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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. "
Elements of Geometry: Containing the First Six Books of Euclid, with Two ... - Σελίδα 33
των John Playfair - 1795 - 400 σελίδες
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The elements of plane geometry, Τόμος 1

Mathematical association - 1884
...triangles make up the interior angles of the polygon, therefore the interior angles of the polygon together with four right angles are equal to twice as many right angles as the polygon has sides. QED Ex. 45. Prove Theor. 26 by joining one angular point of the polygon to all the...

The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - 1884
...equal to the angles formed by the second pair. THEOR. 36. All the interior angles of any convex polygon together with four right angles are equal to twice as many right angles as the polygon has sides. Let ABCDE be any convex polygon : A then shall all the interior angles of ABCDE...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885
...straight lines shall be in one and the same straight line. 2. 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. If all the angles of an octagon are equal to one another, find the value of each. 3. Equal triangles...

Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889
...perpendicular without producing the given line. 1. 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. There are two regular polygons, the number of sides of one is double the number of sides of...

Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - 1890 - 172 σελίδες
...one-third of two right angles, or to 60°. 63. THEOE. 6. All the interior angles of any rectilinieal figure together with four right angles, are equal to twice as many right angles as the figure has sides (Euc. I. 32. Cor. 1). Hence the angles of a regular polygon are each equal to the quotient obtained...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 σελίδες
...CBA, BAC, BCA together=two rt. ^s. [Ax. 1. COROLLARY I.— 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. D For any rectl. figure, ABCDE, can be divided into as many As as the figure has sides by drawing...

A Text-book of Geometrical Deductions: Book I [-II] Corresponding ..., Βιβλίο 1

James Andrew Blaikie, William Thomson - 1891
...angles are together equal to two right angles. Cor. i.— 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. Cor. ii.— All the exterior angles of any rectilineal figure are together equal to four right...

The Colliery Manager's Handbook: A Comprehensive Treatise on the Laying-out ...

Caleb Pamely - 1891 - 578 σελίδες
...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...

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...




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