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" It follows that the ratio of the circumference of a circle to its diameter is the same for all circles. "
The National Arithmetic on the Inductive System: Combining the Analytic and ... - Σελίδα 323
των Benjamin Greenleaf - 1851 - 360 σελίδες
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The National Arithmetic on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - 1853 - 360 σελίδες
...triangular beam, that may be hewn from a round piece of timber 80 inches in circumference. Ans. 22.05-f- inches. PROBLEM XII. Having the circumference of a...times .707106 will contain 3.141592. Thus .707106 -5- 3.141592 = .225079 ; therefore, if the circumference of any circle be multiplied by .225079, the...

The National Arithmetic, on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - 1857 - 360 σελίδες
...side of an inscribed square. RULE. — Multiply the circumference by .225079, and tl-.e product it the side of a square inscribed. Rationale. — We...the circumference of a circle to its diameter is as 3.1415S2 to 1; therefore, the ratio of the circumference of a circle to its inscribed square is as...

Elements of Natural Philosophy, Elementary Statics and Dynamics

1862 - 475 σελίδες
...surface in 22 the circle is -y- r*, or rather (3.14159) r2. It has been proved in a variety of ways that the ratio of the circumference of a circle to its diameter is about 22 : 7, or, rather, 3.14159 : 1 ; wherefore, if c be the circumference, 22 c : 2r :: 22 : 7,...

An Elementary Course of Plane Geometry

Richard Wormell - 1868 - 261 σελίδες
...approaches more and more nearly the circumference of the circle circumscribing it. We conclude therefore that the ratio of the circumference of a circle to its diameter is always the same. The constant number which expresses the value of this ratio cannot be found exactly....

An Elementary Course of Plane Geometry

1870 - 16 σελίδες
...approaches more and more nearly the circumference of the circle circumscribing it. We conclude therefore that the ratio of the circumference of a circle to its diameter is always the same. The constant number which expresses the value of this ratio cannot be found exactly....

Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...approaches more and more nearly the circumference of the circle circumscribing it. \Ve conclude, therefore, that the ratio of the circumference of a circle to its diameter is always the same. The constant value of this ratio cannot be expressed exactly by any finite number....

The Complete Arithmetic

Milton Browning Goff - 1876 - 452 σελίδες
...a circle equals the product of the circumference, by one-half the radius. It is proven in Geometry, that the ratio of the circumference of a circle to its diameter is 3.14159, nearly. By means of this truth we deduce various rules for determining different parts of...

Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1877
...root itself? (20.) 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...

In literis Graecis et Latinis

Oxford univ, exam. papers, 1st publ. exam - 1879
...Inscribe an equilateral and equiangular hexagon in a given circle. II. Elements of Geometry. II. 1. Prove that the ratio of the circumference of a circle to its diameter is invariable. Taking this ratio as 2T2, find the length of an arc, subtending an angle of i° at the...

A treatise on elementary trigonometry. [With] Key, by H. Carr

John Bascombe Lock - 1882
...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...




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