Mathews' Euclid examination papers ... on Euc. i.-iv |
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Página 119
... taken for granted ; hence the importance of summarising his knowledge of Euclid in such a manner , that it can be readily applied to any hypothesis requiring demonstration . ( c ) The student must be cautioned against false reasoning ...
... taken for granted ; hence the importance of summarising his knowledge of Euclid in such a manner , that it can be readily applied to any hypothesis requiring demonstration . ( c ) The student must be cautioned against false reasoning ...
Página 128
... taken . 2. Divide a line 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 . Show that the point of section lies between the extremities of the line . 3 ...
... taken . 2. Divide a line 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 . Show that the point of section lies between the extremities of the line . 3 ...
Página 129
Edward Harri Mathews. On two straight lines not in the same plane are taken points A , B , C ; A1 , B1 , C1 respectively , prove that the three straight lines , each of which bisects both straight lines of one of the pairs of BC1 , B1C ...
Edward Harri Mathews. On two straight lines not in the same plane are taken points A , B , C ; A1 , B1 , C1 respectively , prove that the three straight lines , each of which bisects both straight lines of one of the pairs of BC1 , B1C ...
Página 170
... to the sides of a quadrilateral inscribed in a circle , through the middle points of those sides , meet in a point . 3. If any point be taken in the diameter of a circle which is not the centre , of all the straight 170.
... to the sides of a quadrilateral inscribed in a circle , through the middle points of those sides , meet in a point . 3. If any point be taken in the diameter of a circle which is not the centre , of all the straight 170.
Página 173
... taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from this point to the circumference , the greatest is that in which the centre is , and the other part of the dia- meter is the ...
... taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from this point to the circumference , the greatest is that in which the centre is , and the other part of the dia- meter is the ...
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.