The Quadrature of the Circle: The Square Root of Two, and the Right-angled Triangle |
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Page 5
... entire mathematical world will bow in submission to his decree , or submit uncondi- tionally to the power of his reason or the force of his logic ; nor does he desire that the glorious fabric , which the mathematical genius of the world ...
... entire mathematical world will bow in submission to his decree , or submit uncondi- tionally to the power of his reason or the force of his logic ; nor does he desire that the glorious fabric , which the mathematical genius of the world ...
Page 22
... entire circle or of a given sector or segment , without giving indefi- nitely that of any sector or segment whatever . The indefinite quadra- ture , which would be the most perfect by giving the quadrature of any part whatever , would ...
... entire circle or of a given sector or segment , without giving indefi- nitely that of any sector or segment whatever . The indefinite quadra- ture , which would be the most perfect by giving the quadrature of any part whatever , would ...
Page 28
... entire circle . Thus , multiplying this value by 12 , we shall obtain that of the circle for a diameter equal to 2 ; and finally dividing this last one by 4 , we shall have that of the circle to the diameter . The first ten terms above ...
... entire circle . Thus , multiplying this value by 12 , we shall obtain that of the circle for a diameter equal to 2 ; and finally dividing this last one by 4 , we shall have that of the circle to the diameter . The first ten terms above ...
Page 31
... entire circle or the quadrature of any of its sectors whose chord is assumed as known . The last of these prob- lems is considered as having no solution . Gregory and Newton , whose authority is so great , even in a science where ...
... entire circle or the quadrature of any of its sectors whose chord is assumed as known . The last of these prob- lems is considered as having no solution . Gregory and Newton , whose authority is so great , even in a science where ...
Page 73
... entire polygon is equal to the area of the in- scribed polygon . 9. The rectangle contained by the circumscribed double triangle and the number of sides of the entire polygon is equal to the area of the circumscribed polygon . 10. The ...
... entire polygon is equal to the area of the in- scribed polygon . 9. The rectangle contained by the circumscribed double triangle and the number of sides of the entire polygon is equal to the area of the circumscribed polygon . 10. The ...
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The Quadrature of the Circle, the Square Root of Two, and the Right-Angled ... William Alexander. Myers No preview available - 2013 |
Common terms and phrases
apothem arc cutting Archimedes ARTICLE assumed circumference assumed diameter Bisect chord circumscribed double triangle circumscribed polygon consequently cosine cumference curve decimal places deducted demonstration diagonal difference discovery division and cancellation double the number draw expressed extracting the square figures geometricians geometry give given arc given circle given polygon given radius given triangle half the number hyperbola hypothenuse hypothesis infinite inscribed and circumscribed inscribed double triangle inscribed polygon inscribed square James Gregory less limit mathematical mean proportional method multiplied number of sides Oronce Finée parabola perimeter perpendicular Plate polygon of double Polygons are Carried problem PROPOSITION quadrature quantity radius rectangle contained regular polygon result already established right angle right line right-angled triangle Scholium secant sine solution square described square root straight line subtracted tangent theorem triangle DAC trigonometry true circumference true ratio truth unity variable
Popular passages
Page 65 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 39 - It furnishes art with all her materials, and without it judgment itself can at best but " steal wisely : " for art is only like a prudent steward that lives on managing the riches of nature.' Whatever praises may be given to works of judgment, there is not even a single beauty in them to which the invention...
Page 71 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal.
Page 39 - Nor is it a wonder if he has ever been acknowledged the greatest of poets, who most excelled in that which is the very foundation of poetry. It is the invention that in different degrees...
Page 78 - COR. From this it is manifest, that the perpendicular drawn from the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base; and also that each of the sides is a mean proportional between the base, and...
Page 71 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Page 39 - And perhaps the reason why common critics are inclined to prefer a judicious and methodical genius to a great and fruitful one, is, because they find it easier for themselves to pursue their observations through an uniform and bounded walk of art, than to comprehend the vast and various extent of nature.
Page 31 - 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 74 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the sum of the squares described on the sides which contain the right angle.
Page 69 - The circumference of every circle is supposed to be divided into 360 equal parts, • called degrees, each degree into 60 minutes, and each minute into 60 seconds, etc.