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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Página 165
por Euclides - 1814
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 páginas
...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
...point D to its 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 to BC,...
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The Cambridge Examiner, Volumen4

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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The Competitor, Volúmenes1-2

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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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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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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 páginas
...; and it has already been shewn for triangles ; therefore universally, similar rectilineal figures are to one another 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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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...figure BLMN similar and oppositely situated to the figure BAGH be obtained? PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. G Let ABC and DEF be similar triangles, having L. B = LE, and LC — LF, so that BC and EF are homologous...
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Calendar of Dalhousie College and University

Dalhousie University - 1884
...= 0, between 1 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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Some Propositions in Geometry: In Five Parts

John Harris - 1884 - 144 páginas
...area of) the eq. triangle DAB of four to nine. It demonstrates therefore (by inspection) the theorem ; Similar triangles are to one another in the duplicate ratio of their respondent sides. (Euclid, IV. 19.) It also demonstrates that if from an eq. triangle a lesser eq....
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