The Quadrature and Geometry of the Circle Demonstrated |
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25 diameters admit area of circle arithmetical quantity arithmetical symbols assertion BARKELEY HOUSE bisected book of Euclid centre circle of diameter circle X Z circum circumscribing circle circumscribing square construction dear Sir decimals denote the area describe the circle determinate quantity diagonals diameter to circumference dodecagon draw a straight Duke of Buccleuch enclosed diagram equation equilateral triangle equivalent ratios Euclid fact ference follows of necessity geometrical figure Hence hypothenuse indeterminate inscribed circle inscribed square JAMES SMITH join Letter mathematical Mathematician mean proportional meet and terminate metical pairs of numbers parallelogram perimeter perpendicular practical geometry premisses produce proof proposition prove R's PAPER radii radius ratio of diameter regular hexagon regular inscribed hexagon SEAFORTH semi-radius sides that contain similar right-angled triangles similar triangles Squaring the Circle straight line theorem true value whole triangle Windermere Απ
Popular passages
Page 246 - If you forgive me, I rejoice ; if you are angry, I can bear it. The die is cast. The book is written, to be read either now or by posterity — I care not which. It may well wait a century for a reader, since God has waited six thousand years for an observer.
Page 28 - If the circumference of a circle be divided into any number of equal parts, the chords joining the successive points of division form a regular polygon inscribed in the circle ; and the tangents drawn at the points of division form a regular polygon circumscribed about the circle.
Page 100 - ... express the ratio between the area of every square and the area of its inscribed circle. Again : Let the area of the circle X be represented by the digit 5, which stands in the centre of our system "of arithmetical notation, and is the arithmetical mean between the extremes of i and 9, 2 and 8, 3 and 7, and 4 and 6. Then : One pair of numbers will be 25 and 6-25; and the other pair will be 19-53125 and 8; and \/2~5" x 6-25 — ^19-53125 x 8 — : ^156-25 = 12-5.
Page 162 - 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 : 16. And this point is called the centre of the circle.
Page 22 - In any proportion, the product of the means is equal to the product of the extremes.
Page 212 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Page 162 - A CIRCLE is a plane figure bounded by one line called the CIRCUMFERENCE or periphery; to which all straight lines drawn from a certain point within the figure, are equal.
Page 163 - TT denotes the number of times the diameter of a circle is contained in the circumference...
Page 104 - It is usual to divide the circumference of a circle into 360 equal parts, called degrees...
Page 212 - In a right angled triangle, if a perpendicular be drawn from the right angle to the opposite side, the triangles on each side of the perpendicular are similar to the whole triangle, and to each other.