Elements of Geometry and Trigonometry: With Notes |
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Page vii
... Square , are irrational Numbers , 239 V. Containing the Analytical Solution of various Prob- lems concerning the Triangle , the inscribed Quadrila- teral , the Parallelepipedon , and the Triangular Py- ramid , 246 VI . On the shortest ...
... Square , are irrational Numbers , 239 V. Containing the Analytical Solution of various Prob- lems concerning the Triangle , the inscribed Quadrila- teral , the Parallelepipedon , and the Triangular Py- ramid , 246 VI . On the shortest ...
Page xi
... square , B the second term being its diagonal , and the third term C = A + B the sum or the dif- ference of the former two , there could exist no common measure between any of the terms , and no such pair of numbers n and m could be ...
... square , B the second term being its diagonal , and the third term C = A + B the sum or the dif- ference of the former two , there could exist no common measure between any of the terms , and no such pair of numbers n and m could be ...
Page xiv
... square - root of the product formed by multiplying the two extremes . Scholium . From this Proposition is derived the mode of oper- ating in the common arithmetical Rule of Three , where three terms of a proportion being given , it is ...
... square - root of the product formed by multiplying the two extremes . Scholium . From this Proposition is derived the mode of oper- ating in the common arithmetical Rule of Three , where three terms of a proportion being given , it is ...
Page xvi
... square of the first is to the square of the second . The ratio which A bears to C is sometimes called the duplicate of that which it bears to B. Secondly . Having A : B :: B : C , A : B :: C : D , and A : B :: A : B , we shall have A3 ...
... square of the first is to the square of the second . The ratio which A bears to C is sometimes called the duplicate of that which it bears to B. Secondly . Having A : B :: B : C , A : B :: C : D , and A : B :: A : B , we shall have A3 ...
Page 3
... square , which has its sides equal , and its angles right . ( See Prop . 28. I. ) The rectangle , which has its angles right , with- out having its sides equal . ( See the same Prop . ) The parallelogram , or rhomboid , which has its ...
... square , which has its sides equal , and its angles right . ( See Prop . 28. I. ) The rectangle , which has its angles right , with- out having its sides equal . ( See the same Prop . ) The parallelogram , or rhomboid , which has its ...
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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
ACē adjacent adjacent angles altitude angle ACB angle BAC centre chord circ circle circular sector circumference circumscribed common cone consequently construction continued fraction convex surface cosē 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 sinē 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.