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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Αποτελέσματα 1 - 5 από τα 87.
Σελίδα 21
... Whence this = the Construction . — Make AB = the given side , the angle B = given angle , and the line BD = the given sum of BC and AC . Join AD , and make the angle DAC = < ADC , then will ABC be the triangle required . BD ...
... Whence this = the Construction . — Make AB = the given side , the angle B = given angle , and the line BD = the given sum of BC and AC . Join AD , and make the angle DAC = < ADC , then will ABC be the triangle required . BD ...
Σελίδα 22
... whence the sequently ABC , is determined . Whence this Also , since CD ADC , and con- Construction . - Make AB― the given side , and the angle ABC the given angle . Produce CB , making BD = the given difference . Join AD , and make the ...
... whence the sequently ABC , is determined . Whence this Also , since CD ADC , and con- Construction . - Make AB― the given side , and the angle ABC the given angle . Produce CB , making BD = the given difference . Join AD , and make the ...
Σελίδα 23
... Whence this Construction . In any line , make EB the given difference , the angle BEC = 674 ° , and let EC meet a perpendicular erected at B , in C. On BC describe the square ABCD , which will be the one required . Demonstration ...
... Whence this Construction . In any line , make EB the given difference , the angle BEC = 674 ° , and let EC meet a perpendicular erected at B , in C. On BC describe the square ABCD , which will be the one required . Demonstration ...
Σελίδα 25
... whence we have angle CAD ; then , in △ ABC , Case 1 , find AB and BC . Limits , and the discussion of the general problem . 1. In applying the given side AC to the line DF ( see Fig . 2 ) in the above construction , if the arc were ...
... whence we have angle CAD ; then , in △ ABC , Case 1 , find AB and BC . Limits , and the discussion of the general problem . 1. In applying the given side AC to the line DF ( see Fig . 2 ) in the above construction , if the arc were ...
Σελίδα 31
... Whence this Construction . - Draw any line , as AB , on which erect the perpen- dicular FP equal to one of the given perpendiculars . At P draw lines making with PF angles equal to 120 ° , and on them lay PG and PH respectively equal to ...
... Whence this Construction . - Draw any line , as AB , on which erect the perpen- dicular FP equal to one of the given perpendiculars . At P draw lines making with PF angles equal to 120 ° , and on them lay PG and PH respectively equal to ...
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AB² ABCD abscissa AC² AD² Analysis angle ABC angle BAC axis base BC² 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 radius Hence hyperbola hypothenuse inscribed intersect join latus rectum let fall meet parabola parallel to BC parallelogram plane triangle Prob produced quadratrix radii 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 212 - 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 212 - 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 141 - 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 103 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Σελίδα 100 - Describe a circle which shall pass through two given points, and have its centre in a given line.
Σελίδα 27 - 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 142 - 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 32 - 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 151 - 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.