 | James Howard Gore - Geometry - 1898 - 232 pages
...exterior angles is equal to twice as many right angles as the figure has sides. But by (125) the interior angles are equal to twice as many right angles as the figure has sides, less four right angles. Therefore the exterior angles alone are equal to four right angles. QED EXERCISES.... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...added as corollaries to Proposition 32 by Robert Simson, who edited Euclid's text in 1756. COROLLARY 1. All the interior angles of any rectilineal figure,...twice as many right angles as the figure has sides. Let ABODE be any rectilineal figure. Take F, any point within it, and join F to each of the angular... | |
 | Sidney Herbert Wells - Machine design - 1900 - 202 pages
...depends upon Corollary I. of Euclid i., 32, which says that " the interior angles of any straight lined figure together with four right angles are equal to...twice as many right angles as the figure has sides." The most common of the regular polygons used in engineering designs are the pentagon (five-sided),... | |
 | Arthur Thomas Walmisley - Leveling - 1900 - 354 pages
...well-known corollary to the 32nd proposition of the first book of Euclid, which states that the summation of all the interior angles of any rectilineal figure, together with four right angles, are together equal to twice as many right angles as the figure has sides. In a traverse survey the number... | |
 | John Whitelaw - Surveying - 1902 - 634 pages
...measurements before leaving the ground, as " the sum of the interior angles of any rectilinear figure is equal to twice as many right angles as the figure has sides, less four right angles." In the case of Fig. 73, as the figure is four-sided the sum of the interior... | |
 | Education - 1902 - 942 pages
...that LP is less than LM. 3. Prove that the sum of the interior angles of any rectilineal figure is equal to twice as many right angles as the figure has sides, diminished by four right angles. 14. ABC is an equilateral triangle in which AD is drawn perpendicular... | |
 | Euclid, Rupert Deakin - Euclid's Elements - 1903 - 218 pages
...ABC and ACB double of the angle BAC. What is the size of the angle BAC ? ALTERNATIVE PROOF. Corollary 1.— All the interior angles of any rectilineal figure,...twice as many right angles as the figure has sides. Let ABCDE be any rectilineal figure; all the interior angles of ABCDE, together with four right angles,... | |
 | 1903 - 898 pages
...2 and 2A you may take which you please; but only one. So also of questions 3 and 3 A.] 1. Show that all the interior angles of any rectilineal figure...twice as many right angles as the figure has sides. A BCD is a quadrilateral figure, and the angles at A, B, C and D are bisected. Straight lines are drawn... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...ABCDEF oe the given polygon. To prove that the sum of the interior angles A, B, C, D, E, and F, is equal to twice as many right angles as the figure has sides minus two. If from any vertex as A, diagonals AC, AD, AE, are drawn, the polygon will be divided into... | |
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All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing... 
