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" The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side. "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 19
by Euclides - 1860
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...of its sides. 9. To bisect a parallelogram by a line drawn from a point in one of its sides. 10. A line joining the middle points of two sides of a triangle,...parallel to the base, and equal to the half of it. 11. The quadrilateral formed by joining the successiYe middle points of the sides of a given quadrilateral,...
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A complete treatise on Practical Land-Surveying, etc

Thomas Holliday - Surveying - 1838 - 404 pages
...constructed, and the opposite angle to the base is called the vertex. 4. A straight line bisecting any two sides of a triangle is parallel to the base, and equal to one half of it, and the triangle cut off is equal to one fourth of the original triangle. See fig....
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 338 pages
...triangle meet on the internal bisector of the third angle : interpreted the other way, express that the line joining the middle points of two sides of a triangle is parallel to the third side. 5. We give now some examples of the use of these equations of the first degree. Ex. 1....
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Curves, Algebraic - 1852 - 329 pages
...triangle meet on the internal bisector of the third angle : interpreted the other way, express that the line joining the middle points of two sides of a triangle is parallel to the third side. 5. We give now some examples of the use of these equations of the first degree. Ex. 1....
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...to four right angles. 10. To describe a square equal to the difference of two given squares. II. A line joining the middle points of two sides of a triangle is parallel to the "base, and equal to half of it. 12. To bisect a given parallelogram by a line drawn from a point in one of its sides. 13....
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Mathematical Questions and Solutions, from the "Educational Times.", Volume 3

1865 - 128 pages
...B + ft cos3 B + 7 cos C sin2 B) (aa + i0 + C7). 3. To find the equation to the circle described on the line joining the middle points of two sides of a triangle. Let D, F (Fig. 3) be the middle points of BC, BA; join DF and draw the perpendiculars DH, FK. Then...
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Mathematical Questions and Solutions

Mathematics - 1865 - 132 pages
...B + ft cos3 B + y cos C sin2 B) (aa + bft + cy). 3. To find the equation to the circle described on the line joining the middle points of two sides of a triangle. Let D, F (Fig. 3) be the middle points of BC, BA ; join DF and draw the perpendiculars DH, FK. Then...
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Mechanics required for the Additional Subjects for Honours at the Previous ...

James McDowell - Mechanics - 1867 - 120 pages
...same point and cut each other in a point of trisection. (EXERCISES, p. 3, No. 5.) Also the straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it. (1) Let AB CD be a rhombus. In the triangles ABC, ADC, the sides...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 300 pages
...Therefore DQ=D R. Consequently PR, which is equal to P D+DR, is equal to P D+D Q. Therefore EC=P D+D Q. 2. The line joining the middle points of two sides of a triangle is equal to half the third side, and is parallel to it. Let ABC be the triangle, D and E the middle points...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874 - 234 pages
...1, 2, 3, 4, etc. (I. App., schol. 2), the corresponding areas are 1, 4, 9, 16, etc. Conversely. — The line joining the middle points of two sides of a triangle is parallel to the third side, and equal to one-half of it. In the triangle ABC, let AB, AC be bisected in D and E. The...
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