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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 180
av Robert Simson - 1806 - 518 sider
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## Education in Scotland

...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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## The Durham University Journal, Volum 1

University of Durham - 1879
...angle at the base. 6. Define similar triangles, duplicate ratio : — Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 8. Define a conic section, the tangent to a conic section : — If S be the focus, P any point on the...
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## Report of Her Majesty's Civil Service Commissioners: Together ..., Volumer 15-16

1870
...triangles, having ! h.- same ratio to one another that the polygons Jan. 1870. have7. Similar triangles are to one another in the duplicate ratio of their homologous sides. 8. If from any point without a circle lines be drawn touching it, the angle contained by the tangents...
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## The Bombay University Calendar

University of Bombay - 1903
...T, so that DX and DY may be equal. 9. Give the definition of duplicate ratio. 10 Similar triangles are to one another in the duplicate ratio of their homologous sides. Deduce that the duplicate ratios of equal ratios are equal, and also that similar triangles are to...
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## The Calendar of Owens college, Manchester

Manchester univ - 1877
...that equal magnitudes have the same ratio to the same magnitude and conversely. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. Bisect a triangle by a line perpendicular to one of the sides. 11. Enunciate and prove the general...
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## Nature, Volum 69

1904
...liberty which each of these excellent works takes with Euclid's Prop. 19, Bk. vi. — " similar triangles are to one another in the duplicate ratio of their homologous sides " — mysterious but high-sounding to countless generations of schoolboys. Here it is, in identical...
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## The Eclectic Review, Volum 1;Volum 19

...have met it before. The demonstration of the 19th Prop, of Euclid's Oth book, ie " Similar triangles are to one another in the duplicate ratio of their homologous sides," requires the previous or the syn hro nous establishment of Props, vi. 11, v. 10, v. 11, vi. 15., and\i....
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## The calendar of the University college of Wales

...and their difference is equal to the difference of their squares. 12. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 13. If two chords of a circle intersect, the rectangles contained by the segments are equal. 14. ABC...
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## The Cambridge University Calendar

University of Cambridge - 1828
...SATURDAY MORNING. ... 9 o'clock to 11. Pint, Second, Third and Fourth Classes. • 1. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 2. If a straight line be at right angles to a plane, every plane passing through that straight line...
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## Report of the examination held (Dec. 1859)-73

...circumference upon the same base, that is upon the same part of the circumference. 5. Similar triangles are to one another in the duplicate ratio of their homologous sides. 6. If two triangles have two sides of the one equal to two sides of the other, and have likewise their...
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