Elements of Geometry and Trigonometry: With Notes |
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Page xi
... similar properties , ought to be included , directly or indirectly , in every definition of proportion . It is likewise certain , that if the Definition given above could be applied to such magnitudes , it would correctly indicate their ...
... similar properties , ought to be included , directly or indirectly , in every definition of proportion . It is likewise certain , that if the Definition given above could be applied to such magnitudes , it would correctly indicate their ...
Page xiv
... similar reason . Cor . 5. If we have A : B :: B : C ; then B2 = AC , and BAC ; hence a mean proportional is equal to the square - root of the product formed by multiplying the two extremes . Scholium . From this Proposition is derived ...
... similar reason . Cor . 5. If we have A : B :: B : C ; then B2 = AC , and BAC ; hence a mean proportional is equal to the square - root of the product formed by multiplying the two extremes . Scholium . From this Proposition is derived ...
Page xv
... similar . Cor . 2. By the very same process we deduce A : A - B :: C : C - D , or A - B : B :: C - D : D ; which is said to be dividendo . Cor . 3. And combining these two Corollaries with Cor . 4. of the last Theorem , we have A + B ...
... similar . Cor . 2. By the very same process we deduce A : A - B :: C : C - D , or A - B : B :: C - D : D ; which is said to be dividendo . Cor . 3. And combining these two Corollaries with Cor . 4. of the last Theorem , we have A + B ...
Page 35
... similar , it may be shewn that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; hence we have Angle ACB : angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
... similar , it may be shewn that the fourth term of the proportion cannot be less than AD ; hence it is AD itself ; hence we have Angle ACB : angle ACD :: arc AB : arc AD . Cor . Since the angle at the centre of a circle , and the arc ...
Page 47
... other , coincide in all their points : of this kind are two circles , which have equal radii ; two triangles , which have all their sides equal respectively , & c . II . Two figures are similar , when they have BOOK III . 47.
... other , coincide in all their points : of this kind are two circles , which have equal radii ; two triangles , which have all their sides equal respectively , & c . II . Two figures are similar , when they have BOOK III . 47.
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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.