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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 ... - Σελίδα 155
των Euclid, Robert Simson - 1821 - 516 σελίδες
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1723 - 444 σελίδες
...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,...

Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1772 - 462 σελίδες
...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,...

The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ...

Benjamin Donne - 1775 - 338 σελίδες
...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,...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 σελίδες
...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...

A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

John Bonnycastle - 1806 - 464 σελίδες
...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...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813 - 714 σελίδες
...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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 350 σελίδες
...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...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 σελίδες
...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...

Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 442 σελίδες
...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...

Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 444 σελίδες
...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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