 | Matthew Iley - 1820 - 512 σελίδες
...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 σελίδες
...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... | |
 | Benjamin Peirce - 1837 - 216 σελίδες
...AM and AN are equal. 151. Problem. To inscribe a circle in a given triangle ABC (fig. 84). Solution. Bisect the angles A and B by the lines AO and BO, and their point of intersection O is the centre of the required circle, and the perpendicular OD let... | |
 | James Bates Thomson - 1844 - 268 σελίδες
...equal to AB, and also the angle CAD to CAB. PROBLEM XV. To inscribe a circle in a given triangle ABC. Bisect the angles A and B by the lines AO and BO,...perpendiculars OD, OE, OF, on the three sides of the triangle : /^S» these perpendiculars will all be ^ equal. For, by construction, we have the angle D AO = O... | |
 | Euclides - 1846 - 292 σελίδες
...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... | |
 | Charles Davies - 1846 - 254 σελίδες
...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... | |
 | George Roberts Perkins - 1847 - 326 σελίδες
...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 σελίδες
...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 σελίδες
...equal to AB, and also the angle CAD to CAB. And as there can be but one line bisecting the angle BAC, it follows, that the line which bisects the angle...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... | |
 | Elias Loomis - 1849 - 252 σελίδες
...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 required to inscribe a circle in it. Bisect the angles B and C by the lines BD, CD, meeting each... | |
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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 at the point 0. 
