The Quadrature of the Circle: The Square Root of Two, and the Right-angled Triangle |
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Page 16
... circumscribed polygon of 236 : the stubborn and irritable old man died in 1647 , per- suaded that he alone was right against all . : About the same time a new pretender to the honor of squaring the circle appeared in France , in the ...
... circumscribed polygon of 236 : the stubborn and irritable old man died in 1647 , per- suaded that he alone was right against all . : About the same time a new pretender to the honor of squaring the circle appeared in France , in the ...
Page 22
... circumscribed polygon of 12 sides . Even at the present time , citizen Tardi , an old engineer , applies to the institute , the Corps Legislatif and all the world , to show his quad- rature . He is having pamphlets printed , but is ...
... circumscribed polygon of 12 sides . Even at the present time , citizen Tardi , an old engineer , applies to the institute , the Corps Legislatif and all the world , to show his quad- rature . He is having pamphlets printed , but is ...
Page 35
... polygon inscribed in a circle is a mean proportional between the inscribed and circumscribed polygons of half the number of sides . THEOREM 6. If two straight lines cut one another the opposite or vertrical angles are equal . THEOREM 7 ...
... polygon inscribed in a circle is a mean proportional between the inscribed and circumscribed polygons of half the number of sides . THEOREM 6. If two straight lines cut one another the opposite or vertrical angles are equal . THEOREM 7 ...
Page 44
... polygon must not at any time extend outside the given circle nor the circumscribed polygon come within it ; and any method which may be adopted for the solution of the quadrature of the circle by the means of regular inscribed and ...
... polygon must not at any time extend outside the given circle nor the circumscribed polygon come within it ; and any method which may be adopted for the solution of the quadrature of the circle by the means of regular inscribed and ...
Page 46
... polygon of six sides ( Prob . 28 , B. IV ) , and each side will be equal to the radius CA ; hence , the whole ... circumscribed polygon is six times that of the triangle CBD . Let the area of the inscribed polygon be represented by p ...
... polygon of six sides ( Prob . 28 , B. IV ) , and each side will be equal to the radius CA ; hence , the whole ... circumscribed polygon is six times that of the triangle CBD . Let the area of the inscribed polygon be represented by p ...
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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.