ON INSTRUMENTS FROM ITAL V. 107 



tainty that the telescope had already been made, were of such use, that, 

 without them, I should in all probability never have made the dis- 

 covery. To this I answer, that the help given me by the information 

 I received undoubtedly awoke in me the determination to apply my 

 mind to this subject, and without it I should very likely never have 

 turned my thoughts in that direction ; but besides this, that I cannot 

 believe that the notice I had had could in any way render the invention 

 easier. I say, moreover, that to find the solution of a problem already 

 thought out and expressed, requires far greater genius than to discover 

 one not previously thought of ; for in the latter, chance can play a great 

 part, whilst the former is entirely the work of reasoning. We know 

 that the Dutchman, the first inventor of telescopes, was simply a 

 common spectacle-maker, who handling by chance glasses of various 

 kinds, happened, at the same moment, to look through two, the one 

 concave, the other convex, placed at different distances from his eyes ; 

 and in this wise observed the effect which followed, and thus invented 

 the instrument ; but I, warned by the aforesaid notice, came to the 

 same conclusion by dint of reasoning ; and since the reasoning is by 

 no means difficult I should much like to lay it before you. 



" This, then, was my reasoning : this instrument must either consist 

 of one glass, or of more than one ; it cannot be of one alone, because 

 its figure must be either concave or convex or comprised within two 

 parallel superficies, but neither of these shapes alter in the least the 

 objects seen, although increasing or diminishing them ; for it is true 

 that the concave glass diminishes, and that the convex one increases 

 them ; but both show them very indistinctly, and hence one glass is 

 not sufficient to produce the effect. Passing en to two glasses, and 

 knowing that the glass of parallel superficies has no effect at all, I 

 concluded that the desired result could not possibly follow by adding 

 this one to the other two. I therefore restricted my experiments to 

 combinations of the other two glasses ; and I saw how this brought 

 me to the result I desired. Such was the progress of my discovery, in 

 which you see of how much avail was the knowledge of the truth of 

 the conclusion. But Signor Sarsi, or others, believe that the certainty 

 of the result affords great help in producing it and carrying it into 

 effect. Let them read history, and they will find that Archites made a 

 dove that could fly, and that Archimedes made a mirror that burned 



