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" ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 376
by Rev. John Allen - 1822 - 494 pages
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A Treatise on Land-Surveying Comprising The Theory Developed from Five ...

W.M. Gillespie, A.M., Civ. Eng - 1855
...proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is equal to twice as many right angles, as the figure has sides less two ; since the figure can be divided into that number of triangles. Hence this common rule. "...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...superposition. 3. Prove that all the internal angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides; and that all the external angles are together equal to four right angles. In what sense are these propositions...
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Elementary text book for young surveyors and levellers

Henry James Castle - Surveying - 1856 - 185 pages
...angles are the exterior angles of an irregular polygon ; and as the sum of all the interior angles are equal to twice as many right angles, as the figure has sides, wanting four ; and as the sum of all the exterior, together with all the interior angles, are equal...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...straight lines from a point F within the figure to each of the angles. And by the last proposition all the angles of these triangles are equal to twice as many right angles as there are triangles or sides to the figure. And the same angles are equal to the internal angles of...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Surveying - 1856 - 464 pages
...proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is equal to twice as many right angles, as the figure has sides less two ; since the figure can be divided into that number of triangles. Hence this common rule. "...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Surveying - 1857 - 524 pages
...proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is equal to twice as many right angles, as the figure has sides less two ; since the figure can be divided into that number of triangles. Hence this common rule. "...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...F, that is, together with four right angles (Prop. V., Cor. 2). Therefore the angles of the polygon are equal to twice as many right angles as the figure has sides, wanting four right angles. Cor. 1. The sum of the angles of a quadrilateral is four right angles ;...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...and in an irregular polygon they may be all unequal. The interior angles of a polygon are together equal to twice as many right angles as the figure has sides, less four. On this is based the theory of the traverse, of which further explanation will be given...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

Surveying - 1878 - 508 pages
...proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is equal to twice as many right angles, as the figure has sides less two; since the figure can be divided into that number of triangles. Hence this common rule. "...
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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 132 pages
...other, the remaining angles must be equal. Cor. 2. The sum of all the interior angles of a polygon is equal to twice as many right angles as the figure has sides, minus four right angles. In the case of the triangle, this corollary has just been demonstrated; for,...
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