Elements of Geometry and Trigonometry: With Notes |
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Page 51
... divided into 7 equal parts , AE will contain 4 of those parts : at each point of division erect a perpendicular to the base ; seven partial rect- angles will thus be formed , all equal to each other , because all have the same base and ...
... divided into 7 equal parts , AE will contain 4 of those parts : at each point of division erect a perpendicular to the base ; seven partial rect- angles will thus be formed , all equal to each other , because all have the same base and ...
Page 55
... divided into two parts AB , BC , the square described on the whole line AC , will include the square de- scribed on the part AB , the square described on the part BC , and twice the rectangle contained under AB , BC ; a pro- perty which ...
... divided into two parts AB , BC , the square described on the whole line AC , will include the square de- scribed on the part AB , the square described on the part BC , and twice the rectangle contained under AB , BC ; a pro- perty which ...
Page 64
... divided into triangles , and any triangle into two right - angled triangles . Thus the general properties of triangles include , by implica- tion , those of all figures . PROPOSITION XX . THEOREM . Two triangles which have an equal ...
... divided into triangles , and any triangle into two right - angled triangles . Thus the general properties of triangles include , by implica- tion , those of all figures . PROPOSITION XX . THEOREM . Two triangles which have an equal ...
Page 66
... divided into equal parts at the points F , G , H , the parallel DE would also be divided into equal parts at the points I , K , L. PROPOSITION XXIII . THEOREM . If from the right angle A of a right - angled triangle , the per ...
... divided into equal parts at the points F , G , H , the parallel DE would also be divided into equal parts at the points I , K , L. PROPOSITION XXIII . THEOREM . If from the right angle A of a right - angled triangle , the per ...
Page 75
... then draw CI parallel to F GB : AI will be the fifth part of the line AB ; and thus , by applying AI five times upon AB , the line AB will be divided into five equal parts . E -K M B For since CI is parallel to GB , the sides BOOK III . 75.
... then draw CI parallel to F GB : AI will be the fifth part of the line AB ; and thus , by applying AI five times upon AB , the line AB will be divided into five equal parts . E -K M B For since CI is parallel to GB , the sides BOOK III . 75.
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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.