The Quadrature of the Circle: The Square Root of Two, and the Right-angled TriangleWilstach, Baldwin & Company, printers, 1873 - 164 páginas |
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... number of squares within the arc , and there are 196 squares in the quadrant . 196 154 14 11 ' Then 154 is to 196 as 11 is to 14 , for Again , of the 154 blocks within the arc , if 98 be deducted , we shall have 56 between the side of ...
... number of squares within the arc , and there are 196 squares in the quadrant . 196 154 14 11 ' Then 154 is to 196 as 11 is to 14 , for Again , of the 154 blocks within the arc , if 98 be deducted , we shall have 56 between the side of ...
Página
... number of squares within the arc , and there are 196 squares in the quadrant . Then 154 is to 196 as 11 is to 14 , for 196 14 154 11 ' Again , of the 154 blocks within the arc , if 98 be deducted , we shall have 56 between the side of ...
... number of squares within the arc , and there are 196 squares in the quadrant . Then 154 is to 196 as 11 is to 14 , for 196 14 154 11 ' Again , of the 154 blocks within the arc , if 98 be deducted , we shall have 56 between the side of ...
Página 8
... number 7 , which is the base of the system . Again , by PROPOSITION 3 , PART 1 , it is proved that , if from the sums of the squares of the two sides of any square the th be deducted , the square root of the remaining can be extracted ...
... number 7 , which is the base of the system . Again , by PROPOSITION 3 , PART 1 , it is proved that , if from the sums of the squares of the two sides of any square the th be deducted , the square root of the remaining can be extracted ...
Página 20
... sides . There is a quantity of other couples of numbers enjoying the proper- ties deemed so wonderful by Leistner , and which gives a value nearer the circumference , as was shown by Lambert in his Beytrage or Me- moires de ...
... sides . There is a quantity of other couples of numbers enjoying the proper- ties deemed so wonderful by Leistner , and which gives a value nearer the circumference , as was shown by Lambert in his Beytrage or Me- moires de ...
Página 24
... 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 the equation between the ...
... 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 the equation between the ...
Otras ediciones - Ver todas
The Quadrature of the Circle the Square Root of Two and the Right-Angled ... William Alexander Myers Vista previa limitada - 2023 |
The Quadrature of the Circle the Square Root of Two and the Right-Angled ... William Alexander Myers Vista previa limitada - 2023 |
The Quadrature of the Circle, the Square Root of Two, and the Right-Angled ... William Alexander. Myers Sin vista previa disponible - 2013 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 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...
Página 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...
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.