122

to y, y — Hence by multiplying theseequations together, we obtain sy =

= ty or s = t.

Whence it appears that when t is a mi-nimum. with respect to y, the tangent FRFig. cuts the axis DC produced, at the samePagei is^oint as the directrix RQ. does.

19 . Problem. Given any one of the fivequantities c, cc, t, z, y, to find the other fourgeometrically, when t is a minimum withrespect to y.

CASE i.

When c is given, to find the rest.

Fig. 24. j? rom an y point A in the straight lineAC , draw AD, making the angle CAD=56 ° 28 ', on AC take AB= the given quan-tity c, and through B draw BD perpen-dicular to AC cutting AD in D : with thecentre A and distance AD describe an arcFDC, cutting AC in C, and through Cdraw CE parallel to BD.

Lastly, through A draw AE perpendicu-lar to AD, meeting CE in E; then shallCB=a, BD=2, AD or AC =t and CE—3/.