Mathews' Euclid examination papers ... on Euc. i.-iv |
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Page 129
... points of section . The diagonals of a quadrilateral meet in E , and F is the middle point of the straight line joining the middle points of the diagonals : prove that the sum of the squares on the straight lines joining E to the angular ...
... points of section . The diagonals of a quadrilateral meet in E , and F is the middle point of the straight line joining the middle points of the diagonals : prove that the sum of the squares on the straight lines joining E to the angular ...
Page 130
... points by four times the square on EF 3. If a straight line touch a circle , and from the point of contact a ... angular point to the next angular point but one ; if four of these straight lines are parallel to the opposite sides of the ...
... points by four times the square on EF 3. If a straight line touch a circle , and from the point of contact a ... angular point to the next angular point but one ; if four of these straight lines are parallel to the opposite sides of the ...
Page 131
... angular points A , B , C of a triangle are drawn three parallel straight lines meeting the opposite sides in A1 , B ' , C1 respectively ; prove that the triangles AB1C1 , BC11 , CA1B1 are all equal . 2. If a straight line be bisected ...
... angular points A , B , C of a triangle are drawn three parallel straight lines meeting the opposite sides in A1 , B ' , C1 respectively ; prove that the triangles AB1C1 , BC11 , CA1B1 are all equal . 2. If a straight line be bisected ...
Page 132
... point ; prove that the middle points of its sides lie on a fixed circle . A quadrilateral is divided into four equal triangles by lines joining its angular points to a point within it , prove that one of its diagonals must be bisected ...
... point ; prove that the middle points of its sides lie on a fixed circle . A quadrilateral is divided into four equal triangles by lines joining its angular points to a point within it , prove that one of its diagonals must be bisected ...
Page 133
Edward Harri Mathews. Having given an angular point of a triangle , the circum- scribed circle , and the centre of ... points of one triangle lie on the sides of another ; if the latter triangle be thus divided into four equal parts ...
Edward Harri Mathews. Having given an angular point of a triangle , the circum- scribed circle , and the centre of ... points of one triangle lie on the sides of another ; if the latter triangle be thus divided into four equal parts ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 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.
Page 156 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 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.
Page 153 - Any two sides of a triangle are together greater than the third side.
Page 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.
Page 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.
Page 130 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 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.