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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 ... - Σελίδα 138
των Euclid, James Thomson - 1837 - 390 σελίδες
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

Euclid, John Keill - 1723 - 364 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 - 399 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 - 159 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,...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 σελίδες
...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...

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

John Playfair - 1806 - 311 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 - 419 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
...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...

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...

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

Euclides - 1816 - 528 σελίδες
...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. -...

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

John Playfair - 1819 - 333 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...




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