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" 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 46 INTERCEPTS BY PARALLEL LINES. "
A Text-book of Euclid's Elements for the Use of Schools - Strona 79
autor: Euclid - 1904 - Liczba stron: 456
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - Liczba stron: 240
...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, is parallel to the base, and equal to the half of it. 11. The quadrilateral formed by joining the successiYe middle points...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - 1852 - Liczba stron: 316
...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. Tiie bisectors...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...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...
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The American Journal of Education and College Review, Tom 2

1856
...is an easy deduction, from any one of this series, that a straight line cutting off' equimultiples of two sides of a triangle is parallel to the third side ; and, conversely, a parallel to one side cuts off equimultiples of the other two sides. We need now...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...from P, and the line BC joining them is parallel to AE. EXERCISE XLIX. — THEOREM. The line joining the middle points of two sides of a triangle is parallel to the base, and equal to the half of it. Let ABC be a triangle, the line DE, that joins the middle points...
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Mechanics required for the Additional Subjects for Honours at the Previous ...

James McDowell - 1867 - Liczba stron: 102
...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 AB, AC are...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - Liczba stron: 400
...between these diagonals, then the area of the triangle is equal to the area of the quadrilateral. 106. The straight line which joins the middle points of two sides of any triangle is parallel to the base. . 107. Straight lines joining the middle points of adjacent sides...
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An Elementary Course of Plane Geometry

Richard Wormell - 1870 - Liczba stron: 16
...is frequently of use in solving problems on the intersection of lines : — "A straight line joining the middle points of two sides of a triangle is parallel to the third and equal to half the third." We will here give a few problems in which this fact is applied. 354....
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...(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 line joining...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...Join PO and draw AQ- parallel to it. Then PQ shall bisect the triangle.] 53. 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. 54. The straight lines joining the middle points of the four sides of any...
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