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" Of all triangles having the same vertical angle, and whose bases pass through a given point, the least is that whose base is bisected in the given point. "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 2
by Euclides - 1860
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...being parallel to DF, DC : DF :: BC : BG, whence BC : BG :: BC : DE + DF, and .. BG = DE + DF. (12.) Of all triangles having the same vertical angle, and...point, the least is that whose base is bisected in the given point, Let BAC be the vertical angle of any number of triangles, whose bases pass through...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...shall be equal to a perpendicular drawn from either extremity of the base to the opposite side. 12. Of all triangles having the same vertical angle, and...point, the least is that whose base is bisected in the given point. 13. If from the angles at the base of a triangle, perpendicular* be let fall on a...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833 - 304 pages
...triangle EAB, which is = to CAB, (prop. 37, 1. Elr.) is less than DAB. PROP. 16. THEOR. Of all the triangles, having the same vertical angle, and whose bases pass through a given point (A), the least is that (viz. CBD), whose base (BD) is bisected in the given point. Fig. 12. Let CEI...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...thig point, that is the least which is perpendicular to the diameter. 3. Of all triangles that have the same vertical angle, and whose bases pass through a given point, that whose base ii tisected by the point is a minimum. of any quadrilateral from the intersection of...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...same base and the same perimeter, that is the greatest which has the two undetermined sides equal. 65. Of all triangles having the same vertical angle, and...point, the least is that whose base is bisected in the given point. 66. ^If from the base to the opposite sides of an isosceles triangle three straight...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...between the given point and the nearest line may be equal to the part between the two given lines. 40. Of all triangles, having the same vertical angle,...least is that whose base is bisected in that point. 41. Find a point in the diagonal produced of a square, from which if a line be drawn parallel to any...
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The First Book of Euclid's Elements, Simplified, Explained, and Illustrated ...

Euclides - 1847 - 128 pages
...same st. line with BC. The following Theorem may now be solved : — PROP. W. THEOR. GEN. ENUN. — Of all triangles having the same vertical angle, and...bases pass through a given point, the least is that of which the base is bisected in the given point. PART. ENUN. — Let BAC be the vertical L of any...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852 - 148 pages
...triangle from which lines drawn to the several angles will divide the triangle into three equal parts. Of all triangles having the same vertical angle, and...point, the least is that whose base is bisected in the given point. The sum of the sides of an isosceles triangle is less than the sum of the sides of...
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The Popular Educator, Volume 5

1856
...XXXI. Of all triangles having the same vertical angle, and hating their bases passing through the same point, the least is that whose base is bisected in that point. In fig. c, let в А с be the vertical angle of any number of triangles, whose bases pass through...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...two sides of a triangle be given, the triangle will be greatest when they contain a right angle. 110. Of all triangles having the same vertical angle, and...point, the least is that whose base is bisected in the given point. 111. Of all triangles having the same base and the same perimeter, that is the greatest...
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