184 Mr. Haworth's Dccad of new Succulent Plants. 



The first proposition of the tenth book of Euclid says, " If 

 from the greater of two unequal magnitudes there be taken 

 away more than its half, and from the remainder more than 

 its half, and so on, there shall at length remain a magnitude, 

 less than the least of the proposed magnitudes." This pro- 

 position, on a slight view of it, appears very specious. But 

 by examining it more deeply, we shall perceive that it asserts 

 the absurdity, that a magnitude is less than itself. In effect, 

 let any indeterminate magnitude be the greater, and any in- 

 determinate part of it be the less ; then, if from the greater 

 there be taken away more than its half, and from the remain- 

 der more than its half, and so on, there shall at length re- 

 main a magnitude less than any indeterminate part of the 

 whole : but the remaining magnitude is an indeterminate part 

 of the whole ; therefore there shall at length remain a mag- 

 nitude that is less than itself. Such is the true nature of the 

 absurd lemma of the ancients, and of all similar propositions. 

 And such is the nature of the sophism, by which Euclid has 

 attempted to demonstrate the chief propositions of the twelfth 

 book of his Elements. The properties of the circle, sphere, 

 cone, and cylinder, were deduced by analogy from the like 

 properties, demonstrated to belong to figures bounded by 

 straight lines and plane surfaces. These properties, with 

 regard to the round figures, are demonstrated algebraically 

 by the binomial calculus ; but they are not yet demonstrated 

 by elementary geometry. 



The excrescences that have accumulated on the sciences of 

 geometry and algebra should be pruned ; — sciences that have 

 tended more to the advancement of society than all others. 

 They should be freed from all empirical reasoning. They 

 should be placed before young mathematical students in their 

 real state, that their judgements may not be wai-ped, and that 

 aspiring genius may with the more effect exert itself in dis- 

 covering the yet latent principles of these sciences. 



Cork, Aug. 2, 1824. J. WALSH. 



XXXI. Decas novarum Plantarum Succulentarum ; Autore 

 A. H. Haworth, Soc. Linn. Lond. — Soc. Horticult. Land. — 

 necnon Soc. Ccesar. Nat. Curios. Moscoviensis Socio, fyc.fyc. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



"LT ERE WITH I have the satisfaction of forwarding to you, 



-*• ■*■ for your Magazine, a pretty complete description of ten 



new species of succulent plants, belonging or allied to the genus 



Crassida 



