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Δημοφιλή αποσπάσματα

Σελίδα 8 - Any two sides of a triangle are together greater than the third side.
Σελίδα 52 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Σελίδα 89 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Σελίδα 40 - To express the cosine of an angle of a triangle in terms of the sides. Let ABC be a triangle ; and retaining the usual notation of Trigonometry, let CB = a, CA=ß; then (vector AB)' =(a- ß)' = a'-2Saß + ß
Σελίδα 68 - Ex. 5. To find the locus of a point such that the ratio of its distances from a given point and a given straight line is constant — all in one plane. Let S be the given point, DQ the given straight line, SP = ePQ the given relation. Let vector SD = a,SP = p, DQ = yy, y being the unit vector along DQ, then eT(PQ), 5—2 gives p~ = e'PQ', where PQ is a vector, = i'(a»)" = eVa'. = a+yy; . : Sap + xa' = a', for Say = 0; and a;V = (a...
Σελίδα 72 - P is a surfaco of the second order. 3. Prove that the section of this surface by a plane perpendicular to the lin.e to which the generating lines are drawn perpendicular is a circle. 4. Prove that the locus of a point whose distances from two given straight lines have a constant ratio is a surface of the second order. 5. A straight line moves parallel to a fixed plane and is terminated by two given straight lines not in one plane ; find the locus of the point which divides the line into parts which...
Σελίδα 9 - FG [Hypothesit. and joined towards the same parts by the straight lines BE, CH. But straight lines which join the extremities of equal and parallel straight lines towards the same parts are themselves equal and parallel.
Σελίδα 90 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Σελίδα 32 - G : shew that FG is parallel to CD. 346. From any point in the base of a triangle straight lines are drawn parallel to the sides : shew that the intersection of the diagonals of every parallelogram so formed lies in a certain straight line. 347. In a triangle ABC a straight...
Σελίδα 90 - IP we define a conic section as " the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line

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