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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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Report on Foreign Systems of Naval Education

James Russell Soley - 1880 - 346 páginas
...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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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881 - 236 páginas
...different nngles. The proof In thus also more easlly established. PROP. XIX. THEOREM. Similar triangles are to one another in the 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...
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The Cambridge Examiner, Volumen4

1884 - 532 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. . / 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 - 148 páginas
...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, Volúmenes1-2

1882 - 476 páginas
...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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 426 páginas
...to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for triangles ; therefore universally, similar rectilineal...in the duplicate ratio of their homologous sides. COROLLARY 2. If to AB and FG, two of the homologous sides, a third proportional M be taken, [VI. 11....
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 páginas
...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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Some Propositions in Geometry: In Five Parts

John Harris - 1884 - 188 páginas
...the square on A c, including the diagonal A e of the square on A b. Then because similar trianglcs are to one another in the duplicate ratio of their homologous sides (Euclid VI. 19) and the triangles A eb and Afc are similar, the " '' triangle A eb has the ratio to...
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Calendar of Dalhousie College and University

Dalhousie University - 1884 - 184 páginas
...and 2. GEOMETRY AND MENSURATION.— SECOND YEAR. APRIL 15iH.— 10 AM TO 1 p. M. I. Similar triangles are to one another in the duplicate ratio of their homologous sides. Prove this : and represent the ratio of the two triangles by means of two straight lines whereof one...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 páginas
...that these triangles have each to each the same ratio which the polygons have ; and that the polygons are to one another in the duplicate ratio of their homologous sides. Join BE, EC, GL, LH. Because the polygon ABCDE is similar to the polygon FGHKL, .-. LA = LF, and BA...
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