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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 figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 54
by Euclides - 1840

## Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...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,...

## 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 sides of a triangle, it shall cut the other sides, or those produced, proportionally ; and conversely, if the sides or the...

## 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,...

## Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 246 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 of...

## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...BOOK VI. Triangles, and also parallelograms, of the same altitude are to one another as their bases. If a straight line be drawn parallel to one of the sides of a triangle it will cut the other two sides proportionally. If any angle of a triangle be bisected by a straight line which cuts the...

## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 516 pages
...: then, if the same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. 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,...

## The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...construction be made aq in the proposition, the demonstration will be the same. PROPOSITION II. ^ See N. THEOR. — 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 tides, or the sides produced,...

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...another. Then, if the same construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. If a straight line be drawn parallel to one of the See N. sides of a triangle, it will cut the other sides, or the other sides produced, proportionally...

## The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...base and altitude, therefore triangles of equal altitude are to one another as their bases. PROP. III. THEOR. \ 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...

## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...triangle ADE ; and * The enunciation of this proposition, as given by Dr. Simson, is as follows : " 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,...