 | Henry William Watson, Edward John Routh - Mathematics - 1860 - 240 pages
...through O and cut the circle in C' and DE in P. Then as before the angle APD = ABC' = a right angle. iv. Describe an isosceles triangle having each of the angles at the base double of the third angle. If A be the vertex, and BD the base of the constructed triangle, D being one of the points of intersection... | |
 | Mathematics - 1860 - 294 pages
...STUDENTS. to find x and y by quadratics. — Communicated by Prof. K W. EVANS, Marietta College, Ohio. II. Describe an isosceles triangle having each of the angles at the base double of the third angle. III. Which is greater, 2 tan~ 1 (y/2 — 1), or 3 tan- 1 £ -f- tan~ 1 -fa ? — Communicated by PROF.... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...extremities of the other three, and be described about the square ABCD. QEF PROPOSITION X. PROBLEM. To describe an isosceles triangle, having each of the angles at the bate double of the third angle. Take any straight line AB, and diride it in the point C, (ll. 11.)... | |
 | Euclides - 1861 - 464 pages
...6 Ax. 7 & 6. I. Sim. Ax. 1. 9, III. 7 8 9 10 D. 8. 11 Dcf. 6, IV. PROP. 10. — PROB. To construct an isosceles triangle, having each of the angles at the base double of the third, or vertical angle. CON. Pst. 3. 1. IV. Pet. 1. 5, IV. 11, II. To divide a given line into two parts,... | |
 | War office - 1861 - 714 pages
...Describe an isosceles triangle having each of the angles at the base double of the third angle. Also describe an isosceles triangle having each of the angles at the base one-third of the third angle. 2. If two triangles have one angle of the one equal to one angle of the... | |
 | Euclides - 1862 - 172 pages
...of the third angle. (References— Prop. i. 5, 6, 32 ; n. 11 ; in. 32, 37 ; iv. 1, 5.) CONSTRUCTION Take any straight line AB, and divide it in the point C, so that tht rectangle AB, BC, may be equal to the square of CA ; (n. 11) and from the centre A, at the distance... | |
 | Euclides - 1862 - 140 pages
...triangle. 9. Inscribe a square in a given semicircle. Prop. 10 to 16. 10. On a given straight line as base, describe an isosceles triangle, having each of the angles at the base one-third of the vertical angle. 11. The square of one of the diagonals of a regular pentagon inscribed... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...constructed on DF as the one given line is to the other. PROBLEM XXXIV. 339. Upon a given base to construct an isosceles triangle, having each of the angles at the base double the vertical angle. Let AB be the given base. Produce AB to some point C till the rectangle ACXBC shall... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...constructed on DP as the one given line is to the other. PKOBLEM XXXIV. 339. Upon a given base to construct an isosceles triangle, having each of the angles at the base double the г^ег Heal angle. Let А В be the given base. Produce А В to some point С till the rectangle... | |
 | Euclides - 1863 - 122 pages
...triangle ABD has each of its angles ABD and ADB double of the angle BAD. PHOP. X. (PnaELEM.)— 7 ' 0 describe an isosceles triangle, having each, of the angles at the base rfowWe of the third angle. Join DC, and about the triangle ADC describe the circle ACD (IV. 5). Because... | |
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PBOR. —To describe an isosceles triangle, having each of the angles at the base, double of the third angle. Take any straight... 
