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 xi
... Hence : a right angle 30 ° = 90 ° — 30 ° 60 ° = the angles A B D and AC D , and the angles at the base of the triangle ABC are equal ; and it follows , that the three angles of the triangle ABC ( 60 ° + 60 ° + 60 ° ) 180 ° , and are ...
... Hence : a right angle 30 ° = 90 ° — 30 ° 60 ° = the angles A B D and AC D , and the angles at the base of the triangle ABC are equal ; and it follows , that the three angles of the triangle ABC ( 60 ° + 60 ° + 60 ° ) 180 ° , and are ...
Side xiii
... triangles A N B , BNC , and CNA are isosceles triangles and therefore have the angles at the base equal . Hence : The three angles ANB , BN C , and CN A at the centre of the circle , are together equal to the sum of the six angles N xiii .
... triangles A N B , BNC , and CNA are isosceles triangles and therefore have the angles at the base equal . Hence : The three angles ANB , BN C , and CN A at the centre of the circle , are together equal to the sum of the six angles N xiii .
Side xiv
... Hence : If the angles of the equilateral triangle ABC be angles of 60 ° , and therefore together equal to two right angles : the angles A N B , BN C , and CNA at the centre of the circle will be angles of 120 ° . These angles are ...
... Hence : If the angles of the equilateral triangle ABC be angles of 60 ° , and therefore together equal to two right angles : the angles A N B , BN C , and CNA at the centre of the circle will be angles of 120 ° . These angles are ...
Side xvii
... Hence : The angles at the centre of the circle contained by the diameters K C and H B , or , H B and E G , are together equal to four right angles . The circumference of the circle ( in Fig . 4 ) is divided into two semi - circles by ...
... Hence : The angles at the centre of the circle contained by the diameters K C and H B , or , H B and E G , are together equal to four right angles . The circumference of the circle ( in Fig . 4 ) is divided into two semi - circles by ...
Side xviii
... Hence , although we can conceive that two triangles may " coincide " in all respects , we can never geometrically apply one triangle to another . Mr. Wilson in his " Treatise on Elementary Geo- metry " ( Section 3 , Plane Triangles ) ...
... Hence , although we can conceive that two triangles may " coincide " in all respects , we can never geometrically apply one triangle to another . Mr. Wilson in his " Treatise on Elementary Geo- metry " ( Section 3 , Plane Triangles ) ...
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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...