M. T. S. Davies on Geomefnj and Geometers. 



541 



blems tave not formed the basis of Mr. Swale's Mascheronian 

 ones. His plane constructions must have been mainly original ; 

 for to original ones they reduce back (with few exceptions) upon 

 I'estoring the ruler as a companion-instrument of constmction 

 with the compasses. 



This work is so nearly ready for printing that I woidd safely 

 undertake to complete it, were there the least reason to expect 

 that its publication coiild be effected without an almost total 

 sacrifice of the money expended in doing so. The great amount 

 of geometrical power evinced throughout would do much to 

 remove any objections arising of the direct inutility of the sub- 

 ject ; whilst the constructions of pure geometiy implied in its 

 operations would constitute a valuable assemblage of studies for 

 the young geometer. All hope, however, of s\ich publication 

 must be ^^sionary ; at least till a greater change is worked in 

 English mathematical prejudices against pure geometry than is 

 yet likely to take place. 



Instead of selecting any of the more elaborate coustructions 

 as a specimen, I shall give one of the simplest I can find ; since 

 it really furnishes a neater and less troublesome practical con- 

 struction of a problem of frequent occurrence, than that gi^-en by 

 Euclid and generally adopted. ^'*-;' '" r^^i^ni'i-a^yi ■cm.m.i 



,,,,!!,, "To find the centre of a given circle. 



i'>;ffTo any point P (in the periphery) describe the circle PABL; 



mt>J8^« W3U 



inflect BL=BP; and let AL meet the given circle in II 

 II L (=HB) is its radius." (MS. vol.i. p. 68. 



then 



