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" F, which is the common vertex of the triangles ; that is, together with four right angles. 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. "
The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... - Seite 38
von Robert Simson - 1775 - 520 Seiten
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...all the angles of these triangles are equal to twice as many right angles as the figure has sides. Therefore all the angles of the figure together with...equal to twice as many right angles as the figure has sides. СOR. 2. — All the exterior angles of any rectilineal figure, made by producing the sides...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...angles as there are triangles or sides to the figure. And the same angles are equal to the internal angles of the figure, together with the angles at...equal to twice as many right angles as the figure has sides. XVI. If two triangles have two sides of the one equal to two sides of the other, each to each,...
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The Popular Educator, Band 5

1856
...all the angles of all the triangles thus formed are equal to all the angles of the figure (Const.) ; therefore all the angles of the figure, together with...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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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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Elementary text book for young surveyors and levellers

Henry James Castle - 1856 - 185 Seiten
...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 ..., Bände 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, Bände 11-13

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 - 1858 - 234 Seiten
...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 plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...with the angles at the point O, which is the common vertex of the triangles ; that is (I. 15, Cor. 2), together with four right angles. Therefore all the...equal to twice as many right angles as the figure has sides. Let the sum of the interior angles be denoted by I, the number of sides by n, and a right angle...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 Seiten
...that the angles of the triangles are equal to twice as many right angles as the figure has sides ; therefore all the angles of the figure together with...equal to twice as many right angles as the figure has sides. COE. 2. All the exterior angles of any rectilineal figure, made by producing the sides successively...
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