Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes, 1885 - 512 Seiten |
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Seite 31
... bisects the angle at the vertex , and is perpendicular to the base . PROPOSITION XII . THEOREM . If two angles of a triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isosceles . In the ...
... bisects the angle at the vertex , and is perpendicular to the base . PROPOSITION XII . THEOREM . If two angles of a triangle are equal , the sides opposite to them are also equal , and consequently , the triangle is isosceles . In the ...
Seite 50
... bisect ( halve ) two verti- cal angles , form one and the same straight line . 2. Given two lines , BE and AD ; join B ... bisects the exterior vertical angle of an isos- celes triangle is parallel to the base of the triangle . ( P. XXV ...
... bisect ( halve ) two verti- cal angles , form one and the same straight line . 2. Given two lines , BE and AD ; join B ... bisects the exterior vertical angle of an isos- celes triangle is parallel to the base of the triangle . ( P. XXV ...
Seite 51
... bisect the angles of any quadrilateral form , by their in- tersection , another quadrilateral , the opposite angles of which are supplements of each other . [ Twice the angle B is equal to the sum of the angles CDE and DEF . ] + B BOOK ...
... bisect the angles of any quadrilateral form , by their in- tersection , another quadrilateral , the opposite angles of which are supplements of each other . [ Twice the angle B is equal to the sum of the angles CDE and DEF . ] + B BOOK ...
Seite 66
... bisects that chord , and also the arc subtended by it . Let CG be the radius which is perpendicular to the chord AB : then this radius bisects the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right ...
... bisects that chord , and also the arc subtended by it . Let CG be the radius which is perpendicular to the chord AB : then this radius bisects the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right ...
Seite 67
... bisects the chord AB , and also the arc AGB ; which was to be proved . Cor . A straight line , perpendicular to a ... bisect these lines by per- pendiculars DE and FG : then will these perpendiculars meet in some point 0. For , if they ...
... bisects the chord AB , and also the arc AGB ; which was to be proved . Cor . A straight line , perpendicular to a ... bisect these lines by per- pendiculars DE and FG : then will these perpendiculars meet in some point 0. For , if they ...
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Häufige Begriffe und Wortgruppen
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Beliebte Passagen
Seite 28 - If two triangles have two sides of the one equal to two sides of the...
Seite 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Seite 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Seite 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Seite 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Seite 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Seite 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Seite 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.