Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 62
by Euclides - 1840
Full view - About this book

Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...angle at the vertex is the side of a regular decagon inscribed in the same circle. 11. Assuming that similar polygons may be divided into the same number of similar triangles, show that the polygons have to one another the duplicate ratio of their homologous sides. ABOD is a...
Full view - About this book

The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...be described upon a given straight line similar to one given, and so on. QEF PROP. XIX.— THEOBEM. Similar triangles are to one another in the duplicate ratio of their homologous sides. (References— Prop. v. 11, 16, def. 12; vi. 1, 11, 15.) Let ABC, DEF be similar triangles, having...
Full view - About this book

A Rudimentary Treatise on Land and Engineering Surveying, with all the ...

Thomas Baker (Civil engineer) - 1865 - 278 pages
...then, the triangle ABC is to the triangle AED as the square of AB is to I lie. square of AE : that is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of their homologous,...
Full view - About this book

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 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, DEF be similar triangles, having the angle B equal to the angle E, and let AB bo to BC, as...
Full view - About this book

Calendar of the McGill University, Montreal

McGill University - 1865 - 332 pages
...proportion, and show that it agrees with Euclid's. 9. Find a third proportional to two given lines. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. If 3 men can mow 7 acres of grass in 5 days of 9 hours each, in how many days of 8 hours each will...
Full view - About this book

Rudimentary treatise on mensuration and measuring

Thomas Baker (C.E.) - 1865 - 174 pages
...greatest angle : theorem, 17 ; any two angles being Rven, the, becomes known : theorem, ' ; similar, are to one another in the duplicate ratio of their homologous sides: theorem, 17. Triangular prism, definition of, 52. Triangular fields, method of surveying with chain...
Full view - About this book

Report on Education in the Parochial Schools of the Counties of Aberdeen ...

Simon Somerville Laurie - Dick bequest for elevating the character and position of the parochial schools and schoolmasters in the counties of Aberdeen, Banff and Moray - 1865 - 432 pages
...other, and the sides about the equal angles proper tionals, the triangles shall be equiangular. 7. Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another which the polygons have ; and that ratio is the duplicate ratio...
Full view - About this book

A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 426 pages
...together with the segmenta of the former will be equal to the square of the radius of the circle. i 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. If two straight lines be at right angles to the same plane, they shall be parallel to one another....
Full view - About this book

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

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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. Let ABCDE, FGHKL be similar polygons, and let AB be the side homologous to the side FG : the polygons...
Full view - About this book

The Edinburgh university calendar

Edinburgh univ - 1871 - 392 pages
...the part of it without the circle, is equal to the square of the line which touches it. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. Given (b) the base of a triangle, find an expression for the base of a similar triangle whose area...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF