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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 256
by Daniel Cresswell - 1819 - 410 pages
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...divided into two equal angles, by a straight line which cuts a side ; the segments of that side will have the same ratio which the other sides of the triangle have to each other. 55. The four triangles into which a trapezium is divided by its diameters, are proportionals....
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...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 : and conversely, if the segments of the base have the same ratio which the other sides...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1849 - 332 pages
...bisecting line and the extremities of the base have the same ratio which the other sides of the triangles have to one another; And if the segments of the base produced have the same ratio which the ether sides of the triangles have, the straight line, drawn from the vertex to the point of section,...
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The English Journal of Education, Volume 4

Education - 1850 - 488 pages
...which the other sides of the triangle have to one another : and conversely, if the segments of the base have the same ratio which the other sides of the triangle have to one another; the straight line drawn from the vertex to the point of section, divides the vertical...
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The Principles of the Solution of the Senate-house 'riders,' Exemplified by ...

Francis James Jameson - Mathematics - 1851 - 144 pages
...divided into two equal angles by a straight line, which also cuts the base, the segments of the base have the same ratio which the other sides of the triangle have to one another, (vi. 3.) (JB). If A, B, C, be three points in a straight line, and D a point at which...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 196 pages
...divided into two equal angles by a straight line which also cuts the base, the segments of the base have the same ratio which the other sides of the triangle have to one another. If A, B, C be three points in a straight line, and D a point at which AB and EC subtend...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...same ratio which the other sides of the triangle have to one another : and if the segments of the base have the same ratio which the other sides of the triangle have to one another, the straight line drawn from the vertex to the point of section divides the vertical...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 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 ; and if the .ments of the base have the same ratio which the other sides of the triangle...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...triangle be bisected 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. 2. If two triangles have one angle of the one equal to one angh of the other, and the sides about the...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...another, as the other sides of the triangle (AB, AC) have. [2.] And if the segments (BD, DC) of the lose 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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