Mechanical Geometry: An Application to Geometry of Some Propositions in StaticsR. Hardwicke, 1869 - 188 páginas |
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Términos y frases comunes
3G A+B+C a+b+c)0=aA+bB+cC a+b+c+...)G=aA+bB+cC+ a+b+c+etc A+tan a²+b²+c² aA+bB+cC aA+bB+cC+etc area ABC areal equation B+tan BC produced bisector centre of gravity centre of similitude circumscribed circle Corollary denote distances from BC drawn equal equation of forces Examples exterior angle find the areal fixed point geometrical hence the required inscribed circle interior angle intersection Let x+y+z)P=xA+yB+zC line 0=lx+my+nz line at infinity line harmonically divided line joining lines bisecting locus mean point meet BC middle points multiply nine points circle opposite sides parallel forces parallelogram perpendicular on BC point F polygon prove quadrilateral ABCD radical axis radii radius rectangle regular polygon required equation required result right angles right line self-conjugate circle sides BC similarly squares straight line Take distances tangents trapezium triangle ABC triangle of reference true equation whence x+y+z yza²+zxb²+xyc²
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Página 162 - B', A') ; then all the intersections of each pair of lines (as BB', AA') drawn from B and A to the points of section (B', A'), lie in a line that passes through C.
Página 92 - CB and CD. Prove that the resultant force is represented in magnitude and direction by four times the line joining the middle points of the diagonals of the quadrilateral.
Página 24 - Prove that the centre of gravity of a system of uniform bars forming a triangle is the centre of the circle inscribed in the triangle formed by the middle points of the bars.
Página 80 - If from a point without a parallelogram lines be drawn to the extremities of two adjacent sides, and of the diagonal which they include ; of the triangles thus formed, that, whose base is the diagonal, is equal to the sum of the other two.
Página 69 - To find a point in the base BC of a triangle ABC, such that if perpendiculars be drawn from it upon the sides, their sum shall be equal to a given line cr.
Página 173 - To find the conditions that the general equation of the second degree may represent a sphere.
Página 104 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
Página 50 - To find the centre of gravity of an arc of a circle. Let ACB be the arc, O its centre.
Página 132 - If from the middle point of one of the sides of a right-angled triangle, a perpendicular be drawn to the hypotenuse, the difference of the squares on the segments into which it is divided, is equal to the square on the other side.
Página 97 - ... the difference of the squares on these lines is equal to the difference of the squares on the two sides of the triangle.