Books Books Similar triangles are to one another in the duplicate ratio of their homologous sides. Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ... - Page 95
by John Mason Good - 1813 ## Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1879
...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,... ## The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...similarly situated to a given rectilineal figure of six sides ; and so on. y. KF PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BO... ## 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.... ## Military examinations. Mathematical examination papers, set for entrance to ...

...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... ## 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... ## The Cambridge Examiner, Volume 4

Education, Higher - 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... ## University local half-hour examination papers

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

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...proportionals ; therefore they are similar to one another. [VI. Definition 1, PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC... 