the Radiysof the Segment towards jthe Object CB, or CA — r } apd the Radjysof the Segment from the Object K/3, or K «^ and let B/J, thethickness of the Lens, be = r, and then let the Sine of theAngle of Incidence DAG, be to the Sine yf the Refracted AngleH A.G, ,or C Aj>, a? w *9 » j and ia very ixnpJi Apgles 4?e 4>PZlesthsmselv.cs \vi|ll .be jn tfce ferne Prpportiqn j whenxe jit yjff jfoHoyv^ ijhjir,

As d to r, sb tsie Angle at C to the Angle at D, and d -s* r will be as

the Angle of Incidence GAD; and again, as m to m, si d -f- r to — t

which will : bc as the Angle G A H =which js as d, will leave

C A?. This being taken Jronj A CD»

nr

m

AnaJogousto the Angle A?D,

Md tsie Sides being in this Cafe proportional to the Angles they sibtend, it

will

o