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 100.
Σελίδα 3
... line . Join AB , and bisect it in F , and from F draw FE at right angles to AB meet- ing CD in E ; E is the point required ... line given in position , to draw two lines which shall meet in that line , and make equal angles with it , Let A ...
... line . Join AB , and bisect it in F , and from F draw FE at right angles to AB meet- ing CD in E ; E is the point required ... line given in position , to draw two lines which shall meet in that line , and make equal angles with it , Let A ...
Σελίδα 5
... lines equal to each other , viz . one on each side of AD . Make DE = DF , and join AE ... line more remote is equal to one nearer the perpendi- cular , which is ... required . B Draw AE parallel to BD , and .. perpendicular to EF . The ...
... lines equal to each other , viz . one on each side of AD . Make DE = DF , and join AE ... line more remote is equal to one nearer the perpendi- cular , which is ... required . B Draw AE parallel to BD , and .. perpendicular to EF . The ...
Σελίδα 6
... required to draw a line through P which shall be terminated by the given lines , and divided in any given ratio in P , draw PD parallel to AC , and take AD : DE in the given ratio , and draw EPF , it will be the line required . ( 10 ...
... required to draw a line through P which shall be terminated by the given lines , and divided in any given ratio in P , draw PD parallel to AC , and take AD : DE in the given ratio , and draw EPF , it will be the line required . ( 10 ...
Σελίδα 7
... line required . D B P E For since DE is parallel to AC , ( Eucl . vi . 2. ) DB : BE :: AB : BC , i . e . in the given ratio . ( 12. ) If from a given point any number of straight lines be drawn in a straight line given to position ; to ...
... line required . D B P E For since DE is parallel to AC , ( Eucl . vi . 2. ) DB : BE :: AB : BC , i . e . in the given ratio . ( 12. ) If from a given point any number of straight lines be drawn in a straight line given to position ; to ...
Σελίδα 7
... line being drawn parallel to one of the lines containing a given angle and ... required . For since DE and CP are parallel to AB , AD : EB :: DF : EF :: PF ... line required . Draw IK parallel to EG ; then the triangles IEK , EFG are ...
... line being drawn parallel to one of the lines containing a given angle and ... required . For since DE and CP are parallel to AB , AD : EB :: DF : EF :: PF ... line required . Draw IK parallel to EG ; then the triangles IEK , EFG are ...
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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.