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" 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. "
Report on the examination for admission to the Royal military academy at ... - Pagina 19
di Woolwich roy. military acad - 1861
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889
...method of proof must be geometrical. Great importance will be attached to accuracy.] 1 . If a side of a triangle be produced, the exterior angle is equal to the two interior and opposite angles. Through the vertices of a triangle ABC straight lines, falling within the triangle, are drawn making...
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Practical Surveying: A Text-book for Students Preparing for Examinations Or ...

George William Usill - 1889 - 272 pagine
...same straight line are parallel to one another. 18. If a side of any triangle B c be produced to D, the exterior angle is equal to the two interior and opposite angles, and the IS three interior angles of every triangle are together equal to two right angles. 19. The exterior...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pagine
...congruent (I. 8), and have sides AE, DE parallel respectively to BC, AH (I. 27). PROPOSITION 32. THEOREM. If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are together equal to two right . angles. Let ABC be a A having one side BC produced to D ; then ext. L...
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Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 pagine
...method of proof must be geometrical. Great importance will be attached to accuracy^ 1. If a side of a triangle be produced, the exterior angle is equal...and the three interior angles of every triangle are together equal to two right angles. Prove the corollary with regard to the interior angles of any rectilineal...
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Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - 1890 - 172 pagine
...Hence every equilateral triangle is also equiangular, and vice versa. 62. THEOE. 5. If oue side of a triangle be produced, the exterior angle is equal...the two interior and opposite angles ; and the three angles of every triangle are together equal to two right angles (Euc. I. 32). Hence the angles of an...
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - 1891 - 79 pagine
...one another. 31. To draw a straight line through a given point parallel to a given straight line. 32. If a side of any triangle be produced, the exterior...and the three interior angles of every triangle are together equal to two right angles. 33. The straight lines which join the extremities of two equal...
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The Principles of Psychology, Volume 2

Herbert Spencer - 1892
...therefore also the angles CBA, BAC, ACB, are together equal to two right angles. "Therefore if aside of any triangle be produced, the exterior angle is...angles of every triangle are equal to two right angles. QED" Thus in each step by which the special conclusion IB reached, as well as in the step taken from...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898
...DEPARTMENT (YALE COLLEGE) GEOMETRY JUNE 1886. (Four out of five questions are required.) 1. If a side oí any triangle be produced, the exterior angle is equal...and the three interior angles of every triangle are together equal to two right angles. 2. (Problem) To describe a square on a given straight line. (Show...
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Yale University Entrance Examinations in Mathematics: 1884 to 1898

1898 - 208 pagine
...DEPARTMENT (YALE COLLEGE) GEOMETRY JUNE 1886. (Four out of five questions are required.) 1. If a side,of any triangle be produced, the exterior angle is equal...and the three interior angles of every triangle are together equal to two right angles. 2. (Problem) To describe a square on a given straight line. (Show...
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Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

Seymour Eaton - 1899 - 340 pagine
...is drawn through the given point A, parallel to the given straight line BC. PROPOSITION 32. THEOREM If a side of any triangle be produced, the exterior...interior angles of every triangle are equal to two riglit angles. Let ABC be a triangle, and let one of its sides BC be produced to D; then the exterior...
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