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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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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 Seiten
...F, which is the common vertex of all the triangles, arc equal to four right angles (I. 15, Cor. 2) ; Therefore all the angles of the figure, together with four right angles, arc equal to twice as many right angles as the figure has sides. COROLLARY 2. — All the exterior...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 413 Seiten
...Book, of which the above is a corollary, and prove that 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. Each angle of a regular polygon contains £ of a right angle ; what is the number of sides of...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 458 Seiten
...angles as the figure has sides. Let ABCDE be any polygon ; then all its interior angles A, B, C, D, E, together with four right angles, are equal to twice as many right angles as the figure has sides. £3 O For, from any point, F, within it, draw lines FA, FB, FC, etc., to all the angles. The...
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877
...figure, are equal to twice as many right angles as the figure has sides. But all the interior angles, together with four right angles, are equal to twice as many right angles as the figure has sides (I. 32, Cor. 1) ; Therefore all the interior angles, together with all the exterior angles, are...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...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. Cor. 2. All the exterior angles of any rectilineal Jigure, made by producing the sides successively...
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Elementary geometry

James Maurice Wilson - 1878
...angles are equal to twice as many right angles as the figure has sides ; •but all the interior angles, together with four right angles, are equal to twice as many right angles as the figure has sides; (Th. 26.) therefore all the exterior angles are equal to four right angles*. QED THEOREM 27....
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879
...the angles of all 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. COR. 2. All the exterior angles of any rectilineal figure, made by producing the sides successively...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...1) Therefore, if a side of any triangle, &c. QED Cor. 1. 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. For any figure ABCDE can be divided into as many As as it has sides, by drawing st. lines from...
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The Madras University Calendar, Band 1

University of Madras - 1879
...1 PM EUCLID ANT) ALGEBBA. F. 8. BTANS, MA, I. Prove that 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. II. Prove the proposition to which the following is a corollary : The difference of the squares...
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Geometry, Old and New, Its Problems and Principles: A Paper

Benjamin Gratz Brown - 1879 - 70 Seiten
...six-sided figure four times as great, or in other words, all the interior angles of any rectilinear figure together with four right angles, are equal to twice as many right angles as the figure has sides. Again, parallelograms upon equal bases and with the same altitude are equal. Of all figures...
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