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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 figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 54
by Euclides - 1840
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861
...two straight lines shall be parallel. 8. Draw a tangent to a circle from a given point without it. 9. 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. How must a line be drawn parallel to the...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...3, I. 2 C. D. 1 H. 2 C. 1,&26,L 3 Ax. 2, I, C. & 1, VI. Ax. 1, I. 4 5 PROP. 2. — THEOR. If a st. line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or these produced, proportionally ; and conversely, if the sides, or sides...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION n. THEOREM. 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 conversely, if the sides, or the...
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Papers Read at the Royal Institute of British Architects

Architecture - 1865 - 276 pages
...triangle having each of the angles at the base double of the third angle. Book VI. Proposition 2. Theorem. 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 conversely, if the sides, or the...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...construction be made as in the proposition, the demonstration will be the same. PROP. H.— THEOREM. If a straight line be drawn parallel to one of the sides of a triangle, it shall out the other sides, on these produced, proportionally; and conversely, if the sides, or the...
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First Practical Lines of Geometrical Drawing ...

J. F. H. de Rheims - Geometrical drawing - 1865 - 169 pages
...segment less than a semicircle is greater than a right angle. EUCLID, BOOK VI. Prop. 2. — Theorem. 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 side or the sides produced be...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION II. THEOREM. lf 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 conversely, if the sides, or the...
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A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 404 pages
...angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is &c. 4. 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, conversely, if the sides &c. 5....
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION 2. THEOREM. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides...
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The Edinburgh university calendar

Edinburgh univ - 1868
...lines drawn from the angles of a triangle to the bisections of the opposite sides meet in a point. 9. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sideSi or the other sides produced, proportionally ; and if the sides, or the sides produced, be cut...
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