## Elements of Geometry and Trigonometry |

### From inside the book

Page 53

...

...

**similar**, it may be shown . that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; therefore we have Angle ACB angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ... Page 68

...

...

**similar**figures , are called homologous sides or angles . A 3. In two different circles ,**similar**arcs , sectors , or segments , are those which correspond to equal angles at the centre . Thus , if the angles A and O are equal , the ... Page 73

Adrien Marie Legendre. that the area of any other rectangle is computed in a

Adrien Marie Legendre. that the area of any other rectangle is computed in a

**similar**manner , by measuring its sides with the same linear unit ; a second product is thus obtained , and the ratio of the two pro- ducts is the same as that ... Page 84

...

...

**similar**when they have their angles equal , each to each , and their homolo- gous sides proportional ( Def . 1. ) ; consequently the equiangu- lar triangles BAC , CED , are two**similar**figures . Cor . For the similarity of two triangles ... Page 85

...

...

**similar**. In the two triangles BAC , DEF , suppose we have BC : EF :: AB : DE :: AC : DF ; then will the triangles ABC , DEF have their an- gles_equal , namely , A = D , B = E , C = F . At the point E , make the angle = A E FEG B , and ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex