Elements of Geometry and Trigonometry: With Notes |
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Page x
... likewise make equal products . Thus 6 , 15 , 8 , 20 , are proportional ; because , multiplying the first and second by 5 and 2 respectively , so as to make 6 × 5 15 x 2 , we have likewise 8x5 = 20 × 2 A ; and generally , the magnitudes ...
... likewise make equal products . Thus 6 , 15 , 8 , 20 , are proportional ; because , multiplying the first and second by 5 and 2 respectively , so as to make 6 × 5 15 x 2 , we have likewise 8x5 = 20 × 2 A ; and generally , the magnitudes ...
Page xi
... likewise give p C = q D. It is obvious , however , that when the magnitudes A and B are in- commensurable , or have no common measure , this method will not serve . If , for example , the first term A were the side of a square , B the ...
... likewise give p C = q D. It is obvious , however , that when the magnitudes A and B are in- commensurable , or have no common measure , this method will not serve . If , for example , the first term A were the side of a square , B the ...
Page xii
... likewise called the extreme terms , or the ex- tremes ; the second and third 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 ...
... likewise called the extreme terms , or the ex- tremes ; the second and third 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 ...
Page xv
... likewise have A : B :: A ± C ÷ E : B ± D ± F . For by the last Theorem we have AF - BE , AD = BC ; also AB = BA Adding or subtracting which , we have ABAD + AF BA ± BC ± BE = or A ( R ± D ± F ) = B ( A ± C ± E ) . Hence by the last ...
... likewise have A : B :: A ± C ÷ E : B ± D ± F . For by the last Theorem we have AF - BE , AD = BC ; also AB = BA Adding or subtracting which , we have ABAD + AF BA ± BC ± BE = or A ( R ± D ± F ) = B ( A ± C ± E ) . Hence by the last ...
Page 7
... likewise be right . But the part FCE cannot be equal to the whole FCD ; hence the straight lines which have two points A and B common , cannot separate in any point of their production ; hence they form one and the same straight line ...
... likewise be right . But the part FCE cannot be equal to the whole FCD ; hence the straight lines which have two points A and B common , cannot separate in any point of their production ; hence they form one and the same straight line ...
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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.