Mathews' Euclid examination papers ... on Euc. i.-iv |
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Página 127
Edward Harri Mathews. 3. If two straight lines cut one another within a circle , the rectangle contained by the ... half that of the quadrilateral . Fan . 1869 . 1. Equal triangles on equal bases in the same straight line and on the ...
Edward Harri Mathews. 3. If two straight lines cut one another within a circle , the rectangle contained by the ... half that of the quadrilateral . Fan . 1869 . 1. Equal triangles on equal bases in the same straight line and on the ...
Página 129
... line joining D to the pole of BC is parallel to AB . Given the centres of four circles , determine their radii , so ... half the line and of the square on the line between the points of section . The diagonals of a quadrilateral meet in ...
... line joining D to the pole of BC is parallel to AB . Given the centres of four circles , determine their radii , so ... half the line and of the square on the line between the points of section . The diagonals of a quadrilateral meet in ...
Página 131
... line thus produced , and the square on the part of it produced , are together double of the square on half the line bisected and of the square on the line made up of the half and the part produced . Produce a given straight line so that ...
... line thus produced , and the square on the part of it produced , are together double of the square on half the line bisected and of the square on the line made up of the half and the part produced . Produce a given straight line so that ...
Página 136
... lines meeting BC , C1A1 , A1B1 , in a b c respec- tively ; prove that the triangle abc is half the triangle ABC , and that bc passes through A , ca through B , ab through C. 2. The angles in the same segment of a circle are equal to one ...
... lines meeting BC , C1A1 , A1B1 , in a b c respec- tively ; prove that the triangle abc is half the triangle ABC , and that bc passes through A , ca through B , ab through C. 2. The angles in the same segment of a circle are equal to one ...
Página 138
... line DE be drawn at right angles to BC , meeting a side AC in E ; prove ( by the method of the First Book ) that the rectangle contained by EC , AC is half the square on BC , and that the square on EC is equal to the squares on EA , AB ...
... line DE be drawn at right angles to BC , meeting a side AC in E ; prove ( by the method of the First Book ) that the rectangle contained by EC , AC is half the square on BC , and that the square on EC is equal to the squares on EA , AB ...
Términos y frases comunes
acute angle angle contained angle equal angled triangle angular points base centre chord circle are equal circle described circumference cuts the circle Describe a square diameter draw a straight equal circles equal in area equilateral triangle exterior angle fixed circle given circle given point given square given straight line given triangle half the line hypothenuse Inscribe a circle isosceles triangle line be divided line be drawn line is equal LONDON SCHOOL BOARD London University MATRICULATION middle points Notes of Lessons obtuse angle opposite angles opposite sides parallel straight lines parallelogram are equal perpendicular point of contact proposition prove Pupil Teachers quadrilateral figure rectangle contained rectilineal figure rhombus right angles right-angled triangle segment side subtending sides containing sides equal square on half squares described straight line intercepted straight lines cut student tangents theorem third angle touch a circle triangle the square twice the rectangle vertex whole line
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.