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Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Seite 354
von Euclid, Isaac Todhunter - 1867 - 400 Seiten
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Elements of Geometry

Adrien Marie Legendre - 1819 - 208 Seiten
...angle BAD = DAC, and that the angle BDA — ADC ; therefore these two last are right angles. Hence, a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, anil divides the vertical angle into two equal parts....
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - 596 Seiten
...C. 61. COROLLARY 1. — Hence every equilateral triangle is also equiangular. 62. COROLLARY 2. — A straight line drawn from the vertex of an isosceles triangle to the middle of the base will bisect the vertical angle, and be perpendicular to the base. THEOREM 12. 63....
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 Seiten
...angle BAD = DAC, and that the angle BDA = ADC; therefore these two last are right angles, /fence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts....
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 Seiten
...angle BAD — DAC, and that the angle BDA = ADC ; therefore these two last are right angles. Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts....
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Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - 1829 - 172 Seiten
...PC, AB, AC ; PB and PC will be equal (41), and AB and AC will therefore be equal; and AG will be a straight line drawn from the vertex of an isosceles triangle to the middle of the base; that is—BC is perpendicular to the oblique line AG, when it is perpendicular...
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Elements of Geometry

Adrien Marie Legendre - 1841 - 235 Seiten
...angle BAD = DAC, and that the anglf BDA = ADC ; therefore these two last are right angles. Hence a straight line, drawn from the vertex of an isosceles triangle to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts....
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...intersection are together one-third of the squares of the sides of the triangle. 27. Prove that the square of any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square of a side of the triangle by the rectangle contained by the segments of the base. 28. If from one of...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856 - 216 Seiten
...COROLLARY 1. — Hence every equilateral triangle is also equiangular. в с 62. COROLLARY 2. — A straight line drawn from the vertex of an isosceles triangle to the middle of the base will bisect the vertical angle, and be perpendicular to the base. THEOREM 12. 63....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 Seiten
...the middle segment is equivalent to twice the rectangle under the extreme segments. V. 37. Prove that the square on any straight line drawn from the vertex...the rectangle contained by the segments of the base : and conversely. 38. If from one of the equal angles of an isosceles triangle a perpendicular be drawn...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...straight line which bisects the vertical angle of an isosceles triangle, bisects also the base. 3. The straight line drawn from the vertex of an isosceles triangle to the point of bisection of the base, bisects the vertical angle, and is perpendicular to the base. 4. In...
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