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Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.
Elements of Geometry: With, Practical Applications - Σελίδα 96
των George Roberts Perkins - 1850 - 320 σελίδες
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High School Arithemtic: Containing the Elementary and the Higher Principles ...

James B. Dodd - 1852 - 362 σελίδες
...its angles equal, — being equilateral and equiangular. § 39O. Two polygons are similar when they have the angles of the one equal to the angles of the other, each to each, and the sides which contain equal angles proportional. Circle and Ellipse. § 391. A circle is a plane figure bounded...

Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...DEFINITIONS. I. Similar rectilineal figures are those which have the several angles in one equal to those in the other, each to each, and the sides about the equal angles — that is, which include the equal angles, proportionals. IT. Two sides of one figure are said to...

Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - 1855 - 324 σελίδες
...ONS OF FIGU 11 ES DEFINITION'S 1 Similar figures, are those which have the angles of the one n-\1ia\ to' the angles of the other, each to each, and the sides about the equal angles proportional2 Any two sides, or any two angles, which are like placed in the two similar figures, are...

Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856 - 216 σελίδες
...which adjoin equal angles, are homologous. 99. Two figures are similar, when the angles of the one are equal to the angles of the other, each to each, and the homologous sides are proportionals. 100. In two CIRCLES, similar sectors, similar arcs, or similar...

National Society's Monthly Paper

1856
...of one equal to the three s,des of the other each to each, the angles of the one triangle shall be equal to the angles of the other, each to each, and the equal angles shall be opposite to the equal sides. cos a— cos b cos c cos A+cos B cos C 4. In any...

Elements of Geometry and Conic Sections

Elias Loomis - 1858 - 234 σελίδες
...circle may be equivalent to a square, a triangle to a rectangle, &c. 3. Similar figures are such as have the angles of the one equal to the angles of...and the sides about the equal angles proportional. Sides which have the same position in the two figures, or which are adjacent to equal angles, are called...

Carpentry Made Easy: Or, The Science and Art of Framing, on a New and ...

1857 - 134 σελίδες
...polygons are those which coincide with each other in all their parts. (Ax. 13.) 32. Similar polygons hare the angles of the one equal to the angles of the other,...and the sides about the equal angles proportional. 33. Homologous sides and homologous angles are those which have like positions in similar polygons....

Carpentry Made Easy, Or, The Science and Art of Framing, on a New and ...

William E. Bell - 1859 - 134 σελίδες
...polygons are those which coincide with each other in all their parts. (Ax. 13.) 32. Similar polygons have the angles of the one equal to the angles of...and the sides about the equal angles proportional. 33. Homologous sides and homologous angles are those which have like positions in similar polygons....

A Course of Mathematics: Composed for the Use of the Royal Military Academy

Charles Hutton - 1860 - 895 σελίδες
...the same l'n> ur«. 70. Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles pro portional. 71. The Perimeter of a figure, is the sum of all its sides taken together. 72. A Proposition,...

Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1860 - 453 σελίδες
...other. The proof is as follows: The A's ABC' and DnE a.re equal, because the angles of the one are equal' to the angles of the other, each to each, and the hypotenuse AC of the one, is equal to the hypotenuse DE of the other. In like manner, it may be shown...