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" Through a given point to draw a straight line which shall make equal angles with two straight lines given in position. Let P be the given point, and BE, CF the lines given in position. Produce BE, CF to meet in A, and bisect the angle BAG by the line... "
Elementary geometrical drawing - Pagina 47
door Samuel H. Winter - 1861
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 444 pagina’s
...AD, DE, that is, to BD, DE, and is therefore greater than BE, (Eucl. i. 20.) ; therefore, &c. (3.) Through a given point to draw a straight line which shall make equal angles with two straight lines given in position. Let P be the given point, and BE, CF the lines...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 442 pagina’s
...AD, DE, that is, to BD, DE, and is therefore greater than BE, (Eucl. i. 2O.) ; therefore, &c. (3.) Through a given point to draw a straight line which shall make equal angles with two straight lines given in position. Let P be the given point, and BE, CF the lines...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pagina’s
...parallelogram, whose diagonals intersect at right angles, is equilateral. (Euclid, i. 4. Cape, i. 6.) 22. Through a given point to draw a straight line which shall make equal angles with two given straight lines. (Euclid, i. 10, 12. Cape, prob, 1, 3.) 23. The area of...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846 - 128 pagina’s
...perpendicular from the point of intersection of these lines upon the third side will bisect that side. 1 1 . Through a given point to draw a straight line which shall make equal angles with two given straight lines. 12. A perpendicular to the base of an isos-celes triangle...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pagina’s
...ED has been shown to be equal to AE, and FD to FB, therefore AE, EF, FBare equal to one another. 3. Through a given point to draw a straight line which shall make equal angles with two straight lines given in position. Let P be the given point, and BE and CF the...
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A Rudimentary Treatise on Analytical Geometry and Conic Sections

James Hann - 1850 - 146 pagina’s
...1 this result is positive or negative, according as the point B is above or below the origin. (20.) Through a given point to draw a straight line which shall make a given angle with a given straight line. Let the given line be represented by the equation y -=mx + h, then, because...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pagina’s
...base, it bisects the angle ; and in either case, it cuts the base at right angles. Exercise 2. — Through a given point to draw a straight line which shall make equal angles with two straight lines given in position. PROP. XXVII. THEOREM. If a straight line falling...
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Collection of Examples and Problems in Pure and Mixed Mathematics: With ...

Alfred Wrigley - 1862 - 330 pagina’s
...rectangular. 21. The parallelogram, whose diagonals intersect at right angles, is equilateral. 22. Through a given point to draw a straight line which shall make equal angles with two given straight lines. 23. The area of a rhombus equals half the rectangle contained...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pagina’s
...ЛNMD=.i.MDA; consequently, since these are alternate angles, MN and AB are parallel. PROBLEMS FOR EXERCISE. 1. Through a given point to draw a straight line which shall make a given angle with a given straight line. 2. Find a point in a line which shall be equidistant from two given points....
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Elements of Plane Geometry, Deel 1

Thomas Hunter - 1878 - 142 pagina’s
...equiangular. Therefore EF is equal to ED and DF, or to their equals, AE and FB. Hence AB is trisected. 2. Through, a given point to draw a straight line which shall make equal angles with two straight lines given in position. Let E be the given point, and AB and CD the...
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