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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 - 1837 - 390 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 sider
...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 shall cut the other sides,...be parallel to the remaining side of the triangle. Let DE be drawn parallel to BC, one of the sides of the trian- • gle ABC : BD is to DA, as CE to...
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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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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...be drawn parallel to one of the See N. sides of a triangle, it shall cut the other sides, or these produced,, proportionally : And if the sides, or the...be parallel to the remaining side of the triangle. Join BE, CD ; then the triangle BDE is equal to the triangle CDE a , because they are on the same base...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...be drawn parallel to one of the See.N. sides of a triangle, it shall cut the other sides, or these produced, proportionally : And if the sides, or the...be parallel to the remaining side of the triangle. Let DE be drawn parallel to BC, one of the sides of the triangle ABC : BD is to DA, as CE to EA. -...
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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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