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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. "
Elements of Geometry and Trigonometry - Page 64
by Adrien Marie Legendre - 1837 - 359 pages
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The new practical gager

Matthew Iley - 1820
...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...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pages
...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...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 159 pages
...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...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...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 : /^Sť these perpendiculars will all be ^ equal. For, by construction, we have the angle D AO = O...
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Elements of Drawing and Mensuration Applied to the Mechanic Arts: A Book for ...

Charles Davies - Geometrical drawing - 1846 - 240 pages
...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...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...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...
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Principles of geometry, mensuration, trigonometry, land-surveying, and ...

Thomas Tate (mathematical master.) - 1848
...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...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 359 pages
...hence they are equal (Book I. Prop. XVII.); hence AD is equal to AB, and also the angle CAD to CAB. And as there can be but one line bisecting 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...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 226 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 required to inscribe a circle in it. Bisect the angles B and C by the lines BD, CD, meeting each...
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