Geometrical Problems Deducible from the First Six Books of Euclid: Arranged and Solved: to which is Added an Appendix Containing the Elements of Plane Trigonometry ...J. Smith, 1827 - 377 σελίδες |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα ii
... locus of the points of section , which divide them in a given ratio . 13. A straight line being drawn parallel to one of the lines con- taining a given angle , and produced to meet the other ; through a given point within the angle to ...
... locus of the points of section , which divide them in a given ratio . 13. A straight line being drawn parallel to one of the lines con- taining a given angle , and produced to meet the other ; through a given point within the angle to ...
Σελίδα iv
... locus of the extremity of the other . 34. If from two given points straight lines be drawn containing a given angle , and from each of them segments be cut off having a given ratio ; and the extremities of the segments of the lines ...
... locus of the extremity of the other . 34. If from two given points straight lines be drawn containing a given angle , and from each of them segments be cut off having a given ratio ; and the extremities of the segments of the lines ...
Σελίδα v
... outer ; it will be bisected at the point of contact . 10. If any number of equal straight lines be placed in a circle ; to determine the locus of their points of bisection . iv 11. If from a point in the circumference of CONTENTS . < : vii.
... outer ; it will be bisected at the point of contact . 10. If any number of equal straight lines be placed in a circle ; to determine the locus of their points of bisection . iv 11. If from a point in the circumference of CONTENTS . < : vii.
Σελίδα vi
... locus of the ex- tremities of these lines . 13. If from a given point without a given circle straight lines be drawn and terminated by the circumference ; to determine the locus of the points which divide them in a given ratio . 14 ...
... locus of the ex- tremities of these lines . 13. If from a given point without a given circle straight lines be drawn and terminated by the circumference ; to determine the locus of the points which divide them in a given ratio . 14 ...
Σελίδα xx
... locus of its intersection with the line parallel to the hypothenuse will be a straight line . 32. If from the angles of a triangle , lines , each equal to a given line , be drawn to the opposite sides ( produced if necessary ) ; and ...
... locus of its intersection with the line parallel to the hypothenuse will be a straight line . 32. If from the angles of a triangle , lines , each equal to a given line , be drawn to the opposite sides ( produced if necessary ) ; and ...
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Άλλες εκδόσεις - Προβολή όλων
Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ... Miles Bland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Geometrical Problems Deducible From the First Six Books of Euclid: Arranged ... Miles Bland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ... Miles Bland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC base bisect the angle centre chord circle ABC circles cut circumference describe a circle divided draw a line drawn parallel duplicate ratio equal angles equiangular Eucl extremities G draw given angle given circle given in position given line given point given ratio given square given straight line intercepted isosceles triangle Join AB Join AE Join BD Let AB Let ABC let fall line given line joining line required lines be drawn lines drawn mean proportional opposite sides parallel to AC parallelogram pendicular point of bisection point of contact point of intersection radius rectangle rectangle contained right angles right-angled triangle segments semicircle shewn tangent touching the circle trapezium triangle ABC whence
Δημοφιλή αποσπάσματα
Σελίδα 10 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Σελίδα xv - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
Σελίδα xxx - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 303 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Σελίδα 140 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other...
Σελίδα 329 - CE is equal to the difference of the segments of the base made by the perpendicular.
Σελίδα 109 - If from a point, without a parallelogram, there be drawn two straight lines to the extremities of the two opposite sides, between which, when produced, the point does not lie, the difference of the triangles thus formed is equal to half the parallelogram. Ex. 2. The two triangles, formed by drawing straight lines from any point within a parallelogram to the extremities of its opposite sides, are together half of the parallelogram.
Σελίδα 164 - PROPOSITION I. PROBLEM. — To describe an equilateral triangle upon a given finite straight line. Let AB be the given straight line; it is required to describe an equilateral triangle upon it.
Σελίδα 281 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.
Σελίδα 270 - AB describe a segment of a circle containing an angle equal to the given angle, (in.