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" ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one... "
A Supplement to the Elements of Euclid - Page 296
by Daniel Cresswell - 1819 - 410 pages
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 pages
...of a triangle be divided by a straight line which also cuts the base, and the segments of the base have the same ratio which the other sides of the triangle have to one another, the vertical angle of the triangle shall be divided into two equal angles. MECHANICS...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...adjacent segment of the base as the other side is to the other segment, and the segments of the base shall have the same ratio which the other sides of the triangle have to one another. Any two triangles having an equal angle in each, contained by proportional sides, are...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pages
...divided into two equal angles by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another. If, on the same side of a point 0 in the same straight line, points A, C, B be taken...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 pages
...divided into two equal parts by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have. 9. Shew how to measure on the ground the angle contained between any two inaccessible lines. 10. Through...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1860 - 334 pages
...and the extremities of the base have the same ratio which the other sides of the triangles have ta one another; And if the segments of the base produced have the same ratio which the other sides of the triangles have, the straight line, drawn from the vertex to the point of section, bisects the exterior...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...base, have the same ratio which the other sides of the triangle have to one another: and conversely, if the segments of the base produced have the same ratio which the other sides of the tria-nglc have; the straight line drawn from the vertex to the point of section divides the outward...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...to one another, as the other sides of the triangle (AB, AC) have. [2.] And if the segments (BD, DC) of the base produced, have the same ratio which the other sides of the triangle (AB, AC) have, the straight line (AD) drawn from the vertex to the point of section bisects the exterior...
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Cambridge Senate-house Problems and Riders for the Year 1860: With Solutions

Henry William Watson, Edward John Routh - Mathematics - 1860 - 240 pages
...also cuts the base produced ; the segments between the dividing line and the extremities of the base have the same ratio which the other sides of the triangle have to one another. If the two sides, containing the angle through which the bisecting line is drawn, be...
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Cambridge Senate-house Problems and Riders for the Year 1860: With Solutions

Henry William Watson, Edward John Routh - Mathematics - 1860 - 240 pages
...also cuts the base produced ; the segments between the dividing line and the extremities of the base have the same ratio which the other sides of the triangle have to one another. If the two sides, containing the angle through which the bisecting line is drawn, be...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...base, have the same ratio which the other sides of fIie triangle have to one another ; and conversely, if the segments of the base produced have the same...ratio which the other sides of the triangle have ; the st. line drawn from the vertex to the point of section, divides the outward angle of the triangle into...
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