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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. "
The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 27
by Euclid, James Thomson - 1845 - 352 pages
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three angles of every triangle are together equal to two right angles. Let ABC (Fig. 9) be a triangle, and let one of its sides, BC, be produced to D ; the exterior angle ACD is...
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The English Journal of Education, Volumes 11-13

Education - 1857 - 1266 pages
...efficient. EUCLID. FIRST YEAR. SECTION I. — 1. The angles at the base of an isosceles triangle arc equal. 2. The three interior angles of every triangle are together equal to two right angles. 3. To a given straight line apply a rectangle equal to a given rectilineal figure. SECTION II. —...
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Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 390 pages
...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 together equal to two right angles. At what angles are the sides of a regular duodecagon inclined to each other? 3. If a straight line...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...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 together equal to two right angles. CONSTRUCTION. — P. 31. To draw a st. line, through a fjiven point, parallel to a given st. line....
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Parliamentary Papers, Volume 25

Great Britain. Parliament. House of Commons - Bills, Legislative - 1858 - 694 pages
...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 together equal to two right angles. 4. Enunciate and prove the corollaries of the last proposition. 5. PROP. XLIV. — To a given straight...
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Report of Her Majesty's Civil Service Commissioners: Together with ..., Volume 3

1858 - 398 pages
...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 together equal to two right angles. 4. Enunciate and prove the corollaries of the last proposition. 5. PUOP. XLIV. — To a given straight...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pages
...of a triangle be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of every triangle are together equal to two right angles. State Euclid's corollaries to this proposition. VOLUNTARY PORTION. 1. Given the centre of the circle...
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A Treatise on Practical Mensuration

Anthony Nesbit - Measurement - 1859 - 494 pages
...produced to D; the exterior angle ACD is equal to the two interior and opposite angles CAB, ABC ; also the three interior angles of every triangle are together equal to two right angles. (Euc. I. 32. Simp. I. 9 & 10. Em. H. 1 & 2.) THEOREM V. Parallelograms standing on the same base, and...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 pages
...triangle be produced the exterior angle is equal to both the two interior and opposite angles, and the three interior angles of every triangle are together equal to two right angles. Hence show that all the exterior angles of any rectilineal figure made by producing the sides successively...
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Return to an Address of the Honourable the House of Commons, Dated 10 ...

Education - 1859 - 412 pages
...than the third side. Madras ^e difference of any two sides is always less than the third side. " 4. The three interior angles of every triangle are together equal to two right angles. How many degrees are there in an angle of a regular octagon? 5. In any right angled triangle, tire...
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