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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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 155
av Euclid, Robert Simson - 1821 - 516 sider
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1723 - 364 sider
...are to each other a* -their Bafes; which was to be demonftrated. PROPOSITION II. THEOREM. If it Right Line be drawn parallel to one of the Sides of a "Triangle, it frail cut the Sides of the Triangle * proportionally ; and if the Sides of the Triangle be cut proportionally,...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1772 - 399 sider
...fameBafe, J are between the fame Parallels; therefoie DE is parallel to B C. Wherefore, if c Right Lint be drawn parallel to one of the Sides of a Triangle, it jhall cut the Si Jo of the Triangle proportionally ; and if the Sines cf the Triangle be cut proportionally,...
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The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ...

Benjamin Donne - 1775 - 159 sider
...other Sides, or thefe Side* produced, proportionally, (viz. BD : DA :: CE : EA, or AB : AD :: AC : AE.) And if the Sides, or the Sides produced, be cut proportionally, the Une DE, which joins the Points of Se8ion, ßall be parallel to the remaining Side of the Iriangle,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 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 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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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 419 sider
...semicircle, or that which stands upon half the circumference, is a right angle, or 90°. 8. If a right line be drawn parallel to one of the sides of a triangle, it will cut the other sides proportionally. It may also be remarked, that some of the simplest cases of...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1813
...Triangles and parallelograms of the same altitude are one to another as their, basesProp. II. Theor. If a straight line be drawn parallel to one of the sides of a triangle, it shall cat the other sides, or those produced, proportionally: and if the sides, or the sides produced, be...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 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 of a triangle, it ' will cut the other sides, or the other sides produced, proportionally : And if the sides, or the...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 377 sider
...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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 377 sider
...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...
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