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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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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...and triangles, having equal bases, are to one another as their altitudes. PROPOSITION II. THEOBEM. If a straight line be drawn parallel to one of the...sides of a triangle, it shall cut the other sides, or the other sides produced ^proportionally ; and if the sides, or the sides produced, be cut proportionally,...
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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...the other sides or those produced proportionally. How must a line be drawn parallel to the base of a triangle, so as to be equal to half the base. 10....
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 pages
...angle. VOLUNTARY PORTION. 1. Inscribe an equiangular and equilateral pentagon in a given circle. 2. 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 straight...
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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 produced, be cut proportionally,...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861
...circle be respectively parallel to their opposite sides, the remaining sides are parallel to each other. straight line which joins the points of section shall...be parallel to the remaining side of the triangle. If two triangles be on equal bases and between the same parallels, shew that the sides of the triangles...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...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 sides produced, be cut proportionally,...
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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 or those produced proportionally, and if the side or the sides produced be cut proportionally, the straight line which joins the points of section...
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Papers Read at the Royal Institute of British Architects

Architecture - 1865
...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 sides produced, be cut proportionally,...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...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 sides...
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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. If two straight lines meeting...
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