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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

## The mechanical Euclid, containing the elements of mechanics and hydrostatics

William Whewell - 1837 - 226 pages
...i. Triangles and parallelograms of the same altitude are to one another as their bases. *PROP. ii. 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: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 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,...

## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 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 sides of « triangle, it shall cut the other sides, or these produced, proportionally : and if the sides, or...

## An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839 - 498 pages
...about the equal angles are proportional, viz. AB : BC : : A& : be, and AB '. BC '. ' AC ; AC, &c. (72) If a straight line be drawn parallel to one of the sides of a plane triangle, it will cut the other two sides proportionally. (73) An oblique-angled triangle is...

## Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...PROP. II. THEOR. If a straight (DE) be drawn parallel to one of the sides (BC) of a triangle (BAC), it will cut the other sides, or the other sides produced, proportionally : and if the sides (AC, AB), or the sides produced, be cut proportionally, the straight line (DE) which joins the points...

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

Euclides - 1841 - 378 pages
...23.1 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 Q * 37. 1. . 1.6. of a triangle, it shall cut the other sides, or these produced, proportionally. And...

## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 pages
...them) they, also, are to one another in a ratio compounded of the ratios of their bases and altitudes. 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 these produced, proportionally : and if the sides, or the sides produced,...

## An epitome of navigation, and nautical astronomy, with the improved lunar tables

Janet Taylor - Nautical astronomy - 1842 - 588 pages
...equal angles are proportional, viz : CA : AB : : CD : DE AC : CB : : DC : CE CB : BA : : CE : ED Henee, if a straight line be drawn parallel to one of the sides of a plane triangle, it will cut the other two sides proportionally. Any two sides of a triangle added together,...