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 18
... another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn joining 18 GEOMETRY .
... another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn joining 18 GEOMETRY .
Seite 19
... given straight line , either from a point without , or from a point on the line . 7. A straight line may be drawn , making with a given straight line an angle equal to a given angle . 8. A ... a straight line meets another BOOK I. 19.
... given straight line , either from a point without , or from a point on the line . 7. A straight line may be drawn , making with a given straight line an angle equal to a given angle . 8. A ... a straight line meets another BOOK I. 19.
Seite 20
... a right angle , the other must also be a right angle . Cor . 2. The sum of the an- gles BAC , CAD , DAE , EAF , formed about a given point on the same side of a straight line BF , is equal For , their to two right angles . sum is equal ...
... a right angle , the other must also be a right angle . Cor . 2. The sum of the an- gles BAC , CAD , DAE , EAF , formed about a given point on the same side of a straight line BF , is equal For , their to two right angles . sum is equal ...
Seite 23
... given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III THEOREM . If two straight lines have two points in common , they coincide throughout their whole ... a straight line meets BOOK I. 23.
... given angles ( A. 9 ) . Hence , the sum of the given angles is equal to four right angles . PROPOSITION III THEOREM . If two straight lines have two points in common , they coincide throughout their whole ... a straight line meets BOOK I. 23.
Seite 26
... A being at the same time on the lines ED and FD , it must be at their ... straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ... given lines may rep- resent the sides of a triangle , the sum of 26 GEOMETRY .
... A being at the same time on the lines ED and FD , it must be at their ... straight line AC ( A. 12 ) : hence , the sum of AB and BC is greater than AC ... given lines may rep- resent the sides of a triangle , the sum of 26 GEOMETRY .
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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.