!- J /// K CUKVK8 811 



it Hun wholly between the y-axi* and 

 r2a; that it ptJMt ihlOOgh t untie* ^ainl A" 



..I tin- iluuut-t.-r p. riH-mlirular t" <M ; alul that It ha* 



iiitiniu- branches to each of which the line z 2a U an 



i r. 1. The polar equation of the cissoid referred to the initial line 

 ole O, U also easily fuu: lie polar coordinates of P he 



i 0; then, 



p=0/>= Q.S' = as'-OQ, . . (4) 



1 ' O = 2aaec& and OQ = 2acon0, 



p = 2 a ec $ - 2 a <x$ m 2a(aeo tf - oo* 0), 

 p = 2 a tati sin ^, . 

 is the polar equation sought 



NOT i luplicate the cube" by means of the ciseoid,* 



!k : CA" =a t draw tl,.- 1m.- II. \ ruttin- the ciseoid 



' // 2 CA, therefore EJ~X. 

 lut from equat 



' '/ ' . 



I ' 



w let M be the edge of any given cube, and let it be required to 

 construct a line n such that the cube on n shall be equal to the double of 

 the cube on m. Construct n so that 



OE:EJ:.m 



MB 6P :&* = *:*, 



and, sinoe ST = 2.02*, therefore n 



. ciMoid may also be defined in either of the following 

 ) as the locut ,,f tt> ') in which the chord f 



U that ordinal? . which b equal to NQ. ami (J) a^ 



-M, ,,f the foot of the perpendicular let fall from the vertex of a 

 rabola upon a tangent The derivation of the equation of the ear?* 

 sed upon these definitions U left as an exercise for the student. 



^^-- - ^-^-^ -..- ^ ^^-- * ^-^~^^^^^-i^-- 



insert two mean proportionals between two given lints by 

 dtsnid. See Cantor, Qesehlohte der Maitamauk, lid. I.. S. 8981 



