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 17
... rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2. A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral ...
... rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2. A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral ...
Page 95
... . 7 ) ; which was to be proved Cor . Triangles having equal bases and equal altitudes are equal , for they are halves of equal parallelograms . PROPOSITION III . THEOREM . Rectangles having equal altitudes , BOOK IV . 95.
... . 7 ) ; which was to be proved Cor . Triangles having equal bases and equal altitudes are equal , for they are halves of equal parallelograms . PROPOSITION III . THEOREM . Rectangles having equal altitudes , BOOK IV . 95.
Page 96
... Rectangles having equal altitudes , are proportional to their bases . There may be two cases : the bases may be commensu rable , or they may be incommensurable . 1 ° . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are ...
... Rectangles having equal altitudes , are proportional to their bases . There may be two cases : the bases may be commensu rable , or they may be incommensurable . 1 ° . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are ...
Page 97
... rectangles be incommensurable : then will the rectangles be proportional to their bases . For , place the rectangle HEFK upon the rectangle ABCD , so that it shall take the position AEFD . Then , if the rectangles are not pro- portional ...
... rectangles be incommensurable : then will the rectangles be proportional to their bases . For , place the rectangle HEFK upon the rectangle ABCD , so that it shall take the position AEFD . Then , if the rectangles are not pro- portional ...
Page 98
... rectangles are to each other as the products of their bases and altitudes . Let ABCD and AEGF be two rectangles : then ... rectangle AEGF will be the superficial unit , and we shall have , ABCD 1 :: AB × AD : 1 ; ABCD AB × A.D : hence ...
... rectangles are to each other as the products of their bases and altitudes . Let ABCD and AEGF be two rectangles : then ... rectangle AEGF will be the superficial unit , and we shall have , ABCD 1 :: AB × AD : 1 ; ABCD AB × A.D : 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.