The Quadrature of the Circle: Correspondence Between an Eminent Mathematician and James Smith, Esq |
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Common terms and phrases
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 radius of circle ratio of diameter rectangle represent the circumference side A B side B C side of square square A K L B square ABCD square circumscribed square D square described square E F G H subtends superficial area supposed third side three and one-eighth trapezium ARLTA triangle A B C true twice the area writer's hypothesis
Popular passages
Page 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.
Page 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...
Page 75 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 26 - Rule. — Multiply half the circumference by half the diameter, and the product will be the area.
Page 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...
Page 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...
Page 26 - The diamoter of a circle being given, to find the circumference. RULE.
Page 58 - TT denotes the number of times the diameter of a circle is contained in the circumference...
Page 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...
Page 1 - The question: Are there any commensurable relations between a circle and other Geometrical figures?