The Elements of Analytical Geometry ...Carey, Lea, & Blanchard, 1833 - 288 من الصفحات |
المحتوى
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طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
abscissa AC² AD² asymptotes axis of abscissas axis of x base becomes bisects called centre chords drawn circumference coefficients conical surface conjugate diameters consequently construction coordinates cos.² cosine curve denote difference directrix distance draw drawn parallel ellipse equa equal equation equilateral expression focus formulas Geom geometrical given point gles hence hyperbola inclination inscribed circle latus rectum length Let ABC locus major diameter negative oblique ordinate origin parabola perpendicular plane of xy plane triangle point of contact positive primitive equation principal diameters PROBLEM proposed line radii radius vector rectangle rectangular axes referred represent right angle second order semi-diameters square substituting subtangent supplemental chords suppose surface system of conjugate tangent tion transformed vertex vertical angle whence
مقاطع مشهورة
الصفحة 67 - In a triangle, having given the ratio of the two* sides, together with both the segments of the base, made by a perpendicular from the vertical angle, to determine the sides of the triangle.
الصفحة 108 - They may cut each other, having two points common, when the distance between the centers is less than the sum and greater than the difference of the radii.
الصفحة 31 - To find the side of an equilateral triangle inscribed in a circle, multiply the diameter of the circle by .866.
الصفحة 200 - Given the base and the sum of the sides of a triangle, to find the locus of the point of intersection of lines from the angles bisecting • the opposite sides.
الصفحة 30 - Having given the side of a regular decagon inscribed in a circle whose radius is known, to find the side of a regular pentagon inscribed in the same circle.
الصفحة 163 - FPR, .-.PQ, bisects FD at right angles, and Q, is always on the axis, AY ; for this line, bisecting FE, must bisect every other line, FD, drawn to ED from F ; it follows, therefore,, that a tangent and a perpendicular to it from the focus always intersect on ANALYTICAL GEOMETRY.
الصفحة 30 - PROBLEM XVI. To find the side of a regular octagon inscribed in a circle whose radius is known. Let AB be the side of a square inscribed in the circle AFB, whose centre is E. Draw EG perpendicular to AB, then AG = GB, and the arc AF = arc FB.
الصفحة 153 - A') (x' — , A'), that is, as in the ellipse, the rectangle of the \ subtangent and abscissa of the point of contact is equal to the rectangle of the sum and difference of, the same abscissa and semi-transverse axis Thus OM • MR = A'M • MB'.
الصفحة 260 - Y' + cos. Z cos. Z' = 0 ^ cos. X cos. X" -f- cos. Y cos. Y
الصفحة 37 - In an isosceles triangle, the square of a line drawn from the vertex to any point in the base, together with the rectangle of the segments of the base, is equal to the square of one of the equal sides of the triangle.