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" ... rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid - Página 131
por Euclid - 1838 - 416 páginas
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Manual

1903
...straight line bisecting the angle E makes equal angles with AB and CD. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. Or, 6A. Prove that if two chords of a circle intersect either within or without the circle, the rectangle...
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A Text-book of Euclid's Elements for the Use of Schools, Libro 1

Euclid - 1904 - 484 páginas
...of similar triangles, having the same ratio each to each that the polygons have ; and the polygons are to one another in the duplicate ratio of their homologous sides. H Let ABCDE, FGHKL be similar polygons, and let AB and FG be homologous sides. Then (i) the polygons...
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1908 - 328 páginas
...remaining angles are either equal or supplementary. (30) 44. Show that the areas of similar triangles are to one another in the duplicate ratio of their homologous sides. Show that similar triangles are to each other in the same ratio as the areas of their inscribed circles....
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Books 3-9

Euclid - 1908 - 456 páginas
...i0 corresponding sides. And it was also proved in the case of triangles ; therefore also, generally, similar rectilineal figures are to one another in the duplicate ratio of the corresponding sides. QED 2. in the same ratio as the wholes. The same word fyiiXo-yos is used which...
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Annual Report, Volúmenes2-3

Civil Service Commission of Canada - 1910 - 238 páginas
...or at the circumferences, have the same ratio as the arcs on which they stand. 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the...
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Annual Report of the Association of Ontario Land Surveyors, Volumen17

Association of Ontario Land Surveyors - 1909
...equiangular pentagon in a circle. 8. Inscribe a circle in a given sector ofi a circle. 9. Similar triangles are to one another in the duplicate ratio of their homologous sides. 10. Describe a rectilineal figure which shall be similar to one and equal to another rectilineal figure....
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The Teaching of Mathematics in the United Kingdom

Great Britain. Board of Education - 1912 - 632 páginas
...AB:BC::DE:EF; prove that AD, BE, CF will meet in a point or be parallel. 9. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. If one diagonal of a quadrilateral bisects the angle between two of the sides and is a mean proportional...
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English Mechanic and World of Science: With which are ..., Volumen28

1879 - 666 páginas
...beautifully demonstrated in Euclid's Sixth Book, Propositions 19 and 20, that " similar rectilinear figures are to one another in the duplicate ratio of their homologous sides" — that is, that these figures — meaning the areas of them— are to one another as the squares...
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The Dublin University Calendar, Volumen1

Trinity College (Dublin, Ireland) - 1916
...having the same altitude are to one another as their bases. 6. Prove that the areas of similar triangles are to one another in the duplicate ratio of their homologous sides. 7. Show how to construct a triangle equal in area to a given square and similar to a given triangle....
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Education in Scotland

Great Britain. Scottish Education Dept - 1896 - 642 páginas
...of similar triangles, having the same ratio to one another that the polygons have ; and the polygons are to one another in the duplicate ratio of their homologous sides. Describe a polygon which shall be similar to a given polygon, but shall have half its area. 8. Draw...
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