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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 Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 Seiten
...Wherefore, if a side of any triangle &c. Q EB COROLLARY 1. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as thejigure has side.". For any rectilineal figure ABCDE can be divided into as many triangles as the...
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A Dictionary of Science, Literature, & Art: Comprising the ..., Band 3

William Thomas Brande, George William Cox - 1867
...polygons, the first corollary to his prop. 32, book i. (according to which all the interior angles, together with four right angles, are equal to twice as many right angles as tie figure has sides), is also true for concave polygons. His second corollary, however, according...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 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. COB. 2. All the exterior angles of any rectilineal figure, made by producing the sides successively...
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Modern Methods in Elementary Geometry

E. M. Reynolds - 1868 - 112 Seiten
...angles are together equal to twice as many right "angles as the figure has sides. , Hence the interior angles are equal to twice as many right angles as the figure has sides, diminished by four right angles. COR. The exterior angle of any regular polygon of n sides is...
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Annual Report of the Commissioners ..., Band 36

1870
...hours a day. Geometry and Mensuration. — 1. Show 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. (12 marks). 2. Enunciate and prove the 32nd proposition of the First Book of Euclid's Elements....
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On Intelligence

Hippolyte Taine - 1871 - 542 Seiten
...together equal to four right angles ; hence it follows that the polygon contains a number of angles which, together with four right angles, are equal to twice as many right angles as there are sides. — Here the explanatory intermediate is a character comprised in all the elements...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 58 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 foui right angles...
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Euclid's Elements of Geometry

Euclid - 1872 - 261 Seiten
...internal, are equal to twice as many right angles as there are sides of the figure ; but the internal with four right angles, are equal to twice as many right angles as there are sides of the figure (by Cor. 6) ; take away from both the internal angles, and, the external...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873
...triangles; that is, together with four right angles. Therefore all the angles of the figure, together witb four right angles, are equal to twice as many right angles as the figure has sides. XXXIII. — The straight lines which join the extremities of two equal and parallel straight...
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873
...angles (Prop. 9). Proposition 32.— Theorem. The inner angles of a rectilinear figure, with four riyht angles, are equal to twice as many right angles as the figure lMS sides. The figure may be divided into as p many triangles as it has sides, by joining the angular...
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