Books Books IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles. Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 105
by Euclides - 1858 ## Principles of psychology

Herbert Spencer - Philosophy - 1910 - 780 pages
...foregoing theorem is inconveniently long. We shall find a titter one in Proposition xxxii. " If the side of any triangle be produced, the exterior angle...every triangle are together equal to two right angles. " Let ABC be a triangle, and let one of its sides BC be produced to D; then the exterior angle ACD... ## The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 360 pages
...is equal to two right angles. Euclid stated this as follows : " In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles." This states more than is necessary for the basal fact... ## The Sewerage of Sea Coast Towns

Henry Charles Adams - Sewerage - 1911 - 196 pages
...object with regard to the coast, by observations taken from the object. They are Euclid I. (32), " The three interior angles of every triangle are together equal to two right angles " ; Euclid III. (20), " The angle at the centre of a circle is double that of the angle at the circumference... ## The Teaching of Mathematics in the United Kingdom

Great Britain. Board of Education - Mathematics - 1912 - 632 pages
...polygons. Measure exterior angle and the two interior and opposite angles of a triangle, and show that the exterior angle is equal to the two interior and opposite angles. Show that the greater angle of a triangle is opposite to the greatei side, &c. Third Year. Simple interest.... ## Special Reports on Educational Subjects, Volumes 26-27

Great Britain. Board of Education - Education - 1912 - 1048 pages
...polygons. Measure exterior angle and the two interior and opposite angles of a triangle, and show that the exterior angle is equal to the two interior and opposite angles. Show that the greater angle of a triangle is opposite to the greater side, &c. Third Tear. Arithmetic.... ## The New Age Magazine, Volume 19

Freemasonry - 1913 - 844 pages
...Forty-seventh Problem, there are several other equally important problems ascribed to him. Among these are: the interior angles of every triangle are together equal to two right angles; that the only polygons which fill up the whole space about a given point are the equilateral triangle,... ## Criticism at a Venture

Geraldine Emma Hodgson - English poetry - 1919 - 242 pages
...the domain of the exact sciences. It was understood that, in a general way, such propositions as that the three interior angles of every triangle are together equal to two right angles, are, cceteris paribus, sufficiently demonstrable to pass muster for daily use. Though this might be... ## The Teaching of Geometry in Schools: A Report Prepared for the Mathematical ...

Mathematical Association - Geometry - 1923 - 88 pages
...draw a straight line parallel to a given straight line. I. 32 : In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles. I. 47 : In right-angled triangles the square on the side... ## The Foundations of Geometry and the Non-Euclidean Plane

G.E. Martin - Mathematics - 1997 - 536 pages
...to draw a straight line parallel to a given straight line. 32. In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles. 33. The straight lines joining equal and parallel straight... 