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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 ... - Page 138
by Euclid, James Thomson - 1837 - 390 pages
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...1), 2ACH : 2ADL : : HC : DL (Proper. 30). Therefore, triangles &c. QED ED. PROPOSITION II. THEOREM. If a straight line be drawn parallel to one of the sides of a triangle it will cut the other sides proportionally. Let DK be drawn parallel to BC1, one of the sides of the triangle...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...made aq in the proposition, the demonstration will be the same. PROPOSITION II. ^ See N. 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 tides, or the sides produced, be cut proportionally, the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...parallel to one of the See N. sides of a triangle, it will cut the other sides, or the other sides produced, proportionally : And if the sides, or the...the straight line which joins the points of section will be parallel to the remaining side of the triangle. • Let DE be drawn parallel to BC, one of...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...parallel to one of the See N. sides of a triangle, it will cut the other sides, or the other sides produced, proportionally : And if the sides, or the...the straight line which joins the points of section will be parallel to the remaining side of the triangle. Let DE be drawn parallel to BC, one of the...
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...altitude, therefore triangles of equal altitude are to one another as their bases. PROP. III. 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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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...that triangles and parallelograms that have equal al. titudes, are to one another as their bases. II. 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 Mechanical Euclid: Containing the Elements of Mechanics and Hydrostatics ...

William Whewell - Mechanics - 1837 - 182 pages
...i. Triangles and parallelograms of the same altitude are to one another as their bases. *PROP. ii. If a straight line be drawn parallel to one of the...; and if the sides, or the sides produced, be cut propertionally, the straight line which joins the points of section shall be parallel to the remaining...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...altitudes. PROPOSITION II. THEOREM. 133 a triangle, it shall cut the other sides, or the other sides produced, proportionally; and if the sides, or the...straight line which joins the points of section shall he parallel to the remaining side of the triangle. Let DE be drawn parallel to BC, one of the sides...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - Geometry - 1838 - 416 pages
...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...the straight line which joins the points of section shal 1 be parallel to the remaining side of the triangle.* Let DE be drawn parallel to BC, one of the...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...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 triangle, it shall cut the other sides, or these produced, proportionally : and if the sides, or...
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