The ratio between diameter and circumference in a circle demonstrated by angles, and Euclid's theorem, proposition 32, book 1, proved to be fallacious1870 |
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Side 261
... March , 1870 . I have to thank you for the Liverpool Leader of Saturday . I see the Editor shuts up the controversy . I cannot blame him , for it would be endless . Yet I had prepared a Letter to him proving by three distinct methods ...
... March , 1870 . I have to thank you for the Liverpool Leader of Saturday . I see the Editor shuts up the controversy . I cannot blame him , for it would be endless . Yet I had prepared a Letter to him proving by three distinct methods ...
Side 262
... DEAR SIR , received . WERRINGTON , LAUNCESTON . 14th March , 1870 . I have to thank you for the Liverpool Leader just There is no difference of views between Mr. Whitworth and myself . We agree . If the chord is finite 262.
... DEAR SIR , received . WERRINGTON , LAUNCESTON . 14th March , 1870 . I have to thank you for the Liverpool Leader just There is no difference of views between Mr. Whitworth and myself . We agree . If the chord is finite 262.
Side 263
... March , 1870 . MY DEAR SIR , I have just received your favour of yesterday's date . I have no doubt you agree with Todhunter that 2 πr = the circumference of a circle , when denotes the radius . This being so , and admitted , it follows ...
... March , 1870 . MY DEAR SIR , I have just received your favour of yesterday's date . I have no doubt you agree with Todhunter that 2 πr = the circumference of a circle , when denotes the radius . This being so , and admitted , it follows ...
Side 267
... March , 1870 . MY DEAR SIR , I have to acknowledge the receipt of your favour of yesterday's date . It is obvious that further discussion between us on the arith- metical value of the symbol , with any chance of agreement , is indeed ...
... March , 1870 . MY DEAR SIR , I have to acknowledge the receipt of your favour of yesterday's date . It is obvious that further discussion between us on the arith- metical value of the symbol , with any chance of agreement , is indeed ...
Side 268
... March , 1870 . MY DEAR SIR , I duly received the Liverpool Leader of Saturday last . You may safely challenge all the Mathematicians of Europe in the terms you adopt , for they will , one and all , confess that for a given circumference ...
... March , 1870 . MY DEAR SIR , I duly received the Liverpool Leader of Saturday last . You may safely challenge all the Mathematicians of Europe in the terms you adopt , for they will , one and all , confess that for a given circumference ...
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The Ratio Between Diameter and Circumference in a Circle Demonstrated by ... James Smith Uten tilgangsbegrensning - 1870 |
Vanlige uttrykk og setninger
25 diameters absurd admit angle of 30 arithmetical mean arithmetical quantity assume BARKELEY HOUSE bisected centre chord circle of circumference circle of diameter circle of radius circle X circular measure circum circumscribing circle circumscribing square construction Correspondent DEAR SIR denote the area denote the circumference diagonal diagram diameter unity equation equilateral triangle Euclid exactly equal fact ference finite and determinate follows four right angles G. B. GIBBONS geometrical figure given greater Hence inscribed regular hexagon inscribed square isosceles triangle JAMES SMITH LANEAST LAUNCESTON length Letter Liverpool Leader Logarithms Mathematics metical perimeter polygon proof Prop prove quadrature R. J. MORRISON radius unity readers recognised Mathematicians Reddie regular dodecagon regular inscribed hexagon regular polygon right angle right-angled triangle SEAFORTH self-evident semi-radius sides square A B C D straight line theorem triangle A B C true arithmetical value
Populære avsnitt
Side 25 - If a straight line be divided into any two, parts, the square on the whole line is equal to the sum of the rectangles contained by the whole and each of the parts*.
Side xiv - ... mathematicians on this question, is plainly expressed in the Report of MM. Demogeot and Montucci. ..." I should have to quote very largely indeed if I wished to draw attention to every hazardous statement which has been advanced; I must therefore severely restrain myself. Consider the following : " Unquestionably the best teachers depart largely from his words, and even from his methods. That is, they use the work of Euclid, but they would teach better without it. And this is especially true...
Side i - Now you are here,' said the patient, • I shall be obliged to you, Sir Richard, if you will tell me how I must live, what I may eat, and what not.' My directions as to that point,' replied Sir Richard,
Side 295 - ... 23".5. 40. Since angles at the centre of a circle are to each other as the arcs of the circumference intercepted between their sides (Geom., Prop. XVII. Bk. III.), these arcs may be regarded as the measures of the angles, and the number of units of arc intercepted on the circumference may be used to express both the arc and the corresponding angle. 41. A degree of arc...
Side 22 - If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided...
Side 243 - In any proportion, the product of the means is equal to the product of the extremes.
Side xiv - ... leads me to the conclusion that the syllogistic form instead of being an impediment is really a great assistance, especially to early students. " Unsuggestiveness " has been urged as a fault in Euclid ; which is interpreted to mean that it does not produce ability to solve problems. We are told : " Everybody recollects, even if he have not the daily experience, how unavailable for problems a boy's knowledge of Euclid generally is. Yet this is the true test of geometrical knowledge ; and problems...