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Similar triangles are to one another in the duplicate ratio of their homologous sides.
The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ... - Page 117
by Thomas Gaskin - 1847 - 263 pages

## The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...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...

## Calendar of Dalhousie College and University

Dalhousie University - 1884 - 184 pages
...= 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...

## Examinations Papers

1884 - 610 pages
...magnitude. • 5. Describe a triangle ABC such that each of the angles B and 6' is double of the angle A. 6. Similar triangles are to one another in the duplicate ratio of their homologous sides.- Give Euclid's proof of this proposition, and also shew that it may be established without using any...

## Some Propositions in Geometry: In Five Parts

John Harris - Geometry - 1884 - 188 pages
...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....

## Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

...straight lines. Prove that the sum of the given lines is greater than twice their mean proportional. 9. Similar triangles are to one another in the duplicate ratio of their homologons sides. H в THURSDAY, December 11, 1884. Щ—3. For candidates ander the new regulations....

## Senate Documents, Otherwise Publ. as Public Documents and ..., Volume 3

United States. Congress. Senate - United States - 1880 - 1304 pages
...point on the curve. I the tangents at A, B in D, E ; prove that AB is a mean proportional betwi 12. Similar triangles are to one another in the duplicate ratio of their sides. TRIGONOMETRY. Examiner,— Prof. C. NIVEN. Lieutenants qualifying for gunnery and torpedo officers....

## Nature, Volume 34

Sir Norman Lockyer - Electronic journals - 1886 - 684 pages
...book. To mention one only- the proof which he judiciously gives of the fundamental proposition that " similar triangles are to one another in the duplicate ratio of their homologous sides " depends directly on the ist Proposition only of the Sixth Book, instead of the chain being carried...

## Calendar of Dalhousie College and University

Dalhousie University - 1887 - 206 pages
...YEAR. APRIL 18.— 10 AM TO 1 PM 1. Explain " duplicate ratio " and prove that, " similar tranples are to one another in the duplicate ratio of their homologous sides." 2. If four straight lines be proportionals, the similar rectilineal figures descriled on them shall also...