Elements of Geometry and Trigonometry: With Notes |
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Page 1
... measurement of space . Space has three dimensions , length , breadth , and height . II . A line is length without breadth . The extremities of a line are called points : a point , there- fore , occupies no space . III . A straight line ...
... measurement of space . Space has three dimensions , length , breadth , and height . II . A line is length without breadth . The extremities of a line are called points : a point , there- fore , occupies no space . III . A straight line ...
Page 14
... measures the true distance of a point from a line , because it is shorter than any other distance . Cor . 2. From the same point three equal straight lines can- not be drawn to the same straight line ; for if there could , we should ...
... measures the true distance of a point from a line , because it is shorter than any other distance . Cor . 2. From the same point three equal straight lines can- not be drawn to the same straight line ; for if there could , we should ...
Page 17
... measurements made on a figure constructed accu- rately , has not the same character of rigorousness with the other demonstrations of elementary geometry . It is given here merely as a simple method of arriving at a conviction of the ...
... measurements made on a figure constructed accu- rately , has not the same character of rigorousness with the other demonstrations of elementary geometry . It is given here merely as a simple method of arriving at a conviction of the ...
Page 20
... measures the distance of the parallels AB and CD at the point E , is equal to the side FH , which measures the distance of the same parallels at the point F. PROPOSITION XXVI . THEOREM . If two angles BAC , DEF have their sides parallel ...
... measures the distance of the parallels AB and CD at the point E , is equal to the side FH , which measures the distance of the same parallels at the point F. PROPOSITION XXVI . THEOREM . If two angles BAC , DEF have their sides parallel ...
Page 24
... MEASUREMENT OF ITS ANGLES . Definitions . I. The circumference of a circle is a curve line , all the points of which are equally distant from a point within , call- ed the centre . The circle is the space terminated by A this curve line ...
... MEASUREMENT OF ITS ANGLES . Definitions . I. The circumference of a circle is a curve line , all the points of which are equally distant from a point within , call- ed the centre . The circle is the space terminated by A this curve line ...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |
Common terms and phrases
AC² adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cos² cosine cylinder demonstration determined diagonal diameter draw drawn equal angles equation equivalent faces figure formulas frustum greater homologous sides hypotenuse inclination inscribed intersection isosceles join less likewise manner measure multiplied number of sides opposite parallel parallelepipedon parallelogram perpendicular plane MN polyedron prism PROBLEM Prop PROPOSITION quadrilateral quantities radii radius ratio rectangle rectilineal triangle regular polygon right angles right-angled triangle SABC Scholium sector segment shew shewn side BC similar sin² sines solid angle sphere spherical polygon spherical triangle square straight line suppose tang tangent THEOREM third side three angles three plane angles triangle ABC triangular pyramids vertex vertices
Popular passages
Page 152 - AMB be a section, made by a plane, in the sphere, whose centre is C. From the...
Page 24 - THEOREM. In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 62 - Similar triangles are to each other as the squares of their homologous sides.
Page 211 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Page 187 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 140 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
Page 150 - The radius of a sphere is a straight line, drawn from the centre to any point...
Page 168 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 135 - XII.) ; in like manner, the two solids AQ, AK, having the same base, AOLE, are to each other as their altitudes AD, A M.