Elements of Geometry and Trigonometry: With Notes |
From inside the book
Results 1-5 of 34
Page xi
... divided by any measure of A , it will leave a certain remainder 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 ...
... divided by any measure of A , it will leave a certain remainder 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 ...
Page 5
... divided . 4. From one point to another , only one straight line can be drawn . 5. Two magnitudes , lines , surfaces , or solids , are equal , if , when applied to each other , they coincide throughout their whole extent . PROPOSITION I ...
... divided . 4. From one point to another , only one straight line can be drawn . 5. Two magnitudes , lines , surfaces , or solids , are equal , if , when applied to each other , they coincide throughout their whole extent . PROPOSITION I ...
Page 21
... of all the opposite angles , it is plain that the A polygon will be divided into five triangles , if it has seven sides ; into six triangles , if it has eight ; E and , in general , into as many triangles , BOOK I. 21.
... of all the opposite angles , it is plain that the A polygon will be divided into five triangles , if it has seven sides ; into six triangles , if it has eight ; E and , in general , into as many triangles , BOOK I. 21.
Page 34
... divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial arcs Am , mn , np , & c . , will ( 15. II . ) be equal to each of the partial arcs Ax , xy , & c . Therefore the whole arc AB ...
... divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial arcs Am , mn , np , & c . , will ( 15. II . ) be equal to each of the partial arcs Ax , xy , & c . Therefore the whole arc AB ...
Page 39
... divided into two equal parts ; and thus by succes- sive subdivisions , a given angle or a given arc may be divided into four equal parts , into eight , into sixteen , and so on . PROBLEM VI . Through a given point A , to BOOK II . 39.
... divided into two equal parts ; and thus by succes- sive subdivisions , a given angle or a given arc may be divided into four equal parts , into eight , into sixteen , and so on . PROBLEM VI . Through a given point A , to BOOK II . 39.
Other editions - View all
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.