The Quadrature of the Circle: The Square Root of Two, and the Right-angled TriangleWilstach, Baldwin & Company, printers, 1874 - 164 σελίδες |
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Σελίδα 24
... continued curve whose sides ( branches ) are not separated ; in a word , the reasoning of Newton rests solely on this supposition that in the circle an infinite number of areas corresponds to the same abscissa , whence he infers that ...
... continued curve whose sides ( branches ) are not separated ; in a word , the reasoning of Newton rests solely on this supposition that in the circle an infinite number of areas corresponds to the same abscissa , whence he infers that ...
Σελίδα 44
... continued till it would reach the circle , that is to infinity , which is impossible , it would give the true quadrature . 5th . A common measure of two straight lines , as for example the sine and tangent , can not be regarded as a ...
... continued till it would reach the circle , that is to infinity , which is impossible , it would give the true quadrature . 5th . A common measure of two straight lines , as for example the sine and tangent , can not be regarded as a ...
Σελίδα 51
... to 3.3137085 , we have from the same equations , 3.0614674 p ' P 3.1825979 inscribed polygon of 16 sides . circumscribed polygon of 16 sides . By a continued application of these equations , we find INTRODUCTION . 51.
... to 3.3137085 , we have from the same equations , 3.0614674 p ' P 3.1825979 inscribed polygon of 16 sides . circumscribed polygon of 16 sides . By a continued application of these equations , we find INTRODUCTION . 51.
Σελίδα 52
... continued application of these equations , we find the areas indicated in the following TABLE . NUMBER OF SIDES . INSCRIBED POLYGONS . CIRCUMSCRIBED POLYGONS . 4 2.0000000 4.0000000 8 2.8284271 3.3137085 16 3.0614674 3.1825979 32 ...
... continued application of these equations , we find the areas indicated in the following TABLE . NUMBER OF SIDES . INSCRIBED POLYGONS . CIRCUMSCRIBED POLYGONS . 4 2.0000000 4.0000000 8 2.8284271 3.3137085 16 3.0614674 3.1825979 32 ...
Σελίδα 63
... continued fraction , thus : π 1 4 1 + 1 2 + 9 2 + 25 2 + 49 2+ , etc. in which 2 and the squares of the odd numbers appear . This formula has been employed to show that not only , but its square , is incommensurable . Perhaps the ...
... continued fraction , thus : π 1 4 1 + 1 2 + 9 2 + 25 2 + 49 2+ , etc. in which 2 and the squares of the odd numbers appear . This formula has been employed to show that not only , but its square , is incommensurable . Perhaps the ...
Άλλες εκδόσεις - Προβολή όλων
The Quadrature of the Circle: The Square Root of Two, and the Right-Angled ... William Alexander. Myers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
The Quadrature of the Circle: The Square Root of Two, and the Right-Angled ... William Alexander Myers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.