Elements of Geometry and Trigonometry: With Notes |
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Page 5
... quantities equal to a third are equal to each other . 2. The whole is greater than its part . 3. The whole is equal to the sum of the parts into which it has been divided . 4. From one point to another , only one straight line can be ...
... quantities equal to a third are equal to each other . 2. The whole is greater than its part . 3. The whole is equal to the sum of the parts into which it has been divided . 4. From one point to another , only one straight line can be ...
Page 49
... quantities are added together , then expunging the + C and C , which destroy each other , we infer that A + D = B + E , and so of others All this is evident enough of itself ; but in case of difficulty , it will be useful to consult ...
... quantities are added together , then expunging the + C and C , which destroy each other , we infer that A + D = B + E , and so of others All this is evident enough of itself ; but in case of difficulty , it will be useful to consult ...
Page 67
... quantities are equal , we proceed by shewing that if there existed the smallest inequality between the quantities , a train of accurate reasoning would lead us to a ma- nifest and palpable absurdity ; from which we are forced to ...
... quantities are equal , we proceed by shewing that if there existed the smallest inequality between the quantities , a train of accurate reasoning would lead us to a ma- nifest and palpable absurdity ; from which we are forced to ...
Page 73
... quantities be multiplied by the same quantity BC there will result AB.AC.BC = CE.AD.BC ; now AD.BC is double of the surface of the triangle ( 6. III . ) ; there- fore the product of the three sides of a triangle is equal to its surface ...
... quantities be multiplied by the same quantity BC there will result AB.AC.BC = CE.AD.BC ; now AD.BC is double of the surface of the triangle ( 6. III . ) ; there- fore the product of the three sides of a triangle is equal to its surface ...
Page 104
... quantities of the same species ; a minimum is the least . Thus the diameter of a circle is a maximum among all the lines join- ing two points in the circumference ; the perpendicular is a minimum among all the lines drawn from a given ...
... quantities of the same species ; a minimum is the least . Thus the diameter of a circle is a maximum among all the lines join- ing two points in the circumference ; the perpendicular is a minimum among all the lines drawn from a given ...
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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.