The Quadrature of the Circle: The Square Root of Two, and the Right-angled Triangle |
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Page 10
... named Sextus , who claimed to have solved the problem , but his reasoning has not been transmitted to us . Finally , this in- quiry at that carly day became so famous that Aristophanes in ridicul- ing Meton makes him appear on the stage ...
... named Sextus , who claimed to have solved the problem , but his reasoning has not been transmitted to us . Finally , this in- quiry at that carly day became so famous that Aristophanes in ridicul- ing Meton makes him appear on the stage ...
Page 11
... named Philo , of Gadares or Gades , had gone still further , so that the error did not exceed the 100th . The moderns have carried this accuracy much beyond this point . Finally , among the ancients there were many of those persons un ...
... named Philo , of Gadares or Gades , had gone still further , so that the error did not exceed the 100th . The moderns have carried this accuracy much beyond this point . Finally , among the ancients there were many of those persons un ...
Page 13
... named Oronce Finée , who , by his numerous works , acquired a kind of fame . He gave in his Protomathesis a quadrature of the circle , a little more ingenious , in truth , than that of Bovelle ; but which is , nevertheless , a ...
... named Oronce Finée , who , by his numerous works , acquired a kind of fame . He gave in his Protomathesis a quadrature of the circle , a little more ingenious , in truth , than that of Bovelle ; but which is , nevertheless , a ...
Page 14
... . added to the first volume of the preceding works , he speaks ference , and The pretended must be named Tery of Metins " is the same $ .000 of the 6542816 : of the or 22.12 ... 111 the ange , and the ant M 12 INTRODUCTION .
... . added to the first volume of the preceding works , he speaks ference , and The pretended must be named Tery of Metins " is the same $ .000 of the 6542816 : of the or 22.12 ... 111 the ange , and the ant M 12 INTRODUCTION .
Page 14
... named only because it led to the curious and elegant discovery of Metius ; for this relation of 113 to 355 , reduced to decimals , is the same as 10000000 to 31415929 ; which is at the most but 10.000.000 of the diameter in excess . The ...
... named only because it led to the curious and elegant discovery of Metius ; for this relation of 113 to 355 , reduced to decimals , is the same as 10000000 to 31415929 ; which is at the most but 10.000.000 of the diameter in excess . 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 arc DF 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 geometrical geometricians give given arc given circle given polygon given radius given triangle 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 square the circle straight line subtracted tangent theorem triangle DAC trigonometry true circumference true ratio truth unity variable
Popular passages
Page 64 - 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 68 - 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 69 - 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 64 - 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.