The quadrature of the circle: correspondence between an eminent mathematician and James SmithSimpkin, Marshall, 1861 - 200 σελίδες |
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Σελίδα xvii
... diagram , ( see figure A , ) let A B C be a commensurable right - angled triangle , of which the side B C is to the side A B , in the ratio of 3 to 4 ; and D , a circle , of which the diameter is equal to the perpen- dicular of the ...
... diagram , ( see figure A , ) let A B C be a commensurable right - angled triangle , of which the side B C is to the side A B , in the ratio of 3 to 4 ; and D , a circle , of which the diameter is equal to the perpen- dicular of the ...
Σελίδα xvii
... diagram , ( see figure A , ) let A B C be a commensurable right - angled triangle , of which the side B C is to the side A B , in the ratio of 3 to 4 ; and D , a circle , of which the diameter is equal to the perpen- dicular of the ...
... diagram , ( see figure A , ) let A B C be a commensurable right - angled triangle , of which the side B C is to the side A B , in the ratio of 3 to 4 ; and D , a circle , of which the diameter is equal to the perpen- dicular of the ...
Σελίδα 7
... diagram ( see Fig . I. ) let A B C D be a square , E a circle circumscribed about it , and F a circle inscribed in it , the area of which is admitted to be equal in arithmetical value to half the area of circle E. Let X represent the ...
... diagram ( see Fig . I. ) let A B C D be a square , E a circle circumscribed about it , and F a circle inscribed in it , the area of which is admitted to be equal in arithmetical value to half the area of circle E. Let X represent the ...
Σελίδα 7
... diagram ( see Fig . I. ) let A B C D be a square , E a circle circumscribed about it , and F a circle inscribed in it , the area of which is admitted to be equal in arithmetical value to half the area of circle E. Let X represent the ...
... diagram ( see Fig . I. ) let A B C D be a square , E a circle circumscribed about it , and F a circle inscribed in it , the area of which is admitted to be equal in arithmetical value to half the area of circle E. Let X represent the ...
Σελίδα 12
... diagram ( see Fig . II . ) let A be a circle , B C D a right - angled triangle , of which the side B C is the diameter of the circle A , and let the value of the line B C be I. I say the value of the line representing the circum ...
... diagram ( see Fig . II . ) let A be a circle , B C D a right - angled triangle , of which the side B C is the diameter of the circle A , and let the value of the line B C be I. I say the value of the line representing the circum ...
Συχνά εμφανιζόμενοι όροι και φράσεις
angle approximative value area of circle area of square arithmetical mean arithmetical symbols Barkeley House circle inscribed circle X circum circumference of circle cumference decimal demonstrated describe the circle describe the square diameter and circumference diameter is unity diameter of circle diameter to circumference direct your attention EMINENT MATHEMATICIAN equal to half equal to three equal to twice equilateral triangle exactly equal facts ference geometrical figures given number half the area hypotheneuse inscribed circle inscribed square isosceles triangle Let the diameter letter linear unit orthodox data perimeter ratio of diameter rectangle represent the circumference side A B side B C side of square square A B C D square A K L B square ABCD square circumscribed square D square described square E F G H subtends superficial area third side three and one-eighth triangle A B C true twice the area writer's hypothesis
Δημοφιλή αποσπάσματα
Σελίδα 75 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 75 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα xi - Remembering that this association is a popular association, not a secret confraternity of men jealously guarding the mysteries of their profession, but inviting the uninitiated — the public at large — to join them ; having as one of its objects to break down those imaginary and hurtful barriers which exist between men of science and so-called men of practice...
Σελίδα 26 - Rule. — Multiply half the circumference by half the diameter, and the product will be the area.
Σελίδα vii - ... witnesses were cunningly imposed upon, or the wizard himself deluded. If the most numerous ship's company were all to asseverate that they had seen a mermaid, would any rational persons at the present day believe them? That they saw something which they believed to be a mermaid, would be easily conceded. No amount of attestation of innumerable and honest witnesses would ever convince any one, versed in mathematical and mechanical science, that a person had squared the circle or discovered perpetual...
Σελίδα xxii - ... equal to the right angles in the others, and the angle at C forms the angle at the base to every one of the three triangles, that is, it is common to all the three ; and as all the angles of a plane triangle are together equal to two right angles (Art. 5) the remaining or third angle must be equal in all the triangles ; for that angle is the complement (Art. 5) of the angle at C in each of the triangles. Now all plane triangles which are equiangular, have the sides which contain the corresponding...
Σελίδα 26 - The diamoter of a circle being given, to find the circumference. RULE.
Σελίδα 58 - TT denotes the number of times the diameter of a circle is contained in the circumference...
Σελίδα 61 - ... would be not at all the less true if a future state were a chimera, and prudence a quality which was nowhere met with; nor would the truth of the Mathematician's conclusion be shaken, that " circles are to each other as the squares of their diameters...
Σελίδα 143 - I was writing to one earnestly engaged in the search after truth, and my observations were confined to the pointing out to him, how he might convince himself that he was altogether wrong. My letters were not intended for publication, and I protest against their being published, for I do not wish to be gibbeted to the world as having been foolish enough to enter upon, what I feel now to have been, a ridiculous enterprize.