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" 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing... "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 35
av Robert Simson - 1806 - 518 sider
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 sider
...together equal to two right angles. [Axiom 1. Wherefore, if a side of any triangle &c. <JE». COROLLARY 1. All the interior angles of any rectilineal figure,...equal to twice as many right angles as the figure has side*. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides,...
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An elementary treatise on geometrical drawing

John Henry Robson - 1880
...problem is the sth Proposition of Euclid's Fourth Book. 12. By Euc. I. 32, Cor. 1, it is proved that " All the Interior angles of any Rectilineal figure,..."twice as many right angles as the figure has " sides." If, therefore, we suppose the polygon to have n sides, All its interior angles + 4.90 .= 272.90 . -....
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Examination papers, and division lists, &c. [afterw.] General certificate of ...

Oxford univ, local exams - 1880
...explain what you mean by a straight line touching a circle, and by a straight line placed in a circle. 2. All the interior angles of any rectilineal figure,...twice as many right angles as the figure has sides. 3. If the square described on one side of a triangle be equal to the squares described on the other...
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(Report).

Elizabethan club - 1880
...of the acute angles at the other point, and similarly of the obtuse angles. 3. All the angles of a rectilineal figure, together with four right angles,...twice as many right angles as the figure has sides. A floor has to be laid with tiles in the form of regular figures all equal and similar ; show what...
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Nature, Volum 21

Sir Norman Lockyer - 1880
...the flat angle we may take Theorem XXVI. of the syllabus, that the interior angles of any polygon, together with four right angles, are equal to twice as many right angles as the figure has sides. In the new notation we would say that the sum of the interior angles of the polygon is equal to a number...
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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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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...ACB are equal (Ax. 1) to two right angles. Wherefore, if a side of any triangle be produced, &c. a ED COR. 1. — All the interior angles of any rectilineal...twice as many right angles as the figure has sides. Let ABCDE be any rectilineal figure. All the interior angles ABC, BCD, &c. together with four right...
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Practical Geometry for Second Grade Art-pupils and Private Schools

Thomas Newton Andrews - 1881 - 160 sider
...setting off the angles at the base found thus: — In Euclid, Book I., Prop, xxxi11., it is proved that "All the interior angles of any rectilineal figure,...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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