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. Elements of geometry, containing the first two (third and fourth) books of ... - Page 52
by Euclides - 1871 ## The examination papers as set for the preliminary literary examination of ...

...the same : and thence show that two straight lines cannot have a common segment. 4. If the side of a triangle be produced, the exterior angle is equal...every triangle are together equal to two right angles. 5. Describe a square on a given straight line. 6. Define " a gnomon" and " a rectangle." 7. The parallelograms... ## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...drawn through the given point A parallel to the given straight line BC. PROPOSITION XXXII. THEOREM. If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are equal to two right angles. Given a triangle ABC, having one of its sides BC produced to D ; to prove... ## REPORT OF THE DIRECTOR OF PUBLIC INSTRUCTION, BOMBAY, FOR THE YEAR 1858-59.

...\ , <z, O\ '4' 3v A ' 4\ K ' 2 ^ 3 6. If a side of any triangle be produced, the exterior nngle ia equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles. Show how the corners of a triangular piece of paper may be turned down,... ## Lectures Delivered Before the Young Men's Christian Association ..., Volume 15

...a triangle be produced, the exterior angle is equal to the sum of the two angles which subtend it ; and the three interior angles of every triangle are together equal to two right angles." One day, when he was busied with the demonstration of this theorem, his father caught him in the act... ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1860 - 317 pages
...PROP. XXXII. TIIEOR. If a side of any triangle lie produced, the exterior angle is equal to the tiro interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the... ## The Mysteries of Freemasonry

John Fellows - Mysteries, Religious - 1860 - 366 pages
...four. Of the geometrical theorems ascribed to Pythagoras, the following are the principal ; that 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,... ## Report on the examination for admission to the Royal military academy at ...

...I0«(s-s1)=*2-s. 9. Find the value of - — --- Q'^— by means of 10o the logarithmic tables. 10. If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are equal to two right angles. The angle between the lines bisecting two adjacent exterior angles of any... ## The Oxford examiner, ed. by M.W.I. Shilleto, Issues 1-5

Mary W I. Shilleto - 1882
...In Euclid's figure for this proposition, if BG, CF meet in H, show that AH bisects the angle BAG. 2. If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are equal to two right angles. Enunciate and prove the corollaries to this proposition. Trisect a right... ## The Principles of Psychology, Volume 2

Herbert Spencer - Psychology - 1882
...case. therefore also the angles CBA, BAC, ACB, are together equal to two right angles. " Therefore if a side of any triangle be produced, the exterior...and the three interior angles of every triangle are equal to two right angles. QED" Thus in each step by which the special conclusion is reached, as well... 