Mathews' Euclid examination papers ... on Euc. i.-iv |
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Página 127
... touch A in points lying on a tangent to B. In a given quadrilateral a parallelogram is inscribed , whose sides are parallel to the diagonals of the quadrilateral ; prove that the diagonals of all such parallelograms intersect on the ...
... touch A in points lying on a tangent to B. In a given quadrilateral a parallelogram is inscribed , whose sides are parallel to the diagonals of the quadrilateral ; prove that the diagonals of all such parallelograms intersect on the ...
Página 130
... touch a circle , and from the point of contact a straight line be drawn cutting the circle , the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the ...
... touch a circle , and from the point of contact a straight line be drawn cutting the circle , the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the ...
Página 131
... touch a circle , and from the point of contact a straight line be drawn cutting the circle , the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the ...
... touch a circle , and from the point of contact a straight line be drawn cutting the circle , the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the ...
Página 135
... touch externally ; prove that the line drawn at right angles to this straight line , through` its intersection with the tangent at the common point , passes through the point midway between the centres . 4. In a given circle inscribe a ...
... touch externally ; prove that the line drawn at right angles to this straight line , through` its intersection with the tangent at the common point , passes through the point midway between the centres . 4. In a given circle inscribe a ...
Página 136
... touching the fixed circle at P and Q ; prove that the two circles so described will inter- sect on another fixed circle . 4. Describe an isosceles triangle having each of the angles at the base double of the third angle . Prove that the ...
... touching the fixed circle at P and Q ; prove that the two circles so described will inter- sect on another fixed circle . 4. Describe an isosceles triangle having each of the angles at the base double of the third angle . Prove that the ...
Términos y frases comunes
acute angle angle equal angled triangle angular points base bisect CANDIDATES centre Certificate chord Christmas circle described circumference common Complete Construct cuts the circle diagonals diameter difference double draw a straight equiangular equilateral triangle EUCLID Examinations exercises exterior angle fall figure Find fixed circle four GEOMETRY given circle given point given straight line given triangle greater half the line inscribed interior isosceles triangle length less line be divided line be drawn line drawn line is equal line joining London Mathematical MATRICULATION meet middle points obtuse angle opposite angles opposite sides pair parallel parallelogram pass pentagon perpendicular point of contact problem produced proposition prove Pupil Teachers quadrilateral questions rectangle contained regular respectively rhombus right angles right-angled triangle Scholarship Section segment side subtending sides containing squares described student taken tangents theorem third angle touch twice the rectangle unequal whole line Write
Pasajes populares
Página 160 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 154 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Página 184 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Página 156 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Página 182 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Página 153 - Any two sides of a triangle are together greater than the third side.
Página 167 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Página 164 - 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.
Página 130 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Página 154 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.