## The quadrature of the circle: correspondence between an eminent mathematician and James Smith |

### Common terms and phrases

adjacent admitted angle approximative value area of circle area of square argument arithmetical symbols arrive Association assume base circle X circum circumference of circle circumscribed commensurable conclusion construction contained correspondence course decimal demonstrated diagram diameter is unity diameter of circle difference divided Draw equal to half equal to twice equilateral triangle evident exactly equal examine example exist expressed facts fallacy ference figures four give hexagon inscribed square JAMES SMITH letter linear mean measuring miles obtain opinion perimeter polygon possible produce proof quantity question radius ratio reasoning rectangle reference relation remark represent right-angled triangle side of square square A B C D square circumscribed square described square E F G H superficial area supposed taken theory third side tion trapezium triangle A B C true truth twice the area units 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 75 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

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 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 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.