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 59
... CHORD is a straight line joining the extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . 7. A ...
... CHORD is a straight line joining the extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord . 7. A ...
Seite 60
... chords . } 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the circum- ference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line which ...
... chords . } 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the circum- ference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line which ...
Seite 61
... chord . Let AD be a chord , and AB a diameter through one extremity , as A : then will AB be greater than AD . Draw the radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is ...
... chord . Let AD be a chord , and AB a diameter through one extremity , as A : then will AB be greater than AD . Draw the radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is ...
Seite 62
... chords ; and conversely , equal chords subtend equal arcs . 1o . In the equal cir- D cles ADB and EGF , M let the arcs AMD and A ENG be equal then N BE will the ... chord AD will coincide with EG ( A. 11 ) , and is , therefore 62 GEOMETRY .
... chords ; and conversely , equal chords subtend equal arcs . 1o . In the equal cir- D cles ADB and EGF , M let the arcs AMD and A ENG be equal then N BE will the ... chord AD will coincide with EG ( A. 11 ) , and is , therefore 62 GEOMETRY .
Seite 63
... chord ; and conversely , a greater chord subtends a greater • arc . 1o . In the equal circles ADL and EGK , let the arc EGP be greater than the arc AMD : then will the chord EP be greater than the chord AD . D H M A P For , place the ...
... chord ; and conversely , a greater chord subtends a greater • arc . 1o . In the equal circles ADL and EGK , let the arc EGP be greater than the arc AMD : then will the chord EP be greater than the chord AD . D H M A P For , place the ...
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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.