Elements of Geometry and Trigonometry: With Notes |
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Page xi
... less than that measure : if B is then divided by a half , a third , a ninth , a six- teenth , or any submultiple of that measure , the remainder will evidently in each case be less than that submultiple ; and as the submultiple , which ...
... less than that measure : if B is then divided by a half , a third , a ninth , a six- teenth , or any submultiple of that measure , the remainder will evidently in each case be less than that submultiple ; and as the submultiple , which ...
Page xii
... less or greater than another ratio . IV . The first and third terms of a proportion are called the antecedents ; the second and fourth the consequents . The first and fourth are likewise called the extreme terms , or the ex- tremes ...
... less or greater than another ratio . IV . The first and third terms of a proportion are called the antecedents ; the second and fourth the consequents . The first and fourth are likewise called the extreme terms , or the ex- tremes ...
Page xiii
... less than the measure , and therefore still less than F. By the same Definition , we shall have n C = m ( D - D ′ ) , D ' being a positive quantity . Hence we have n A × m ( D — D ' ) = n ) = n C × m ( B — B ' ) ; that is nm AD- ) —n m ...
... less than the measure , and therefore still less than F. By the same Definition , we shall have n C = m ( D - D ′ ) , D ' being a positive quantity . Hence we have n A × m ( D — D ' ) = n ) = n C × m ( B — B ' ) ; that is nm AD- ) —n m ...
Page 1
... less , by which they are separated from each other in regard to their position , is called an angle ; the point of intersection A is the vertex of the A angle ; the lines AB , AC , are its sides . A ن The angle is sometimes designated ...
... less , by which they are separated from each other in regard to their position , is called an angle ; the point of intersection A is the vertex of the A angle ; the lines AB , AC , are its sides . A ن The angle is sometimes designated ...
Page 2
... less than D right angle , is an acute angle ; every angle DEF , greater than a right angle , is an obtuse angle . E XII . Two lines are said to be parallel , when , being situated in the same plane , they cannot meet , how far soever ...
... less than D right angle , is an acute angle ; every angle DEF , greater than a right angle , is an obtuse angle . E XII . Two lines are said to be parallel , when , being situated in the same plane , they cannot meet , how far soever ...
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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.