 | Matthew Iley - 1820 - 512 Seiten
...at right angles. Then join AB, BD, DC, and CA ; the figure ABCD is the square required. PROBLEM III. To inscribe a circle in a given triangle. Let ABC be the triangle in which ii is required to inscribe a circle. About the angular points B and C, with any convenient... | |
 | Euclid - 1826 - 234 Seiten
...equiangular to the triangle DEF. Therefore about a given circle, &c. QEF I PROPOSITION IV. 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, AC в, by the right... | |
 | Adrien Marie Legendre - 1828 - 346 Seiten
...CB=CD ; hence they are equal ; hence AD is equal to AB, and also the angle CAD to CAB. PROBLEM. 1 53. To inscribe a circle in a given triangle. Let ABC...triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point O ; from the point O, let fall the perpendiculars OD, OE, OF, on the... | |
 | Adrien Marie Legendre - 1836 - 394 Seiten
...the line which bisects the angle formed by two tangents, must pass through the centre .of the circle. PROBLEM XV. To inscribe a circle in a given triangle....triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point O ; from the point O, let fall the perpendiculars OD, OE, OF, on the... | |
 | Nathan Scholfield - 1845 - 894 Seiten
...segment would be a semicircle; and consequently the centre would be the middle of AB. PROBLEM XVIII. To inscribe a circle in a given triangle. • Let...triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point O ; from the point O, let fall the perpendiculars OD, OE, OF, on the... | |
 | Charles Davies - 1846 - 254 Seiten
...point of intersection, draw the lines AD and CD, and ABCD will be the required rhombus. 42. How do you inscribe a circle in a given triangle? Let ABC be the given triangle. Bisect either two of the angles, as A and C, by the lines AO and CO, and the point of intersection O will... | |
 | Euclides - 1846 - 292 Seiten
...equiangular to the given triangle DEF, and it is described about the given circle ABC. QEF PROP. IV. PBOB. 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... | |
 | George Roberts Perkins - 1847 - 326 Seiten
...lines AB, AC, must be situated in the line AD, which bisects the angle BAC. PROPOSITION III. PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angle BAC by the line AD ; also bisect the angle ABC by the line BD ( B. I, Prop. xi). Then, if from... | |
 | Thomas Tate (mathematical master.) - 1848 - 284 Seiten
...Regular polygons are not only equilateral, but also equiangular ; thus, /ABC=Z.BCD — &c. 69. PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle; bisect A the angles BCA and CBA (Art. 21.) by the lines CD and BD meeting each other in the point D; from... | |
 | Charles Davies - 1849 - 372 Seiten
...the line which bisects the angle formed by two tangents^ must pass through the centre of the circle. PROBLEM XV. To inscribe a circle in a given triangle. Let ABC be the given triangle. linn, we have the angle DAO=OAF, the right angle ADO = AFO ; hence the third angle AOD is equal to... | |
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PROBLEM XV. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point 0 (Prob. 
