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 xiii
... describe the circle X , and about the equilateral triangle A B C , describe the circle Y. Join N B and N C. Now , Euclid shews us ( Prop . 5 , Book 4 ) how to de- scribe a circle about a given triangle , that is , about any triangle ...
... describe the circle X , and about the equilateral triangle A B C , describe the circle Y. Join N B and N C. Now , Euclid shews us ( Prop . 5 , Book 4 ) how to de- scribe a circle about a given triangle , that is , about any triangle ...
Side xxi
... this makes an angle of 60 ° to be subtended by an arc of 120 ° . How is this to be explained ? Nothing easier ! With K as centre , and KB or KG as radius , describe another circle . not only be subtended also be xxi .
... this makes an angle of 60 ° to be subtended by an arc of 120 ° . How is this to be explained ? Nothing easier ! With K as centre , and KB or KG as radius , describe another circle . not only be subtended also be xxi .
Side xxii
James Smith. describe another circle . not only be subtended also be be subtended by another arc , smaller than , and therefore within the arc BCG . In fact , it will be subtended by an arc equal to one sixth part of the circumference of ...
James Smith. describe another circle . not only be subtended also be be subtended by another arc , smaller than , and therefore within the arc BCG . In fact , it will be subtended by an arc equal to one sixth part of the circumference of ...
Side xxix
... same arc ; and apparently this makes an angle of 60 ° to be subtended by an arc of 120 ° . How is this to be explained ? Nothing easier ! With K as centre , and KB or KG as radius , describe another circle . In fact , it will be xxi .
... same arc ; and apparently this makes an angle of 60 ° to be subtended by an arc of 120 ° . How is this to be explained ? Nothing easier ! With K as centre , and KB or KG as radius , describe another circle . In fact , it will be xxi .
Side xxix
James Smith. describe another circle . In fact , it will be Then the angle BKG will not only be subtended by the arc BCG , but will also be subtended by another arc , smaller than , and therefore within the arc BCG . subtended by an arc ...
James Smith. describe another circle . In fact , it will be Then the angle BKG will not only be subtended by the arc BCG , but will also be subtended by another arc , smaller than , and therefore within the arc BCG . subtended by an arc ...
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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...