# Perpendiculars Sentence Examples

- Also the auxiliarly circle is the locus of the feet of the
**perpendiculars**from the foci on any tangent. - Inside an equilateral triangle, for instance, of height h, - 2Ra/3y/h, (8) where a, 13, y are the
**perpendiculars**on the sides of the triangle. - The orthogonal projection of a section of this surface by a plane containing one of the
**perpendiculars**and inclined to the axis is the quadratrix. - From every point of the curve of intersection,
**perpendiculars**are drawn to the axis. - Represented by a point P, so chosen that the perpendicular Pa on to the side BC gives the percentage of A in the alloy, and the
**perpendiculars**Pb and Pc give the percentages of B and C respectively. - The quadrilateral, for instance, consists of two triangles, and its area is the product of half the length of one diagonal by the sum of the
**perpendiculars**drawn to this diagonal from the other two angular points. - (iii) Take any straight line intersecting or not intersecting the figure, and draw
**perpendiculars**Aa, Bb, Cc, Dd,. - Or generally, if M 1 M2 M3 are the moments of the external forces to the left of 0, A, and B respectively, and s, t and c the
**perpendiculars**from 0, A and B on the directions of the forces cut by the section, then Ss=M11 Tt=M2andCc=M3. - In the same preface is included (a) the famous problem known by Pappus's name, often enunciated thus: Having given a number of straight lines, to find the geometric locus of a point such that the lengths of the
**perpendiculars**upon, or (more generally) the lines drawn from it obliquely at given inclinations to, the given lines satisfy the condition that the product of certain of them may bear a constant ratio to the product of the remaining ones; (Pappus does not express it in this form but by means of composition of ratios, saying that if the ratio is given which is compounded of the ratios of pairs - one of one set and one of another - of the lines so drawn, and of the ratio of the odd one, if any, to a given straight line, the point will lie on a curve given in position), (b) the theorems which were rediscovered by and named after Paul Guldin, but appear to have been discovered by Pappus himself. - Since - the side OA is common, we have o to prove that the sum of the - -
**perpendiculars**from B and C on - -. - The triangles OAB, RHK are similar, and if the
**perpendiculars**OM, RN be drawn we have HK .OM~rAB. - Hence also the ratio of the com ponents of the velocities of two points A and B in the directions AP and BW respectively, both in the plane of rotation, is equal to the ratio of the
**perpendiculars**Fni and Fn. - Application to a Pair of TurnIng Fseces.Let ai, a2 be the angular velocities of a pair of turning pieces; Of, Oi the angles which their line of connection makes with their respective planes of rotation; Ti, r2 the common
**perpendiculars**let fall from the line of connection upon the respective axes of rotation of the pieces. - Then the equal components, along the line of connection, of the velocities of the points where those
**perpendiculars**meet that line are airi cos 0i = afri cos Oi; consequently, the comparative motion of the pieces is given by the equation ai_rieos0i ~I - Let CiP1, C2P2 be
**perpendiculars**let Pi ~ ~ fall from the centres of the i~) wheels on the line of contact. - The axes of rotation of a pair of turning pieces connected by a link are almost always parallel, and perpendicular to the line of connection n which case the angular velocity ratio at any instant is the recipocal of the ratio of the common
**perpendiculars**let fall from the me of connection upon the respective axes of rotation. - But, p and q being respectively the
**perpendiculars**to the lines of action of the forces, this equation reduces to Pp=Rq, FIG. - Of the properties of a tangent it may be noticed that the tangent at any point is equally inclined to the focal distances of that point; that the feet of the
**perpendiculars**from the foci on any tangent always lie on the auxiliary circle, and the product of these**perpendiculars**is constant, and equal to the product of the distances of a focus from the two vertices.