Elements of Geometry and Trigonometry: With Notes |
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Page x
... manner , exhibiting the leading truths of the subject , when referred to mere numbers , or to magnitudes capable of being completely represented by num- bers . DEFINITIONS . I. One magnitude is a multiple of another , when the former ...
... manner , exhibiting the leading truths of the subject , when referred to mere numbers , or to magnitudes capable of being completely represented by num- bers . DEFINITIONS . I. One magnitude is a multiple of another , when the former ...
Page xi
... manner our Definition can be brought to bear on this class of magnitudes , with regard to which , it appears to be , as it were , potentially true , though never actually applicable . If B is divided by any measure of A , it will leave ...
... manner our Definition can be brought to bear on this class of magnitudes , with regard to which , it appears to be , as it were , potentially true , though never actually applicable . If B is divided by any measure of A , it will leave ...
Page 6
... manner AB will be perpendicular to DE . For , since DE is perpendicular to AB , the angle ACD must be equal to its adjacent one DCB , and both of them must be right . But since ACD is a right angle , its adjacent K B one ACE must also ...
... manner AB will be perpendicular to DE . For , since DE is perpendicular to AB , the angle ACD must be equal to its adjacent one DCB , and both of them must be right . But since ACD is a right angle , its adjacent K B one ACE must also ...
Page 7
... manner , that the angle ACE is equal to its opposite angle BCD . Scholium . The four angles formed about a point by two straight lines which intersect each other , are together equal to four right angles : for the two angles ACE , BCE ...
... manner , that the angle ACE is equal to its opposite angle BCD . Scholium . The four angles formed about a point by two straight lines which intersect each other , are together equal to four right angles : for the two angles ACE , BCE ...
Page 9
... manner , since the angle F is equal to the angle C , the line FD will take the di- rection CA , and the point D will be found somewhere in the line CA. Hence , the point D , occurring at the same time in the two straight lines BA and CA ...
... manner , since the angle F is equal to the angle C , the line FD will take the di- rection CA , and the point D will be found somewhere in the line CA. Hence , the point D , occurring at the same time in the two straight lines BA and CA ...
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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.