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" It follows that the ratio of the circumference of a circle to its diameter is the same for all circles. "
Yale University Entrance Examinations in Mathematics: 1884 to 1898 - Page 186
1898 - 208 pages
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The Practical Teacher, Volume 1, Issue 1

Education - 1882 - 676 pages
...162337. Ans. (3). i 34. Find in degrees and decimals, an arc equal | in length to the radius, assuming that the ratio of the circumference of a circle to its diameter is 355 : 113. By how much does the length of arc, thus found, differ from that given by assuming the ratio...
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Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884 - 148 pages
...1. Assuming that a circle may be treated as a regular polygon with an infinite number of sides, shew that the ratio of the circumference of a circle to its diameter is constant. What is the circular measure of the least angle whose sine is j, and what is the measure...
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A Treatise on Elementary Trigonometry

John Bascombe Lock - Trigonometry - 1885 - 368 pages
...just as 180 stands for the number one hundred and eighty, and for nothing else. * 30. "We proceed to prove that the ratio of the circumference of a circle to its diameter is the same for all circles. The proof depends on the following important principle ; The length of the circumference of a circle...
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Mathematical Questions and Solutions, from the "Educational Times ..., Volume 43

W. J. C. Miller - Mathematics - 1885 - 242 pages
...approximately, we mean that a and b differ by at least some conceivable quantity. Thus, we say rightly that the ratio of the circumference of a circle to its diameter is approximately equal to 3-14 159266 ; but it would be wrong to say that it is approximately equal to...
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Exercises in Arithmetic

George Albert Wentworth, George Anthony Hill - Arithmetic - 1887 - 448 pages
...doubled ; or, if the diameter be trebled, the circumference will also be trebled ; and BO on. It follows that the ratio of the circumference of a circle to its diameter is the same for all circles. The exact value of this ratio cannot be expressed by numbers, but the value near enough for most practical...
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A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...areas are to each other as the rectangles of the sides including those angles. 7. The ratio of the circumference of a circle to its diameter is the same for all circles. 8. Find the side of the largest square that can be cut from a tree whose circumference is 14 feet....
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 356 pages
...1. Assuming that a circle may be treated as a regular polygon with an infinite number of sides, shew that the ratio of the circumference of a circle to its diameter is constant. What is the circular measure of the least angle whose sine is J, and what is the measure...
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The Teaching and History of Mathematics in the United States, Volumes 890-893

Florian Cajori - Mathematics - 1890 - 414 pages
...different direction and by newly discovered paths. Lanbert, an Alsacian mathematician, proved in 1761 that the ratio of the circumference of a circle to its diameter is incommensurable. Ony nine years ago Lindemann, a German mathematician, demonstratid that this ratio...
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Circular of Information of the Bureau of Education, for ..., Issues 1-3

United States. Office of Education - Digital images - 1890 - 958 pages
...different direction and by newly discovered paths. Lambert, an Alsacian mathematician, proved in 1761 that the ratio of the circumference of a circle to its diameter is incommensurable. Only nine years ago Lindemann, a German mathematician, demonstrated that this ratio...
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A Treatise on Plane Trigonometry

Ernest William Hobson - Exponential functions - 1891 - 380 pages
...В is of constant magnitude independent of the particular circle used. 7. It will be shewn hereafter that the ratio of the circumference of a circle to its diameter is incommensurable, that is, we are unable to give any integers m and 7г such that m/n is exactly equal...
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