| Elias Loomis - Geometry - 1880 - 443 pages
...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... | |
| William Frothingham Bradbury - Geometry - 1880 - 240 pages
...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... | |
| William Mitchell Gillespie - Surveying - 1880 - 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. "... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 114 pages
...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,... | |
| 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.... | |
| 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... | |
| 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... | |
| Thomas Newton Andrews - Geometry - 1881 - 160 pages
...— 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... | |
| 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... | |
| Education, Higher - 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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