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

Thomas Keith - 1839
...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...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...triangles and parallelograms, having equal altitudes, are proportional to their bases. PROP. II. THEOR. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides, or the other sides produced, proportionally: and if the sides, or the sides...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...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...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...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, be cut proportionally, the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...construction be made as in the proposition, the demonstration will be the same. PROP. II. THEOR. IJ a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides, or the other sides produced, proportionally : And if the sides, or the sides...
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An epitome of navigation, and nautical astronomy, with the improved lunar tables

Janet Taylor - Nautical astronomy - 1842
...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,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 317 pages
...and parallelograms that have equal altitudes, are to one another as their bases. PROP. II. THEOR. lj a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides, or the other sides produced, proportionally: And if the sides, or the sides...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...(Prop. 4, Cor.), and 4DP is the square of DB ; hence AD2-|-DC2+AB2+BC2=AC2+DB2. PROP. XII. THEOREM. If a line be drawn parallel to one of the sides of a triangle, it will cut the other sides proportionally. FiŤ- 69- Let DE be drawn parallel to the side AB of the triangle...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...2s. i. be made as in the proposition, the demonstration will be the same. PROPOSITION 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, be cut proportionally, the...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION II. THEOREM. 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 conversely, if the sides, or the sides produced, be cut proportionally,...
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