The Quadrature of the Circle: The Square Root of Two, and the Right-angled Triangle |
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Page 23
... inscribed and circumscribed polygons whose limit is the circle itself . But this demonstration did not appear conclusive to Huygens , and it was the cause of a contest between these two geome- tricians which occupied the newspapers of ...
... inscribed and circumscribed polygons whose limit is the circle itself . But this demonstration did not appear conclusive to Huygens , and it was the cause of a contest between these two geome- tricians which occupied the newspapers of ...
Page 35
... 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 ...
... 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
... inscribed 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 ...
... inscribed 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 ...
Page 45
... inscribed and circumscribed polygons to 6144 sides , commencing with the hexagon ; it is as follows : PROPOSITION III . - THEOREM . When the radius of a circle is unity , its area and semi - circumference are numeri- cally equal . Let R ...
... inscribed and circumscribed polygons to 6144 sides , commencing with the hexagon ; it is as follows : PROPOSITION III . - THEOREM . When the radius of a circle is unity , its area and semi - circumference are numeri- cally equal . Let R ...
Page 46
... inscribed and cir- cumscribed hexagons . D A B d a Conceive a circle described with the radius CA , and in this ... circumscribed polygon is six times that of the triangle CBD . Let the area of the inscribed polygon be represented by p ...
... inscribed and cir- cumscribed hexagons . D A B d a Conceive a circle described with the radius CA , and in this ... circumscribed polygon is six times that of the triangle CBD . Let the area of the inscribed polygon be represented by p ...
Other editions - View all
The Quadrature of the Circle: The Square Root of Two, and the Right-Angled ... William Alexander. Myers No preview available - 2015 |
The Quadrature of the Circle: The Square Root of Two, and the Right-Angled ... William Alexander Myers No preview available - 2018 |
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 geometrical geometricians give given arc given circle given polygon given radius given square 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 parabola perimeter perpendicular Plate polygon of double 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 Substituting the numbers subtracted tangent theorem trigonometry true circumference true ratio truth unity variable
Popular passages
Page 43 - 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 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 72 - 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 43 - 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 73 - 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 43 - 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 42 - The star that bids the shepherd fold, Now the top of heaven doth hold ; And the gilded car of day His glowing axle doth allay In the steep Atlantic stream, And the slope sun his upward beam Shoots against the dusky pole, Pacing toward the other goal Of his chamber in the east.
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 67 - 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.
Page 64 - A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles.