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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, the parts read in the University of Cambridge [book ... - Side 33
av Euclides - 1846
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1880 - 443 sider
...is the complement of the other. PROPOSITION XXVIII. THEOREM. All the interior angles of a polygon, together with four right angles, are equal to twice as many right angles as the figure IMS sides. Let ABCDE be any polygon ; then all its interior angles A, B, C, D, E, together with four...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1880 - 524 sider
...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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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - 1880 - 240 sider
...minus two. Let ABCDEF be the given polygon ; the sum of all the interior angles A, B, C, D, E, F, is equal to twice as many right angles as the figure has sides minus two. For if from any vertex A, diagonals AC, AD, AE, are drawn, the polygon will be divided into...
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Key to Exercises in Euclid

Isaac Todhunter - 1880 - 114 sider
...Similarly AD is equal to FC. 47. The figure has eight equal sides, and eight equal angles : the interior angles of the figure together with four right angles are equal to sixteen right angles : therefore all the interior angles of the figure are equal to twelve right angles,...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...angles of these triangles are equal to twico as mauy right angles as the figure has sides. Therefore all the angles of the figure together with four right...All the exterior angles of any rectilineal figure, made by producing the sides successively in the same direction, are together equal to four right angles....
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The practical surveyor

Thomas Holloway (surveyor.) - 1881
...four right angles or three hundred and sixty degrees. 3. All the interior angles of any rectilineal figure, together with four right angles, are equal...twice as many right angles as the figure has sides. Although further systems of proof could easily be quoted, I consider the foregoing quite sufficient...
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Guide to preliminary army examination

John Gibson - 1881
...greater side, or has the greater side opposite to it. 3. All the interior angles of any rectilineal figure, together with four right angles, are equal...twice as many right angles as the figure has sides. 4. Describe a parallelogram that shall be equal to a given triangle BCD, and have one of its angles...
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Practical Geometry for Second Grade Art-pupils and Private Schools

Thomas Newton Andrews - 1881 - 160 sider
...— In Euclid, Book I., Prop, xxxi11., it is proved that "All the interior angles of any rectilineal figure, together with four right angles, are equal...twice as many right angles as the figure has sides." If we have to describe a pentagon on the base AB, we must first calculate the angles at the base. Thus...
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The Competitor, Volumer 1-2

1882
...In corollaries to the same proposition it is shown that all the internal angles of any rectilineal figure, together with four right angles, are equal...twice as many right angles as the figure has sides ; also, that all the external angles of any rectilineal figure formed by producing the sides in the...
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The Cambridge Examiner, Volum 2

1882
...also equal, the triangles must be equal in every respect. 4 All the interior angles of any rectilineal figure together with four right angles, are equal...twice as many right angles as the figure has sides. 5. Equal triangles upon equal bases in the same straight line and towards the same parts are between...
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