| 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.... | |
| 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 - 200 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 - 344 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 - 636 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 - 212 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... | |
| Alfred Baker - Geometry - 1903 - 154 pages
...From the result reached in the previous question, show that all the interior angles of any polygon **are equal to twice as many right angles as the figure has** angles (or sides), less four right angles. 5. How many right angles is the sum of all the angles in... | |
| American School (Chicago, Ill.) - Engineering - 1903 - 392 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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