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 & Company, 1872 - 455 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 a 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 a solution . 9. A POSTULATE is a self - evident Problem . Theorems , Axioms , Problems , and Postulates , are all ...
Seite 19
... . for Scholium . In referring to the same Book , the number of the Book is not given ; in referring to any other Book , the number of the Book is given . ! PROPOSITION I. THEOREM . If a straight line meet another BOOK I. 19.
... . for Scholium . In referring to the same Book , the number of the Book is not given ; in referring to any other Book , the number of the Book is given . ! PROPOSITION I. THEOREM . If a straight line meet another BOOK I. 19.
Seite 23
... THEOREM . If two straight lines have twoc points in common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines coincide throughout ...
... THEOREM . If two straight lines have twoc points in common , they will coincide throughout their whole extent , and form one and the same line . Let A and B be two points common to two lines : then will the lines coincide throughout ...
Seite 24
... THEOREM . If a straight line meet 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 will form one and the same straight line . Let DC meet AC and BC at C ...
... THEOREM . If a straight line meet 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 will form one and the same straight line . Let DC meet AC and BC at C ...
Seite 26
... THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will B the sum of any two sides , as AB , BC , be greater than the third side AC . For , the distance from A to C , A4 ...
... THEOREM . The sum of any two sides of a triangle is greater than the third side . Let ABC be a triangle : then will B the sum of any two sides , as AB , BC , be greater than the third side AC . For , the distance from A to C , A4 ...
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Häufige Begriffe und Wortgruppen
AB² ABCD AC² adjacent angles altitude apothem Applying logarithms centre chord circle circumference circumscribed complement cone consequently convex surface cosec cosine Cotang cylinder decimal denote diameter difference distance divided draw drawn edges equal to AC Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polar triangle pole polyedral angle polyedron prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium segment semi-circumference side BC similar sine six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triedral angle upper base vertex vertices volume whence
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Seite 101 - The area of a parallelogram is equal to the product of its base and altitude.
Seite 92 - PROBLEM XV. To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B, by the lines AO and BO, meeting in the point 0 (Prob.
Seite 48 - 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 45 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Seite 106 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Seite 33 - THEOREM. If two angles of a triangle are equal, the sides opposite to them are also equal, and consequently, the triangle is isosceles.
Seite 18 - A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle GH I.
Seite 30 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included angles unequal, the third sides will be unequal; and the greater side will belong to the triangle which has the greater included angle.
Seite 8 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 156 - DE, are like parts of the circumferences to which they belong, and similar sectors, as A CH and 'D OE, are like parts of the circles to which they belong : hence, similar arcs are to each other as their radii, and similar sectors are to each other as the squares of their radii.