Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 18
... distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only ene straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn ...
... distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only ene straight line can be drawn parallel to a given straight line . POSTULATES . 1. A straight line can be drawn ...
Page 26
... distance from A to C , A4 measured on any broken line AB , BC , C is greater than the distance measured on the straight line AC ( A. 12 ) : bence , the sum of AB and BC is greater than AC ; which was to be proved . Cor . If from both ...
... distance from A to C , A4 measured on any broken line AB , BC , C is greater than the distance measured on the straight line AC ( A. 12 ) : bence , the sum of AB and BC is greater than AC ; which was to be proved . Cor . If from both ...
Page 34
... distance will be the longer . Let A be a given point , DE a given straight line , AB a perpendicular to DE , and AD , AC , AE oblique lines , BC being equal to BE , and BD greater than BC . Then will AB be less than any of the oblique ...
... distance will be the longer . Let A be a given point , DE a given straight line , AB a perpendicular to DE , and AD , AC , AE oblique lines , BC being equal to BE , and BD greater than BC . Then will AB be less than any of the oblique ...
Page 35
... distance from a point to a line . Cor . 2. From a given point to a given straight line , only two equal straight lines can be drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the ...
... distance from a point to a line . Cor . 2. From a given point to a given straight line , only two equal straight lines can be drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the ...
Page 42
... distance between AB and CD , at the points F and E. The lines FH and EG are parallel ( P. XVIII . ) : hence , the alternate angles HFG and FGE are equal ( P. XX . , C. 2 ) . The lines AB and CD are parallel , by hypothesis : hence ...
... distance between AB and CD , at the points F and E. The lines FH and EG are parallel ( P. XVIII . ) : hence , the alternate angles HFG and FGE are equal ( P. XX . , C. 2 ) . The lines AB and CD are parallel , by hypothesis : hence ...
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Common terms and phrases
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
Popular passages
Page 101 - The area of a parallelogram is equal to the product of its base and altitude.
Page 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.
Page 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.
Page 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.
Page 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.
Page 33 - THEOREM. If two angles of a triangle are equal, the sides opposite to them are also equal, and consequently, the triangle is isosceles.
Page 18 - A SCALENE TRIANGLE is one which has no two of its sides equal ; as the triangle GH I.
Page 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.
Page 8 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 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.