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" The difference of the angles at the base of any triangle, is double the angle contained by a line drawn from the vertex perpendicular to the base, and another bisecting the angle at the vertex. "
Key to Robinson's New Geometry and Trigonometry, and Conic Sections and ... - Page 46
by Horatio Nelson Robinson - 1875
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...DBE. In the same way it may be shewn to be equal to FEC and ADF; and .-. it is one fourth of ABC. (5.) The difference .of the angles at the base of any triangle...base, and another bisecting the angle at the vertex. • From B the vertex of the triangle ABC let BE be drawn perpendicular to the base, and BD bisecting...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...DBE. In the same way it may be shewn to be equal to FEC and ADF; and .-. it is one fourth of ABC. (5.) The difference of the angles at the base of any triangle...base, and another bisecting the angle at the vertex. From B .the vertex of the triangle ABC let BE be drawn perpendicular to the base, and BD bisecting...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Geometry - 1821 - 898 pages
...ADF; and /. it is one fourth of ABC. (5.) The difference of the angles at the base of any trķangle is double the angle contained by a line drawn from...base, and another bisecting the angle at the vertex. From В the vertex of the triangle ABC\et BE be drawn perpendicular to the base, and BD bisecting the...
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...be joined, the triangle, so formed, will be one-fourth of the given triangle. 16. The difference ot the angles at the base of any triangle, is double...base, and another bisecting the angle at the vertex. 17. If the tangents drawn to every two, of three unequal circles, be produced till they meet, the points...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...isosceles triangle is equal to half the difference between the vertical angle and two right angles. 2. The difference of the angles at the base of any triangle is double the angle contained by the line bisecting the vertical angle and another drawn from the vertexperpendicular to the base. 3....
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...isosceles triangle is equal to half the difference between the vertical angle and two right angles. 2. The difference of the angles at the base of any triangle is double the angle contained by the line bisecting the vertical angle and another drawn from the vertex perpendicular to the base....
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Elements of Geometry with Notes

John Radford Young - Geometry, Modern - 1833 - 240 pages
...the angle CAB, equal to twice the angle CEB, or CEB equal half the angle CAB. PROPOSITION B. THEOREM. The difference of the angles at the base of any triangle...base, and another bisecting the angle at the vertex. Fig. I. Fig. 2. Let ABC denote any triangle; AD perpendicular to the base (produced if necessary),...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...and having the angle A double the angle C; shew that the side AC is less than double the side AB. 8. The difference of the angles at the base of any triangle,...base, and another bisecting the angle at the vertex. 9. If from the right angle of a right-angled triangle two straight lines be drawn, one perpendicular...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...vertical. 48. Trisect a given line : and hence divide an equilateral triangle into nine equal parts. 49. The difference of the angles at the base of any triangle is double of the angle between two lines drawn from the vertex, one bisecting the vertical angle and the other...
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The first book of Euclid's Elements, simplified, explained and illustrated ...

Euclides - 1847 - 128 pages
...base and between the same parallels. (Deducible from Prop. XXVII. and Prop. P.) PROP. y. THEOR. — The difference of the angles at the base of any triangle...the vertex perpendicular to the base, and another line bisecting the angle at the vertex. Let ABC be a A ; draw AD jr to the base BC, and AE bisecting...
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