This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1874 Excerpt: ...triangle having one of the acute angles one.fourth of the other. 73. Describe a right.angled triangle having one of the acute angles half as large again as the other. 74. Describe a triangle having one of its angles half of another and treble the remaining angle. BOOK IV. 1. Describe a circle touching one side of a ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1874 Excerpt: ...triangle having one of the acute angles one.fourth of the other. 73. Describe a right.angled triangle having one of the acute angles half as large again as the other. 74. Describe a triangle having one of its angles half of another and treble the remaining angle. BOOK IV. 1. Describe a circle touching one side of a triangle, and the other two sides produced. 2. On a given straight line describe a regular hexagon. 3. Find a point which is equally distant from three given points. Is this problem always possible? 4. Inscribe a circle in a rhombus. Can a circle be described about a rhombus? 5. Describe a parallelogram about a circle, having an angle equal to a given angle. 6. If a parallelogram be described about a circle, it will be equilateral. 7. Determine the condition that the straight line joining the centres of the circles inscribed in, and described about a given triangle, may pass through one of the angular points of the triangle. 8. What relation exists between the sides of a triangle when the centres of the circles inscribed in and described about the triangle coincide? 9. Describe a regular hexagon having its angular points in the sides of a given equilateral triangle. 10. If the chords which bisect two angles of a triangle inscribed in a circle be equal, prove that either the angles are equal or else the third angle is equal to the angle of an equilateral triangle. 11. If one square be inscribed in another, the difference between their areas is equal to twice the rectangle contained by the segments of any one of the sides of the larger square. 12. If one square be inscribed in another, the area of the smaller square is equal to the squares on the segments of a side of the larger square. 13. Apply the previous deduction to shew how the square descri...
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