 | John Francis Twisden - 1860 - 380 pages
...be found, whose area will differ from A by less than one square inch ; in like manner if -^th, T^th, &c. of a square inch had been assigned ; therefore...suppose that X continually approaches a limit A. while Y approaches B, then it follows that A must equal 15 ; this admits of a demonstration which we have not... | |
 | John Francis Twisden - 1863 - 412 pages
...found, whose area will differ from A by less than one square inch ; in like manner if TVth, y^jth, &c. of a square inch had been assigned ; therefore...suppose that x continually approaches a limit A, while Y approaches B, then it follows that A must equal B ; this admits of a demonstration which we have not... | |
 | John Francis Twisden - 1863 - 390 pages
...found, whose area will differ from A by less than one square inch ; in like manner if T\jth, T'nyth, &c- of a square inch had been assigned ; therefore...it can be proved that two variable quantities x and T remain equal throughout their variations, and suppose that x continually approaches a limit A, while... | |
 | John Francis Twisden - 1868 - 412 pages
...be found, whose area will differ from A by less than one square inch ; in like manner if y1,, TJT, &c., of a square inch had been assigned ; therefore...suppose that x continually approaches a limit A, while r approaches B, then it follows that A must equal B. Thus it can be proved that the area of the inscribed... | |
 | Sir John Francis Twisden - Mechanics - 1880 - 382 pages
...can be found, whose area will differ from A by less than one square inch ; in like manner if ^, ^^, &c., of a square inch had been assigned ; therefore...suppose that x continually approaches a limit A, while Y approaches B, then it follows that A must equal B. Thus it can be proved that the area of the regular... | |
 | John Francis Twisden - Mechanics, Applied - 1884 - 382 pages
...found, whose area will differ from A by less than one square inch; in like manner if ^, -rJ-^, <fec., of a square inch had been assigned; therefore the...is the limit of the area of the inscribed polygon. proaches B, then it follows that A must equal B. Thus it can be proved that the area of the regular... | |
 | bart John Francis Twisden (Sir) - Mechanics, Applied - 1888 - 378 pages
...found, whose area will differ from A by less than one square inch ; in like manner if -^j, ^f, <fcc., of a square inch had been assigned ; therefore the...suppose that x continually approaches a limit A, while Y approaches B, then it follows that A must equal B. Thus it can be proved that the area of the regular... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...plane perpendicular to the elements of the cylinder. 689. Properties of circular cylinders. By Art. 441 the area of a circle is the limit of the area of an inscribed or circumscribed polygon, and the circumference is the limit of the perimeters of these... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...about the base of the cone. , polygon circumscribed 715. Properties of circular cones. By Art. 441 the area of a circle is the limit of the area of an inscribed, or of a circumscribed polygon, and the circumference is the limit of the perimeters of... | |
 | Edgar Jerome Townsend, George Alfred Goodenough - Calculus - 1908 - 522 pages
...and geometry also with the case where the independent variable increases without limit. For example, the area of a circle is the limit of the area of a regular inscribed polygon as the number of sides increases without limit. Again, we obtain the value... | |
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... whose area is A; if we continually increase the number of sides, x will continually approach A ; also if we assign any magnitude, say one square inch, a polygon with a certain number of sides can be found, whose area will differ from A by less than... 
