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 11
... THEOREM is a truth requiring demonstration . 7. An AXIOM is a self - evident truth . 8. A PROBLEM is a question requiring solution . 9. A POSTULATE is a self - evident Problem . Theorems , Axioms , Problems , and Postulates , are all ...
... THEOREM is a truth requiring demonstration . 7. An AXIOM is a self - evident truth . 8. A PROBLEM is a question requiring solution . 9. A POSTULATE is a self - evident Problem . Theorems , Axioms , Problems , and Postulates , are all ...
Seite 20
... THEOREM . If a straight line meets another straight line , the sum of the adjacent angles is equal to two right angles . Let DC meet AB at C : then is the sum of the angles DCA and DCB equal to two right an- gles . At C , let CE be ...
... THEOREM . If a straight line meets another straight line , the sum of the adjacent angles is equal to two right angles . Let DC meet AB at C : then is the sum of the angles DCA and DCB equal to two right an- gles . At C , let CE be ...
Seite 23
... THEOREM . If two straight lines have two points in common , they coincide throughout their whole extent , and form one and the same line . Let A and B B be two points common to two lines : then the lines coincide throughout . E A- B C D ...
... THEOREM . If two straight lines have two points in common , they coincide throughout their whole extent , and form one and the same line . Let A and B B be two points common to two lines : then the lines coincide throughout . E A- B C D ...
Seite 24
... THEOREM . If a straight line meets two other straight lines at a com- mon point , making the sum of the contiguous angles equal to two right angles , the two lines met form one and the same straight line . Let DC meet AC and BC at C ...
... THEOREM . If a straight line meets two other straight lines at a com- mon point , making the sum of the contiguous angles equal to two right angles , the two lines met form one and the same straight line . Let DC meet AC and BC at C ...
Seite 27
... THEOREM . if from any point within a triangle two straight lines are drawn to the extremities of any side , their sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let ...
... THEOREM . if from any point within a triangle two straight lines are drawn to the extremities of any side , their sum is less than that of the two remaining sides of the triangle . Let O be any point within the triangle BAC , and let ...
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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
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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.