The Quadrature of the Circle: The Square Root of Two, and the Right-angled Triangle |
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Page 14
... place himself among geometricians . For he was re- futed by Clavius , Viete , Adrianus Romanus , Christman , etc. , who showed each in his own way that the size which he assigned to the cir- cumference of the circle was only a little ...
... place himself among geometricians . For he was re- futed by Clavius , Viete , Adrianus Romanus , Christman , etc. , who showed each in his own way that the size which he assigned to the cir- cumference of the circle was only a little ...
Page 14
... place . But he had not Scaliger's pride ; he acknowl- edged , even in the title of his book , that his discovery was simply the result of divine Grace . We shall see many others gifted with this same spirit of humility . The paralogism ...
... place . But he had not Scaliger's pride ; he acknowl- edged , even in the title of his book , that his discovery was simply the result of divine Grace . We shall see many others gifted with this same spirit of humility . The paralogism ...
Page 19
... place that is a very false idea , since it has been demonstrated that there is no two num- bers which express exactly the ratio of the side of a square to the diago- nal ; and it is also demonstrated that there is none which express the ...
... place that is a very false idea , since it has been demonstrated that there is no two num- bers which express exactly the ratio of the side of a square to the diago- nal ; and it is also demonstrated that there is none which express the ...
Page 24
... which came much nearer to the truth . Viete carried the approximation to 10 decimal places instead of 6 , and taught besides several somewhat simple constructions which gave the value of the circle , or the circumference 24 INTRODUCTION .
... which came much nearer to the truth . Viete carried the approximation to 10 decimal places instead of 6 , and taught besides several somewhat simple constructions which gave the value of the circle , or the circumference 24 INTRODUCTION .
Page 26
... places . Following the example of Huygens , he also gave constructions of straight lines equal to arcs of the circle , and whose error is still less For example , let the chord of the arc of a circle be a , the sum of the two equal in ...
... places . Following the example of Huygens , he also gave constructions of straight lines equal to arcs of the circle , and whose error is still less For example , let the chord of the arc of a circle be a , the sum of the two equal in ...
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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.