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" 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. "
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books - Σελίδα 56
των Euclid - 1765 - 464 σελίδες
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The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - 1892 - 167 σελίδες
...an isosceles triangle. LE 8 118. Corollary 1. All the interior angles of a closed rectilineal figwe together with four right angles are equal to twice as many right angles as the figure has sides. Let ABCDE... represent any rectilineal figure. Take a point P within the figure. Join P to each...

Plane Trigonometry

S. L. Loney - 1893
...regular decagon. The corollary to Eue. I. 32 states that 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. Let the angle of a decagon contain x right angles, so that all the angles are together equal...

Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1894
...to BC ; show that AE is equal to AD. (12.) 9. 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. A five sided figure has four equal angles, and the fifth angle equals a half of one of the four...

Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1897
...the triangles are equal in all respects. 3. Show that all the interior angles of any rectilineal 7 figure, together with four right angles, are equal to twice as many right angles as the figure has sides. 4. Parallelograms on equal bases, and between the 18 same parallels, are equal in area. 5. The...

Plane and Solid Geometry

James Howard Gore - 1898 - 210 σελίδες
...exterior angles is equal to twice as many right angles as the figure has sides. But by (125) the interior angles are equal to twice as many right angles as the figure has sides, less four right angles. Therefore the exterior angles alone are equal to four right angles....

Engineering Drawing and Design (A Text-book Of): Including Practical ...

Sidney Herbert Wells - 1900
...depends upon Corollary I. of Euclid i., 32, which says that " the interior angles of any straight lined figure together with four right angles are equal to twice as many right angles as the figure has sides." The most common of the regular polygons used in engineering designs are the pentagon (five-sided),...

A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Βιβλίο 1

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 σελίδες
...Robert Simson, who edited Euclid's text in 1756. COROLLARY 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. Let ABODE be any rectilineal figure. Take F, any point within it, and join F to each of the...

Manual

1903
...only one. So also of questions 3 and 3 A.] 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. A BCD is a quadrilateral figure, and the angles at A, B, C and D are bisected. Straight lines...

Elementary Plane Geometry: Inductive and Deductive

Alfred Baker - 1903 - 144 σελίδες
...From the result reached in the previous question, show that all the interior angles of any polygon are equal to twice as many right angles as the figure has angles (or sides), less four right angles. 5. How many right angles is the sum of all the angles in...

The Colliery Manager's Handbook

Caleb Pamely - 1904
...tested by Euclid, for, " The sum of all the interior angles of any rectilinear figure, together with 4 right angles, are equal to twice as many right angles as the figure has sides." This is not so thorough a test as the plotting, because it checks only the angles taken and...




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