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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... "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 35
by Robert Simson - 1806 - 518 pages
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 210 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....
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Book 1

Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 304 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...
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Engineering Drawing and Design (A Text-book Of): Including Practical ...

Sidney Herbert Wells - Machine design - 1900
...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),...
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Land Surveying and Levelling

Arthur Thomas Walmisley - Leveling - 1900 - 332 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...
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Surveying, as Practiced by Civil Engineers and Surveyors ...: Intended as a ...

John Whitelaw - Surveying - 1902 - 516 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...
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Report of the Committee of Council on Education in Scotland...[without Appendix]

Education - 1902
...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...
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Euclid, Book 1

Euclid, Rupert Deakin - Euclid's Elements - 1903 - 164 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,...
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Manual

1903
...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...
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Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903
...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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Interim Report of the Commissioners on Certain Parts of Primary Education ...

New South Wales. Commission on primary, secondary, technical, and other branches of education - Education - 1903 - 619 pages
...that LP ie 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, dimished by four right angles. ABC is an equilateral triangle in which AD is drawn perpendicular to...
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