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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Pagina 271
door Euclides - 1864
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Elementary algebra, with brief notices of its history

Robert Potts - 1879
...triplicate ratios in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. (Eue. VI. 19.) Let а, Ь, с ; a', V, ┐ represent the sides of two similar triangles ; Then, because...
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Elementary algebra: with brief notices of its history

Robert Potts - 1879
...triplÝcala ratios in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. (Eue. VI. 19.) Let а, Ь, с ; a', I', c' represent the sides of two similar triangles ; Then, because...
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Report on Foreign Systems of Naval Education

James Russell Soley - 1880 - 335 pagina’s
...BC, AC meet the tangents at A, B in D, E; prove that AB is a mean proportional between AD, BE. 12. Similar triangles are to one another in the duplicate ratio of their homologous sides. TRIGONOMETRY. Examiner.— Prof. C. NIVEN. Lieutenants qualifying for gunnery and torpedo officers....
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880
...inscribe a triangle equiangular to a given triangle. Show how to inscribe a circle in a given rhombus. 9. Similar triangles are to one another in the duplicate ratio of their homologous sidos. The sides of a regular hexagon ABCDEF are produced both ways, forming with each other six points...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 pagina’s
...In like manner it may be shewn that similar four-sided figures, or figures of any number of sides, are to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for triangles ; therefore universally, similar rectilineal figures...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...drnwn from the point D to its different nngles. The proof In thus also more easlly established. PROP. XIX. THEOREM. Similar triangles are to one another...duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, and let the angle ABC be equal to the angle DEF, and let AB be to BC,...
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The Cambridge Examiner, Volume 4

1884
...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. . / 16. "From the same point in a given plane, there cannot be two straight lines at right angles to...
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University local half-hour examination papers

John Robertson (LL.D., of Upton Park sch.) - 1882
...to the square on the line which meets the circle, the line which meets the circle shall touch it. 7. Similar triangles are to one another in the duplicate ratio of their homologous sides. TnEEE-nouE PAPEE. 1. Quote the passages in Genesis which relate to a SAVIOUE, as nearly as you can...
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The Competitor, Volumes 1-2

1882
...than a right angle. 4. Inscribe a regular equilateral and equiangular pentagon in a given circle. 5. Similar triangles are to one another in the duplicate ratio of their homologous sides. 6. Two circles whose centres are A and B, intersect in C and D, shew that AB bisects CD at right angles....
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their...
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