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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

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...