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" Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. "
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books - Page 56
by Euclid - 1765 - 464 pages
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...also without construction, by 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...
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The Popular Educator, Volume 5

1856
...triangles thus formed are equal to all the angles of the figure (Const.) ; therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure nas sides (Лх. 1). QED The demonstration of Euclid's Cor. II. viz. "that all the pxterior angles...
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Elementary text book for young surveyors and levellers

Henry James Castle - Surveying - 1856 - 185 pages
...that these 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...
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The Educational record, with the proceedings at large of the ..., Volumes 3-4

British and foreign school society - 1857
...produced to meet the alternate sides, also produced, the angles formed by these lines, together with eight right angles, are equal to twice as many right angles as the polygon has sides. 4. If two chords intersect in a circle, the difference of their squares is equal...
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The English Journal of Education, Volumes 11-13

Education - 1857
...produced to meet the alternate sides, also produced, the angles formed by these lines, together with eight right angles are equal to twice as many right angles as the polygon has sides. 4. If two chords intersect in a circle, the difference of their squares is equal...
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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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...sides, then n0 is the sum of all the interior angles. But 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 sides, that is, if ir be assumed to designate two right angles, .'. 9 + 2ir = mr, and nfl = mr —...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860
...angles of a triangle are together equal to two right angles ; and all the angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. 6. The opposite sides and angles of parallelograms are equal to one another, and the diameter...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...wherefore the salient angles F, G, H, T, K, with twice the angles m, n, , e, w, that is, with eight right angles, are equal to twice as many right angles as the figure has sides. COR. — The salient angles with four right angles, are equal to the interior angles of the...
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The Mathematical Monthly, Volume 2

1860
...figure must be aliquot parts of the circle or of four right angles. All the angles of any such figure are equal to twice as many right angles as the figure has sides minus four right angles, or if be the number of sides, the sum of all the angles is (2n —...
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