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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 ... - Side 138
av Euclid, James Thomson - 1837 - 390 sider
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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 - 1841 - 351 sider
...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 - 1842 - 317 sider
...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 - 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 - 1844 - 317 sider
...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 - 1844 - 96 sider
...(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. Fi«- 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 - 1845 - 199 sider
...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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