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" IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section... "
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 138
by Euclid, James Thomson - 1837 - 390 pages
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...drawn parallel to one of the sides of a triangle, it will tut the otlter sides, or the other sides produced, proportionally : And if the sides, or the...sides produced, be cut proportionally, the straight like which joins the points of section will be parallel to the remaining side of the triangle. Let...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 377 pages
...drawn through P parallel to AB or DC, it may be shewn that APE, DPC together are half of ABCD. (8.) If a straight line be drawn parallel to one of the sides of a parallelogram, and one extremity of this line be joined to the opposite one of the parallel side, by...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 377 pages
...parallelogram to the extremities of two opposite sides, are together half of the parallelogram. 8. If a straight line be drawn parallel to one of the sides of a parallelogram, and one extremity of this line be joined to the opposite one of the parallel side, by...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 516 pages
...construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. x IF a straight line be drawn parallel to one of the...be parallel to the remaining side of the triangle.* Let DE be drawn parallel to BC, one of the sides of the triangle ABC; BD is to DA, as CE to EA. Join...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...parallel to one of the sides BC, of a triangle ABC, it will cut the other sides, or the other sides produced proportionally ; and if the sides, or the...the straight line which joins the points of section, will be parallel to the remaining side of the triangle. Join BE and CD ; then the triangle BDE is equivalent...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...parallelograms having equal bases, are to each other as their altitudes. PROPOSITION II. THEOREM. У a right line be drawn parallel to one of the sides of a triangle, it shall cut the sides of the triangle proportionally j and if the sides of a triangle be cut proportionally, the right...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pages
...lines be proportional, their squares shall also be proportional. PROPOSITION II. THEOREM. If a, right line be drawn parallel to one of the sides of a triangle, it shall cut the sides of the triangle proportionally ; and if the sides of a triangle be cut proportionally, the right...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...; but by hypothesis, A2 : B" :': A : C, hence (Prop. IX. Cor. 3. BV), Q=C. PROPOSITION V. THEOREM. If a straight line be drawn parallel to one of the...other sides, or those produced, proportionally ; and conversely, if the sides or the sides produced, be cut proportionally, the cutting line will be parallel...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...construction be made as in the pro, . - position, the demonstration will be the same. PROP. II. THEOR. 3ee N. If a straight line be drawn parallel to one of the...sides of a triangle, it shall cut the other sides, or these produced, proportionally : and if the sides, or the sides produced, be a1t proportionally, the...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...triangle are respectively equal to those of another, the triangles are similar. Cor. 2. Therefore if a line be drawn parallel to one of the sides of a triangle it will cut off a triangle similar to the whole. PROPOSITION x. THEOREM. {Converse of Prop. IX.} The angles...
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