# The Quadrature and Geometry of the Circle Demonstrated

Howell, 1872 - Circle-squaring - 269 pages
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### 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.