Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. "
Mathematics, mechanics, heat - Page 54
by American School (Chicago, Ill.) - 1903
Full view - About this book

Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...similarly placed. For, it has already been shewn, that the surfaces of two polyedrons may be divided into the same number of triangles similar each to each, and similarly placed. Consider all the triangles of the one polyedron, except those which form the solid angle A, as the...
Full view - About this book

Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 228 pages
...similar, and so on in every pair of corresponding triangles ; hence, similar polygons may be divided into the same number of triangles, similar each to each, and similarly situated. Conversely. Let the polygons be composed of the Same number of similar triangles similarly...
Full view - About this book

Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...two angles in each respectively equal. Second. Two polygons are similar when both may be divided info the same number of triangles, similar each to each, and similarly placed. But to prevent this latter definition itself from including any superfluous conditions, the number...
Full view - About this book

Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...described on any other two homologous sides. PROPOSITION XXVI. THEOEEM. Two similar polygons may be divided into the same number of triangles, similar each to each, and similarly placed. Let AEDCB, FKIHG, be two similar polygons. From any angle A, in the polygon AEDCB, draw diagonals, AD,...
Full view - About this book

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...described on any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar polygons may be div1ded into the same number of triangles, similar each to each, and similarly placed. Let AEDCB, FKIHG, be two similar polygons. From the vertex of any angle A, in the poly• C gon AEDCB,...
Full view - About this book

Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...similarly situated. ELEMENTS OF GEOMETRY. Let ABCDE, FGHIK be two similar polygons ; they may be divided into the same number of triangles similar each to each, and similarly situated. From the homologous angles A and F, draw the diagonals AC, AD and FH, F I. The two polygons...
Full view - About this book

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...any other two homologous sides. PROPOSITION XXX. — THEOREM. 275. Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated. A 0 .' D? ; т d I Oi¡ Let ABODE, FG IJ I К be two ^^f\ . H similar polygons ; they may...
Full view - About this book

Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...P. IV.), we have, ABC : DEF : : AC2 : DF\ PROPOSITION XXVI. THEOREM. Similar polygons may be divided into the same number of triangles, similar, each to each, and similarly placed. Let ABCDE and FGHIK be two similar polygons, the angle A being equal to the angle F, B to Gr, C to H, and...
Full view - About this book

Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...— THEOREM. LLEMfcNTS OF UEOMETRY. H Let ABCDE, FGHIK be two similar polygons; they may be divided into the same number of triangles similar each to each, and similarly situated. From the homologous angles A and F, draw the diagonals AC, AD and FH, F I. The two polygons...
Full view - About this book

An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Modern - 1868 - 286 pages
...surfaces of two similar triangles is equal to the ratio of the squares of the homologous sides. But, two similar polygons may be decomposed into the same number of triangles similar each to each, and having the same ratio of similarity ; therefore, as the ratio of the surfaces of two homologous triangles...
Full view - About this book




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