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" 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. "
Elements of Geometry: With Practical Applications ... - Page 139
by George Roberts Perkins - 1847 - 308 pages
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The new practical gager

Matthew Iley - 1820 - 512 pages
...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 - 236 pages
...triangle 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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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...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 be the given 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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...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. 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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...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 ABC be the given 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...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...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 Drawing and Mensuration Applied to the Mechanic Arts: A Book for ...

Charles Davies - Geometrical drawing - 1846 - 254 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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Principles of geometry, mensuration, trigonometry, land-surveying, and ...

Thomas Tate (mathematical master.) - 1848 - 284 pages
...Cor. 3. 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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Mensuration, Mechanical Powers and Machinery: The Principles of Mensuration ...

Daniel Adams - Arithmetic - 1849 - 142 pages
...and the radius DE, describe a circle, and it will be inscribed in the given polygon. PROBLEM XXXIII. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect any two angles, as A and B, and the point D, where the bisecting lines cross each other, will be the...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...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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