| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...equiangular to the triangle DEF, and it is described about the circle ABC. QEF PROPOSITION 4. PROBLEM. **To inscribe a circle in a given triangle. Let ABC be the given triangle** : it is required to inscribe a circle in the triangle ABC. Bisect the angles ABC, ACB, by the straight... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...equiangular to the triangle DEF, and it is described about the circle ABC. QEF PROPOSITION 4. PROBLEM. **To inscribe a circle in a given triangle. Let ABC be the given triangle** : it is required to inscribe a circle in the triangle ABC. Bisect the angles ABC, ACB, by the straight... | |
| Charles Davies - Geometry - 1870 - 398 pages
...tangent to the circle (Bk. II. Th. 'v). PROBLEM xix / To inscribe a circle in a given triangle. Let ABG **be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting** at the point O. Prom O, let fall the perpendiculars OD, OE, OF, on the three sides of the triangle... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...be drawn; for the circumference whose center is D intersects the given circumference in two points. **PROBLEM xv. To inscribe a circle in a given triangle. Let ABC be the given triangle** ; it is equired to inscribe a circle in it. Bisect the angles B and C by the ines BD, CD, meeting each... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...possible. If one circle is wholly within the other, there is no solution. PROPOSITION XLI.— PROBLEM. 94. **To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect** any two of its angles, aa B and C, by straight lines meeting in O. From the point O let fall perpendiculars... | |
| Henry William Watson - Geometry - 1871 - 316 pages
...through this point and at the point to draw a straight line perpendicular to this diameter. PROBLEM 13. **To inscribe a circle in a given triangle. Let ABC be the given triangle.** It is required to inscribe a circle in ABC. If possible, let there be a circle touching the sides of... | |
| Charles Davies - Geometry - 1872 - 464 pages
...to the angle CAD. The tangents are therefore equal, and the line AC bisects the angle between them. **PROBLEM XV. To inscribe a circle in a given triangle....triangle. Bisect the angles A and B, by the lines** A 0 and BO, meeting in the p9int O (Prob. V.) ; from the point 0 let fall the perpendiculars OD, OE,... | |
| William Frothingham Bradbury - Geometry - 1872 - 124 pages
...through any three given points ; or a circle circumscribed about a given triangle. PROBLEM XIII. 16. **To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect** any two of its angles. With the point D, where the two bisecting lines meet, as a centre, with a radius... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...possible. If one circle is wholly within the other, there is no solution. PROPOSITION XLL—PROBLEM. 94. **To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect** any two of its angles, as B and C, by straight lines meeting in 0. From the point 0 let fall perpendiculars... | |
| William Frothingham Bradbury - Geometry - 1872 - 256 pages
...through any three given points ; or a circle circumscribed about a given triangle. PROBLEM XIII. 16. **To inscrIbe a circle in a given triangle. Let ABC be the given triangle. Bisect** any two of its angles. With the point D, where the two bisecting lines meet, as a centre, with a radius... | |
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