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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

The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 pages
...ABC to ACD and CD to DL as ACD to ADL • But BC to DL as ABC to ADL. TROP. xvii. THEOREM. (E. 6. 2). If- a straight line be drawn parallel to one of the sides of a triangle, it cuts the other two sides, or these sides produced proportionally, so that the segments between the...

The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...Corollary 2.—Triangles of equal altitude are proportional to their bases. Proposition 2. Theorem.—If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides, or those sides produced proportionally; and if the sides of a triangle, or the sides produced, be ad proportionally,...

First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879 - 412 pages
...Describe an isosceles triangle, having each of the angles at the base double of the third angle. 6. 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...

Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879 - 146 pages
...the triangle will bisect that angle. 8. Find a point in the diagonal of a square produced, from which if a straight line be drawn parallel to one of the sides, and meeting another side produced, it will form with the produced diagonal and produced side a triangle...

Military examinations. Mathematical examination papers, set at entrance to ...

Sandhurst roy. military coll - 1880 - 68 pages
...square, prove 3AD3 = 2AB2. 5. Inscribe a circle in a given equilateral and equiangular pentagon. 6. 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. Construct a triangle similar to a given...

The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 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...

The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1882 - 292 pages
...of equal altitude are proportional to their bases. GEOMETRY— BOOK V. Proposition 2. Theorem. — If a straight line be drawn parallel to one of the...sides of a triangle, it will cut the other sides, or those sides produced proportionally ; and if the sides of a triangle, or the sides produced, be cut...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 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...