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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Σελίδα iii
... meeting the three lines be harmonically divided . 23. If a straight line be divided into two equal and also into two unequal parts , and be produced , so that the part produced may have to the whole line so produced , the same ratio ...
... meeting the three lines be harmonically divided . 23. If a straight line be divided into two equal and also into two unequal parts , and be produced , so that the part produced may have to the whole line so produced , the same ratio ...
Σελίδα iv
... meeting these perpendiculars , will be divided at that point into parts which have the same ratio , that those lines have which are drawn from the extremity of the produced line to the points of intersection with the perpendicular ...
... meeting these perpendiculars , will be divided at that point into parts which have the same ratio , that those lines have which are drawn from the extremity of the produced line to the points of intersection with the perpendicular ...
Σελίδα vi
... meeting a diameter ; the points of intersection are equally distant from the centre . 18. If from the extremities of the diameter of a semicircle per- pendiculars be let fall on any line cutting the semicircle ; the parts intercepted ...
... meeting a diameter ; the points of intersection are equally distant from the centre . 18. If from the extremities of the diameter of a semicircle per- pendiculars be let fall on any line cutting the semicircle ; the parts intercepted ...
Σελίδα viii
... meeting the circumferences ; the part of it intercepted between the circumferences will be bisected by the circle whose diameter is the common chord of the equal circles . 32. If two circles touch each other externally or internally ...
... meeting the circumferences ; the part of it intercepted between the circumferences will be bisected by the circle whose diameter is the common chord of the equal circles . 32. If two circles touch each other externally or internally ...
Σελίδα ix
... meeting the circumferences of the other two circles ; this diameter and the lines joining the points of intersection and contact are in continued proportion . 41. If a common tangent be drawn to any number of circles which touch each ...
... meeting the circumferences of the other two circles ; this diameter and the lines joining the points of intersection and contact are in continued proportion . 41. If a common tangent be drawn to any number of circles which touch each ...
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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.