Elements of Geometry and Trigonometry: With Notes |
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Page xii
... hence nqmp ; hence nqCmp C. But by hypothesis we have n Cm D ; hence nq Cmq D. Now we have already shewn nq Cmp C ; hence mp Cmq D , hence p C = qD . III . The ratio or relation which is perceived to exist be- tween two magnitudes of ...
... hence nqmp ; hence nqCmp C. But by hypothesis we have n Cm D ; hence nq Cmq D. Now we have already shewn nq Cmp C ; hence mp Cmq D , hence p C = qD . III . The ratio or relation which is perceived to exist be- tween two magnitudes of ...
Page xiii
... hence nAxmD = m Bxn C , or nm AD = nm BC , or AD - BC . * Secondly . If we have AD = BC ; then we are to prove that A : B :: C : D. Find the common measure of A and B ; and suppose we have n Am B. Now we have AD = BC , Also mBnA } ; hence ...
... hence nAxmD = m Bxn C , or nm AD = nm BC , or AD - BC . * Secondly . If we have AD = BC ; then we are to prove that A : B :: C : D. Find the common measure of A and B ; and suppose we have n Am B. Now we have AD = BC , Also mBnA } ; hence ...
Page xiv
... Hence also supposing A : B : C : D , we shall have A : B : .pC : pD , p being any number whole or fractional ; because if we have AD = BC , then also p AD = p BC whatever be the value of p . Hence a ratio is not affected by multiplying ...
... Hence also supposing A : B : C : D , we shall have A : B : .pC : pD , p being any number whole or fractional ; because if we have AD = BC , then also p AD = p BC whatever be the value of p . Hence a ratio is not affected by multiplying ...
Page 6
... hence ACK is greater than KCB . Therefore the line GH cannot fall on a line CK different from CD ; there- fore it falls on CD , and the angle EGH on ACD ; therefore all right angles are equal to each other . PROPOSITION II . THEOREM ...
... hence ACK is greater than KCB . Therefore the line GH cannot fall on a line CK different from CD ; there- fore it falls on CD , and the angle EGH on ACD ; therefore all right angles are equal to each other . PROPOSITION II . THEOREM ...
Page 12
... hence the latter two are right angles ; hence the line drawn from the vertex of an isoceles triangle to the middle point of its base , is perpendicular to that base , and divides the angle at the vertex into two equal parts . In a ...
... hence the latter two are right angles ; hence the line drawn from the vertex of an isoceles triangle to the middle point of its base , is perpendicular to that base , and divides the angle at the vertex into two equal parts . In a ...
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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.