The Quadrature of the Circle: The Square Root of Two, and the Right-angled TriangleWilstach, Baldwin & Company, printers, 1874 - 164 sider |
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Side 19
... assumed , of his discovery . He was , like many others , persuaded that in the series of numbers there are two which express the ratio of the diameter to the circumference , and that if the quadra- ture of the circle was not found it is ...
... assumed , of his discovery . He was , like many others , persuaded that in the series of numbers there are two which express the ratio of the diameter to the circumference , and that if the quadra- ture of the circle was not found it is ...
Side 23
... assumed demonstration of this impos- sibility by Hanow . It is only a ... diameter , nor the impos- sibility of measuring the former ; for a ... diameter and its square are irrational numbers , and that had been already demonstrated by ...
... assumed demonstration of this impos- sibility by Hanow . It is only a ... diameter , nor the impos- sibility of measuring the former ; for a ... diameter and its square are irrational numbers , and that had been already demonstrated by ...
Side 31
... diameter to its circumference ; this ratio is the true touchstone to try the pretended quadratures of the circle ... assumed as known . The last of these prob- lems is considered as having no solution . Gregory and Newton , whose ...
... diameter to its circumference ; this ratio is the true touchstone to try the pretended quadratures of the circle ... assumed as known . The last of these prob- lems is considered as having no solution . Gregory and Newton , whose ...
Side 38
... assumed proposition would be false which would contradict a re- sult so well established and so universally admitted ... diameter though very near it , and the double of the sine , is not quite the part of the true circumference though very ...
... assumed proposition would be false which would contradict a re- sult so well established and so universally admitted ... diameter though very near it , and the double of the sine , is not quite the part of the true circumference though very ...
Side 45
... circumference , provided that this radius and circumference are selected in accordance with theorem second , then will the ratio between the assumed diameter and the assumed circumference be the same as the ratio between the true diameter ...
... circumference , provided that this radius and circumference are selected in accordance with theorem second , then will the ratio between the assumed diameter and the assumed circumference be the same as the ratio between the true diameter ...
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The Quadrature of the Circle: The Square Root of Two, and the Right-Angled ... William Alexander. Myers Ingen forhåndsvisning tilgjengelig - 2015 |
The Quadrature of the Circle: The Square Root of Two, and the Right-Angled ... William Alexander Myers Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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.
Side 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.
Side 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...
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.