Elements of Geometry and Trigonometry: With Notes |
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Page ix
... as it occurred , by means of the reductio ad absurdum . He has also in various parts of these Elements in- terspersed explanations of the sense in which geometrical mag- nitudes may be viewed , as coming under the dominion.
... as it occurred , by means of the reductio ad absurdum . He has also in various parts of these Elements in- terspersed explanations of the sense in which geometrical mag- nitudes may be viewed , as coming under the dominion.
Page xii
... mean terms or means . When both the means are the same , either of them is called a mean proportional between the two extremes ; and if in a series of proportional magnitudes each consequent is the same as the next antecedent , those ...
... mean terms or means . When both the means are the same , either of them is called a mean proportional between the two extremes ; and if in a series of proportional magnitudes each consequent is the same as the next antecedent , those ...
Page xiii
... means ; and conversely , if two products are equal , any two factors composing the first will form the extremes of a proportion , in which any two factors com- posing the second form the means . First . Suppose A : B :: C : D ; then is ...
... means ; and conversely , if two products are equal , any two factors composing the first will form the extremes of a proportion , in which any two factors com- posing the second form the means . First . Suppose A : B :: C : D ; then is ...
Page xiv
... means , those of the other extremes . For this reason , if we have and A : B :: C : D , then also we shall have A : C :: B : D , which is termed alternando , B : A :: D : C , which is termed invertendo : because in both cases the ...
... means , those of the other extremes . For this reason , if we have and A : B :: C : D , then also we shall have A : C :: B : D , which is termed alternando , B : A :: D : C , which is termed invertendo : because in both cases the ...
Page xvi
... means of these Theorems , and their Corollaries , it is easy to demonstrate , or even to discover , all the most important facts connected with the doctrine of proportion . The facts given here will enable the student to go through ...
... means of these Theorems , and their Corollaries , it is easy to demonstrate , or even to discover , all the most important facts connected with the doctrine of proportion . The facts given here will enable the student to go through ...
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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.