Elements of Geometry and Trigonometry: With Notes |
From inside the book
Results 1-5 of 100
Page viii
... Triangles , ~ 308 Solution of Right - angled Rectilineal Triangles , nananana Solution of Rectilineal Triangles in general , 311 ... Triangle , ........... 366 INTRODUCTION . ON PROPORTION . THE doctrine of proportion belongs viii CONTENTS .
... Triangles , ~ 308 Solution of Right - angled Rectilineal Triangles , nananana Solution of Rectilineal Triangles in general , 311 ... Triangle , ........... 366 INTRODUCTION . ON PROPORTION . THE doctrine of proportion belongs viii CONTENTS .
Page 8
... triangle ABC be equal to DEF . E For those triangles may be applied to each other , so that they shall perfectly coincide . If the side DE be placed on its equal AB , the point D will fall on A , and the point E on B : and , since the ...
... triangle ABC be equal to DEF . E For those triangles may be applied to each other , so that they shall perfectly coincide . If the side DE be placed on its equal AB , the point D will fall on A , and the point E on B : and , since the ...
Page 9
... triangle DEF be equal to the triangle ABC . For , to bring about the superposition , let EF be placed on its equal BC ; the point E will fall on B , and the point F on C. And , since the angle E is equal to the angle B , the side ED ...
... triangle DEF be equal to the triangle ABC . For , to bring about the superposition , let EF be placed on its equal BC ; the point E will fall on B , and the point F on C. And , since the angle E is equal to the angle B , the side ED ...
Page 11
... triangle ABC , we shall have , by the preceding theorem , AG + GCZAB + BC ; and , taking AG from the one side , and ... triangle ABC are equal to the two DE , EF of the triangle DEF , while the third side , CB of the first triangle , is ...
... triangle ABC , we shall have , by the preceding theorem , AG + GCZAB + BC ; and , taking AG from the one side , and ... triangle ABC are equal to the two DE , EF of the triangle DEF , while the third side , CB of the first triangle , is ...
Page 12
... triangle is likewise equiangular , that is to say , has all its angles equal . Scholium . The equality of the triangles ABD , ACD , proves also that of the angle BAD to DAC , and of BDA to ADC ; hence the latter two are right angles ...
... triangle is likewise equiangular , that is to say , has all its angles equal . Scholium . The equality of the triangles ABD , ACD , proves also that of the angle BAD to DAC , and of BDA to ADC ; hence the latter two are right angles ...
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
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.