| Henry William Watson - 1860
...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
...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 - 361 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
...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 - 12 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
...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
...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 - 490 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 - 490 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
...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... | |
| |