Tht Generationes an Hyberboiical Cyliniroiieby Sir Christopher Wren.ii. 48. x. ?Li.

f'&> 97»

( 188)

Lastly, As to the Effect of turning the two fides of a Lens towards. anObject ; it is evident, that if the thickness of the Lens be very small, so asthat you neglect it, or account t — o, then in all Cafes the Focus of thefame Lens, to whatsoever Beams, will be the fame, withour any differenceupon the turning the Lens : But if you are so curious as to consider thethickncfs, (which is seldom worth accounting for) in the case of Parallel Raysfalling on a Plano Convex of Olafs, if the Piain side be towards the Object,t does occasion no difference, but the Focal distanee f — 1 r . But vvhenthe Convex side is towards the Object, it is contracted to zr — \ t, so thatthe Focus is nearer by f t. If the Lens be Double Convex, the differenceis lefs, if a Meniscus, greater. If the Convexity on both sides be equa!, theFocal Length is about it fhörter than when t = o.< In a Meniscus, theConcave side towards the Object encreases the Focal length, but the Convextowards the Object diininifhcs it. A general Rulc .for the difference arising

on turning the Lens, wherc the Focus is Affirmative, is this-,

3 r -1- 3 s — t

for Double, Convexes of differing Spheres. But for Menisci, the fame diffe-

% Y t “f* 1 f t

rence becomes--——: of which I need give no other , Demonstra-

3 r — 3 ? -+ t

tion, but that by a due Reduction it will so follow from what is Premised’.as will the Theorems for all sorts of "Problems relating to tlie FociOpticlt Glaffes..

XI 1. Sint Hyperbolae Oppositae DB, EC, quarum Axis Tranfvcrfus esei BC, Centrum A, Sc una ex Afymptotis GP j item per Centrum sit O M! ducta ad Angulos Rectos ipsi B C. Quare si circumducantur Hyperbolaecirca Axin O M, manifestum est, ex ea Revolutione generari Corpus Cylin-drqides Hyperbolicum cujus Bases, sectionefque Basi parallelae sunt Circuit.Dico insuper, si idem Corpus secetur per Asymptoten ,G P, erit sectio Paral-lelogrammum.

Secetur per Axin Transversum sectione Circulari" BNC ; item per O 8 c Min Circulos aequales & aequaliter a Centro distantes ; item per Axm in figu-ram Genetricem cujus semifsis est B D E C, in cujus Plano erit AfymptotosG P,,per quam ad Rectos Angulos planum, BD E secetur in Plano FHP';jungantur denique HO.

Quoniam Triangulum O GH est Rectangulum, Ergo quadratum OH,sive OD, minus quadrata O G, - est .aequale quadrato GH: & quoniamDO parallela est' ipsi B A, &C Asymptoten secat in G, erit (ex proprie-tatibus. Hyperbolae, quae in . Conicis demonstrantur) quadratum OG -mnacum quadrato A B aequale quadrato O D, h. c. Quadratum O D minusquadrato OG aequale quadrato ABj sive -quadrato A N. Ergo-qua-dratum GH, aequale est quadrato A N. Quare GH & AN aequantur Lcfiant ad Angulos Rectos ipsi GA ; idemque demonstratur de omnibus aliissectionibus Basi parallelis. Quare Cylindroides Hyperbolica rite secatur perAsymptoten in Parallelogrammum. so e, d. Ors/.q