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 16
... is one that has one right angle . The side opposite the right angle , is called the hypothe nuse . 2d . An OBLIQUE - ANGLED TRIANGLE is one whose angles are all oblique . If one angle of an oblique - angled triangle is 16 GEOMETRY .
... is one that has one right angle . The side opposite the right angle , is called the hypothe nuse . 2d . An OBLIQUE - ANGLED TRIANGLE is one whose angles are all oblique . If one angle of an oblique - angled triangle is 16 GEOMETRY .
Page 17
... opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2. A RHOMBOID ...
... opposite sides parallel , two and two . There are two varieties of parallelograms : rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2. A RHOMBOID ...
Page 21
... OPPOSITE , or VERTICAL ANGLES , are those which lie on opposite sides of both lines ; thus , ACE and DCB , or ACD and ECB , are opposite angles . From the pro- position just demonstrated , the sum of any two adjacent angles is equal to ...
... OPPOSITE , or VERTICAL ANGLES , are those which lie on opposite sides of both lines ; thus , ACE and DCB , or ACD and ECB , are opposite angles . From the pro- position just demonstrated , the sum of any two adjacent angles is equal to ...
Page 22
... opposite angle will also be a right angle . A C is a right angle , For , ( P. I. , C. 1 ) , Ꭰ -B E Cor . 2. If one line DE , is perpendicular to another AB , then will the second line AB For , the angles DCA definition ( D. 12 ) ; and ...
... opposite angle will also be a right angle . A C is a right angle , For , ( P. I. , C. 1 ) , Ꭰ -B E Cor . 2. If one line DE , is perpendicular to another AB , then will the second line AB For , the angles DCA definition ( D. 12 ) ; and ...
Page 30
... opposite the equal angles ; and conversely . PROPOSITION XI . THEOREM . In an isosceles triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then will the ...
... opposite the equal angles ; and conversely . PROPOSITION XI . THEOREM . In an isosceles triangle the angles opposite the equal sides are equal . Let BAC be an isosceles triangle , having the side AB equal to the side AC : then will the ...
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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.