Geometrical Analysis: Or the Construction and Solution of Various Geometrical Problems from Analysis, by Geometry, Algebra, and the Differential Calculus; Also, the Geometrical Construction of Algebraic Equations, and a Mode of Constructing Curves of the Higher Order by Means of PointsJ. B. Lippincott & Company, 1872 - 279 σελίδες |
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Σελίδα 8
... Tangents , Tangent , Normal , Sub- tangent , etc. of a given Ellipse by Construction 258 · To find the Area of an Ellipse by the Calculus 260 260 To construct the Ellipse by Points from its Equation The Hyperbola . - To determine Points ...
... Tangents , Tangent , Normal , Sub- tangent , etc. of a given Ellipse by Construction 258 · To find the Area of an Ellipse by the Calculus 260 260 To construct the Ellipse by Points from its Equation The Hyperbola . - To determine Points ...
Σελίδα 40
... tangent to them at P and L. Whence this = Construction . - Draw CR , bisecting the given angle GCQ . At any point , as G , in CG , erect the perpendicular GD ' = the given radius DF , and on it lay GO ' : the other given radius OE ...
... tangent to them at P and L. Whence this = Construction . - Draw CR , bisecting the given angle GCQ . At any point , as G , in CG , erect the perpendicular GD ' = the given radius DF , and on it lay GO ' : the other given radius OE ...
Σελίδα 41
... tangent . ( III . 9. * ) Calculation . - 1 . In the triangles CFD and CEO , Case 1 , find CD and CF CI ; also CO . Then DO CD - CO , and the angle FDC 90 ° — FCD . 2. In triangle KDO , Case 2 , find angle KDO ; then angle FDA FDL ( FDC ...
... tangent . ( III . 9. * ) Calculation . - 1 . In the triangles CFD and CEO , Case 1 , find CD and CF CI ; also CO . Then DO CD - CO , and the angle FDC 90 ° — FCD . 2. In triangle KDO , Case 2 , find angle KDO ; then angle FDA FDL ( FDC ...
Σελίδα 68
... tangent to the perpendicular BC , at E. = Scholium 2. - If it is desired that DF = 2DE , apply AG 2 AB ; and so of any other ratio ; take AG to AB in the same ratio that it is desired to have DF to DE , and then proceed as in the ...
... tangent to the perpendicular BC , at E. = Scholium 2. - If it is desired that DF = 2DE , apply AG 2 AB ; and so of any other ratio ; take AG to AB in the same ratio that it is desired to have DF to DE , and then proceed as in the ...
Σελίδα 89
... tangent to the semicircle , the sides AB and AC will be equal , BC will be perpendicular to AP , and the shortest possible , or minimum , line that can be drawn through P to meet the lines AB and AC . 3. When MN does not meet the ...
... tangent to the semicircle , the sides AB and AC will be equal , BC will be perpendicular to AP , and the shortest possible , or minimum , line that can be drawn through P to meet the lines AB and AC . 3. When MN does not meet the ...
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AB² ABCD abscissa AC² AD² Analysis angle ABC angle BAC axis base Calculation.-1 CD² centre chord circular segment common tangent construction Construction.-Draw curve describe a circle determine the triangle diagonal diameter differential draw a line ellipse equal equation erect the perpendicular fall the perpendicular find angle given angle given circle given line given point given ratio Hence hyperbola hypothenuse inscribed intersect join latus rectum let fall meet parabola parallel to BC parallelogram perpen plane triangle Prob produced quadratrix quantity radii radius represent the required required triangle rhombus right angle right-angled triangle Scholium segment semicircle side BC similar triangles square tangent Theorem trapezium triangle ABC triangle are given vertical angle Whence
Δημοφιλή αποσπάσματα
Σελίδα 210 - PROP. X. THEOR. IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Σελίδα 210 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Σελίδα 139 - In a triangle, having given the base, the sum of the other two sides, and the length of a line drawn from the vertical angle to the middle of the base, to find the sides of the triangle.
Σελίδα 10 - ... algebra, or the modern analysis, from the mechanical facility of its operations, has contributed, especially on the Continent, to vitiate the taste and destroy the proper relish for the strictness and purity so conspicuous in the ancient method of demonstration. The study of geometrical analysis appears admirably fitted to improve the intellect, by training it to habits of precision, arrangement, and close application. If, the taste thus acquired be not allowed to obtain undue ascendancy, it...
Σελίδα 101 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Σελίδα 98 - Describe a circle which shall pass through two given points, and have its centre in a given line.
Σελίδα 25 - To trisect a right angle. 37. To divide a triangle into two parts by a line drawn parallel to a side, so that these parts shall be to each other as two given straight lines. 38. To divide a triangle into two parts by a line drawn perpendicular to the base, so that these parts shall...
Σελίδα 140 - In any plane triangle, as the base is to the sum of the other two sides, so is the difference of those sides to the difference of the segments of the base made by a perpendicular let fall from the vertical angle.
Σελίδα 30 - The lengths of three lines drawn from the three angles of a plane triangle to the middle of the opposite sides, being 18, 24, and 30, respectively ; it is required to find the sides.
Σελίδα 149 - PROBLEM XVII. IN a Right-angled Triangle, having given the Perimeter or Sum of all the Sides, and the Perpendicular let fall from the Right Angle on the Hypothenuse ; to determine the Triangle, that is, its Sides. PROBLEM XVIII.