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" If from any point within an equilateral triangle perpendiculars be drawn to the three sides, their sum is equal to a perpendicular drawn from one of the angles on the opposite side. Required proof. From the point within the triangle draw... "
Key to Robinson's New Geometry and Trigonometry, and Conic Sections and ... - Page 45
by Horatio Nelson Robinson - 1875
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New Cambridge Guide; Or, A Description of the University, Town, and County ...

Cambridge (England) - 1804 - 476 pages
...20. Shew how the logarithm of 101 may be found. 21. Which is greater, .r3+j/3, or fy + ifx, xyy} 22. If from any point within an equilateral triangle, perpendiculars be drawn to the three sides, their sum equals a perpendicular drawn from one of the angles on the opposite side. Required...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...(Eucl. vi. 2.) BE = EC, and ED is common and at right angles to BC, L e. the half of AB. DC=BD, HE (3.) If from any point within an equilateral triangle perpendiculars...drawn from any of the angles to the opposite side. . From any point D within the equilateral triangle ABC let perpendiculars DE, DF, DG be drawn to the...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...line joining the right angle and the bisection of the hypothenuse is equal to half the hypothenuse. 3. If from any point within an equilateral triangle perpendiculars...drawn from any of the angles to the opposite side. 4. If the points of bisection of the sides of a given triangle be joined ; the triangle so formed will...
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...through the point of intersection, is that which is parallel to the line joining their centres. 14. If from any point within an equilateral triangle perpendiculars...drawn from any of the angles to the opposite side. 1 5 . If the points of bisection of the sides of a given triangle be joined, the triangle, so formed,...
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The Elements of Analytical Geometry ...

John Radford Young - Conic sections - 1833 - 310 pages
...continued ad infinitum ; then s'=s(l + J + TV + &c-) ad infinitum, =4*-r-3 as required. PROBLEM C. If from any point within an equilateral triangle perpendiculars be drawn to the three sides, their sum is equal to a perpendicular drawn from one of the angles on the opposite side....
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The Elements of Analytical Geometry ...

John Radford Young - Geometry, Analytic - 1835 - 298 pages
...continued ad infinitum ; then *'=*(! + i + TV ~t- &c.) ad infinitum, =4*-j-3 as required. PROBLEM C. If from any point within an equilateral triangle perpendiculars be drawn to the three sides, their sum is equal to a perpendicular drawn from one of the angles on the opposite side....
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An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

John D. Williams - Algebra - 1840 - 634 pages
...continued ad infinitum; then s' = s(l -|- J -j- iV -j- &c.) ad infinitum, = 4s -f- 3 as required. 29. If from any point within an equilateral triangle, perpendiculars be drawn to the three sides, their sum is equal to a perpendicular drawn from one of the angles on the opposite side....
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...line between the points of contact is a mean proportional between the diameters of the circles. 19. If from any point within an equilateral triangle,...sides, they are together equal to a perpendicular from any of the angles to the opposite side. 20. The three straight lines which bisect the angles of...
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845 - 222 pages
...bisecting line that is between the angle and the other perpendicular. (Euclid, vi. 4. Cape, iii. 69.) 82. If from any point within an equilateral triangle, perpendiculars be drawn to the sides, the sum of these perpendiculars is equal to the perpendicular drawn from either of the angles to the...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...in position, so that the part of it intercepted by them may be equal to a given line. 20. Prove that if, from any point within an equilateral triangle,...drawn from any of the angles to the opposite side. 21. That if the three sides of a triangle be bisected, the perpendiculars drawn to the sides, at the...
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