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, 1819 - 377 σελίδες |
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Αποτελέσματα 1 - 5 από τα 68.
Σελίδα i
... distances , and any point without the perpendicular is at unequal distances , from the extre- mities of the line . 3. Through a given point , to draw a straight line which shall make equal angles with two straight lines given in ...
... distances , and any point without the perpendicular is at unequal distances , from the extre- mities of the line . 3. Through a given point , to draw a straight line which shall make equal angles with two straight lines given in ...
Σελίδα iii
... distances of the point of unequal section from one extremity of the given line , from its middle point , from the extremity of the part produced , and from the other extremity of the given line , be proportionals . 24. Three points ...
... distances of the point of unequal section from one extremity of the given line , from its middle point , from the extremity of the part produced , and from the other extremity of the given line , be proportionals . 24. Three points ...
Σελίδα iv
... distances from the former points in a given ratio . 28. If a straight line be divided into any two parts and pro- duced , so that the segments may have the same ratio that the whole line produced has to the part produced , and from the ...
... distances from the former points in a given ratio . 28. If a straight line be divided into any two parts and pro- duced , so that the segments may have the same ratio that the whole line produced has to the part produced , and from the ...
Σελίδα ix
... distances of the point without the circle from each extremity of the diameter , have to each other . 43. If from the extremity of the diameter of a given semicircle a straight line be drawn in it , equal to the radius , and from the ...
... distances of the point without the circle from each extremity of the diameter , have to each other . 43. If from the extremity of the diameter of a given semicircle a straight line be drawn in it , equal to the radius , and from the ...
Σελίδα xii
... distances of these points from the circum- ference have . 66. Two circles being given in position and magnitude ; to draw a straight line cutting them so that the chords in each circle may be equal to a given line , not greater than the ...
... distances of these points from the circum- ference have . 66. Two circles being given in position and magnitude ; to draw a straight line cutting them so that the chords in each circle may be equal to a given line , not greater than the ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angles at F base centre chord circle ABC circles cut circles touch circumference describe a circle divided draw a line draw the diameter 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 given triangle intercepted isosceles triangle Join AE Join BD Let AB Let ABC let fall line given line joining line required lines be drawn lines drawn mean proportional opposite side parallel to BC parallelogram pendicular point of bisection point of contact point of intersection point required radius rectangle right angles segments semicircle shewn tangent touching the circle trapezium triangle ABC
Δημοφιλή αποσπάσματα
Σελίδα 14 - 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 xiii - 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 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 327 - 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 158 - 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 212 - FC are equal to one another : wherefore the circle described from the centre F, at the distance of one of them, will pass through the extremities of the other two, and be described about the triangle ABC.
Σελίδα 123 - 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 305 - 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 247 - The perpendicular from the vertex on the base of an equilateral triangle is equal to the side of an equilateral triangle inscribed in a circle, whose diameter is the base.
Σελίδα 299 - AB be equal to the given bisecting line ; and upon it describe a segment of a circle containing an angle equal to the given angle.