Books Books 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 ... - Page 167
by Euclides - 1814 ## Dublin examination papers

Dublin city, univ - 1876
...the other segment. If the whole line be 10 feet long, find the lengths of the segments. 2. Prove that similar triangles are to one another in the duplicate ratio of their sides. Divide a triangle into three equal parts by right lines drawn parallel to its base. 3. Divide... ## Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 413 pages
...have the same base, are to one another as their altitudes. 7. Define duplicate ratio, and prove that similar triangles are to one another in the duplicate ratio of their homologous sides. On the side AB of a triangle ABC, AD is taken equal to one third of AB ; and on AC, AE is taken equal... ## Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877
...HE, HF. Then EHF is the triangle required, for it is isosceles and equal to EFG, that is, to ABC. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. Given a point O in the line AB, find two other points 0, J?, such that a line OP given in direction... ## Elementary geometry

James Maurice Wilson - 1878
...triangle DEF in the duplicate ratio of BC to EF. THEOREM 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Let ABCDE, PQ_RST\3z similar polygons. JD S Divide each of them into the same number of similar triangles... ## The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...and this has been proced of triangles (P. 34). Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Cor. 2. If to AB and FG, two of the homologous sides ; of the polygon, a third proportional M Is taken... ## Elementary algebra: with brief notices of its history

Robert Potts - Algebra - 1879
...triplícala 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... ## 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... ## Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

Euclides, James Hamblin Smith - Euclid's Elements - 1879 - 349 pages
...or more sides may be described, on a given line, similar to a given fig. PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their houwlogous sides. H Let ABC, DEF be similar A s, haying L s at A, B, C= L s at D, E, F respectively,... ## Report on Foreign Systems of Naval Education

James Russell Soley - Naval education - 1880 - 335 pages
...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.... 