Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 25
Page 93
... homologous . The corresponding angles are homologous angles , the corresponding sides are homologous sides , the corresponding diagonals are homologous diagonals , and so on . 3. SIMILAR ARCS , SECTORS , or SEGMENTS , in different ...
... homologous . The corresponding angles are homologous angles , the corresponding sides are homologous sides , the corresponding diagonals are homologous diagonals , and so on . 3. SIMILAR ARCS , SECTORS , or SEGMENTS , in different ...
Page 118
... homologous angles are those included by sides respectively parallel or perpendicular to each other . Scholium . When two triangles have their sides perpen- licular , each to each , they may have a different relative position from that ...
... homologous angles are those included by sides respectively parallel or perpendicular to each other . Scholium . When two triangles have their sides perpen- licular , each to each , they may have a different relative position from that ...
Page 120
... homologous sides are proportional ; hence , BD : AD :: AD : DC ; which was to be proved . and , Cor . 1. From the proportions , BC : AB :: AB : BD , BC : AC : AC : DC , we have ( B. II . , P. I. ) , • and , AB2 = BC × BD , ᎪᏛ = BC DC ...
... homologous sides are proportional ; hence , BD : AD :: AD : DC ; which was to be proved . and , Cor . 1. From the proportions , BC : AB :: AB : BD , BC : AC : AC : DC , we have ( B. II . , P. I. ) , • and , AB2 = BC × BD , ᎪᏛ = BC DC ...
Page 122
... homologous , DE will be parallel to BC , and we shall have , AD АВ :: AE AC ; hence ( B. II . , P. IV . ) , we have , D E ADE : ABE :: ABE : ABC ; that is , ABE is a mean proportional be- tween ADE and ABC . B PROPOSITION XXV . THEOREM ...
... homologous , DE will be parallel to BC , and we shall have , AD АВ :: AE AC ; hence ( B. II . , P. IV . ) , we have , D E ADE : ABE :: ABE : ABC ; that is , ABE is a mean proportional be- tween ADE and ABC . B PROPOSITION XXV . THEOREM ...
Page 123
... homologous sides . Let the triangles ABC and DEF be similar , the angle A being equal to the angle D , B to E , and C to F. then will the triangles be to each other as the squares of any two homologous sides . Because the angles A and D ...
... homologous sides . Let the triangles ABC and DEF be similar , the angle A being equal to the angle D , B to E , and C to F. then will the triangles be to each other as the squares of any two homologous sides . Because the angles A and D ...
Other editions - View all
Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence