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 ... |
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... parallelograms , squares and polygons . The 5th section contains those which require lines to be drawn in certain directions , but which involve properties of rectangles or squares , or such others as were excluded from the three first ...
... parallelograms , squares and polygons . The 5th section contains those which require lines to be drawn in certain directions , but which involve properties of rectangles or squares , or such others as were excluded from the three first ...
Page xxii
... parallelogram . 3. To bisect a parallelogram by a line drawn from a point in one of its sides . 4. If from any point in the diameter ( or diameter produced ) of a parallelogram straight lines be drawn to the opposite angles ; they will ...
... parallelogram . 3. To bisect a parallelogram by a line drawn from a point in one of its sides . 4. If from any point in the diameter ( or diameter produced ) of a parallelogram straight lines be drawn to the opposite angles ; they will ...
Page xxiii
... parallelogram ( in the last problem ) ; and its ratio to the trapezium . 16. If two sides of a trapezium be parallel ; its area is equal to half that of a parallelogram whose base is the sum of those two sides , and altitude the ...
... parallelogram ( in the last problem ) ; and its ratio to the trapezium . 16. If two sides of a trapezium be parallel ; its area is equal to half that of a parallelogram whose base is the sum of those two sides , and altitude the ...
Page xxiv
... parallelograms described on the two sides of a triangle is equal to that of a parallelogram on the base , whose side is equal and parallel to the line drawn from the vertex of the triangle to the intersection of the two sides of the ...
... parallelograms described on the two sides of a triangle is equal to that of a parallelogram on the base , whose side is equal and parallel to the line drawn from the vertex of the triangle to the intersection of the two sides of the ...
Page xxv
... parallelogram lines be drawn to the angular points ; the sums of the squares of those which are drawn to the opposite angles are equal . 34. The squares of the diagonals of a parallelogram are together equal to the squares of the four ...
... parallelogram lines be drawn to the angular points ; the sums of the squares of those which are drawn to the opposite angles are equal . 34. The squares of the diagonals of a parallelogram are together equal to the squares of the four ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 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.
Page 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...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.