 If the circumference of a circle be divided into any number of equal parts, the chords joining the successive points of division form a regular polygon inscribed in the circle ; and the tangents drawn at the points of division form a regular polygon circumscribed...  New Series of The Mathematical Repository - Page 138by Thomas Leybourn - 1819Full view - About this book
 | Matthew Stewart - 1746 - 352 pages
...of AB is equal to the redangle contained by BD, AC. ^ E. Do PROPOSITION IV. THEOREM II. Fig.bj Let the circumference of a circle be divided into any number of equal parts in the points A, B, C, &c. and from the points A, B, C, &c. let there be drawn right lines to any point... | |
 | Pierce Morton - 1830 - 584 pages
...common centre of two circles, the one circumscribed about, the other inscribed in, the polygon . 91 (¿) If the circumference of a circle be divided into any number of equal parts, the chords joining the points of division shall include a regular polygon inscribed in the circle ;... | |
 | John Martin Frederick Wright - 1833 - 1072 pages
...equality, and therefore are accurate measures of them), than the angles themselves. 50. Ex. 1. Let the circumference of a circle be divided into any number of equal parts and the points of division being joined, let there be t tangent drawn at every such point meeting a perpendicular... | |
 | 1835 - 684 pages
...common centre of two circles, the one circumscribed about, the other inscribed in, the polygon . 91 (fr) If the circumference of a circle be divided into any number of equal parts, the chords joining the points of division shall include a regular polygon inscribed in the circle ;... | |
 | William Emerson - 1836 - 498 pages
...and its method of construction, let ABCDE (Fig. 5. Plate B,) be any indefinite right line, and let it be divided into any number of equal parts, and perpendiculars be drawn from all the points ABC, &c. and let their lengths AF, BG, CH, DI, and EK, be a series of geometrical proportions,... | |
 | Charles Davies, William Guy Peck - 1855 - 628 pages
...equal chords, is tangent to the circumference at the point where the two chords meet. 4. If an are of a circle be divided into any number of equal parts, and lines be drawn from the points of division, meeting each other at anv point of the circumference, these... | |
 | Edward Lacy Garbett - 1867 - 276 pages
...Archimedes. It is so called from his demonstrarion of its nature, by which it is proved that if the arc of a circle be divided into any number of equal parts, and radii drawn from the centre to these points, the spiral line commencing at the end of one of those... | |
 | James Smith - 1870 - 634 pages
...TT ; but this ratio does not hold good for a polygon of 3 or of 4 sides inscribed in a circle. But, if the circumference of a circle be divided into any number of equal arcs, and from one of these arcs j'jth part be deducted, and the remainder be multiplied by the sum... | |
 | William Chauvenet - 1871 - 380 pages
...establishes the possibility of regular polygons of any number of sides. PROPOSITION I.— THEOREM. 2. If the circumference of a circle be divided into any number of equal parts, the chords joining the successive points of division form a regular polygon inscribed in the circle... | |
 | William Chauvenet - 1872 - 382 pages
...establishes the possibility of regular polygons of any number of sides. PROPOSITION I.— THEOREM. 2. If the circumference of a circle be divided into any number of equal parts, the chords joining the successive points of division form a regular polygon inscribed in the circle... | |
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