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 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 6
by John Mason Good - 1813
Full view - About this book ## Cambridge examination papers: a suppl. to the University calendar, 1856-59

...are proportionals. Shew how this proposition may be proved by superposition as in Prop. 4, B. 1. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. What can you infer from this as to the ratio of squares to each other ? 5. Describe a rectilineal figure...
Full view - About this book ## National Society's Monthly Paper

1857
...the base, the triangles on each^side of it are similar to the whole triangle and to one another. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both...
Full view - About this book ## Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 59 pages
...triangle. 7. Give Dcf. 5, Book V. of Euclid, and shew whether the areas 3, 4, 7, 8 are proportionals. Similar triangles are to one another in the duplicate ratio of their homologous sides. Shew how to inscribe a rectangle DEFG in a triangle ABC, so that the angles D, E may be in the straight...
Full view - About this book ## Middle-class education. 2, Volume 18

Middle-class education - 1857
...the algebraical expression for the mean proportional between two given quantities ? 19. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 20. Show that, if an equilateral triangle be inscribed in a circle, the square of its side is equal...
Full view - About this book ## Some account of the origin and objects of the new Oxford examinations for ...

...the algebraical expression for the mean proportional between two given quantities ? 19. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 20. Show that, if an equilateral triangle be inscribed in a circle, the square of its side is equal...
Full view - About this book ## Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pages
...Extract the square root of 321489. Voluntary Portion. 1. To describe a circle about a given square. 2. Similar triangles are to one another in the duplicate ratio of their homologous sides. 3. One of the two digits of a number is double the other, and if 27 be added to the number the digits...
Full view - About this book ## Elements of Geometry and Mensuration: With Easy Exercises, Designed for ...

Thomas Lund - Geometry - 1859 - 362 pages
...= / a, JP -# a, tt/ DX * Sometimes called 'homologous sides'. 'f- Euclid's enunciation of this is: 'Similar triangles are to one another in the duplicate ratio of their homologous sides'. X zB=z&, zC=zc; then AB, ab being any two corresponding, or homologous, sides, the triangle ABC shall...
Full view - About this book ## REPORT OF THE DIRECTOR OF PUBLIC INSTRUCTION, BOMBAY, FOR THE YEAR 1858-59.

...has to the fourth ? The sides about the equal angles of equiangular triangles are proportionals. 12. Similar triangles are to one another in the duplicate ratio of their homologous sides. LOGIC. I.—LOWER STANDARD. What ii the use of words ? Explain First and Second Intention. 2. Give...
Full view - About this book ## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, D.EFbe similar triangles, having the angle B equal to the angle E, and let AB be to BC, as...
Full view - About this book ## The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...homologous sides are parallel. PROPOSITION XIX. THEOREM. — If triangles (ABC, DEF) are similar, they are to one another in the duplicate ratio of their homologous sides (BC, EF). CONSMHTCTION. Take BG a third proportional to BC, EF (a), so that BC is to EF, as EF f* to...
Full view - About this book