Mathews' Euclid examination papers ... on Euc. i.-iv |
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Σελίδα 128
... pentagon in a given circle . Show that the circles , each of which touches two sides at the extremities of a third , meet in a point . Given the inscribed and circumscribed circles of a triangle , the centre of perpendiculars will lie ...
... pentagon in a given circle . Show that the circles , each of which touches two sides at the extremities of a third , meet in a point . Given the inscribed and circumscribed circles of a triangle , the centre of perpendiculars will lie ...
Σελίδα 130
... pentagon five straight lines can be drawn by joining each angular point to the next angular point but one ; if four of these straight lines are parallel to the opposite sides of the pentagon and the perpendicular distances between these ...
... pentagon five straight lines can be drawn by joining each angular point to the next angular point but one ; if four of these straight lines are parallel to the opposite sides of the pentagon and the perpendicular distances between these ...
Σελίδα 136
... sides such that a regular pentagon can be inscribed in the circle having these portions as two of its sides . Upon the sides of a triangle , ABC as bases , are described three equilateral triangles , a BC , bCA , and 136.
... sides such that a regular pentagon can be inscribed in the circle having these portions as two of its sides . Upon the sides of a triangle , ABC as bases , are described three equilateral triangles , a BC , bCA , and 136.
Σελίδα 139
... pentagon in a given circle . If ABCDE be the pentagon , and if P be the middle point of the arc AB , prove that AP , together with the radius of the circle , is equal to PC . Prove that , if the tangents at B and C to the circle ABC ...
... pentagon in a given circle . If ABCDE be the pentagon , and if P be the middle point of the arc AB , prove that AP , together with the radius of the circle , is equal to PC . Prove that , if the tangents at B and C to the circle ABC ...
Σελίδα 143
... pentagon inscribe a circle in it . MATRICULATION , JANUARY 1875 . Afternoon , 3 to 6 . GEOMETRY . 1. Construct an isosceles triangle whose base and angle at the vertex are given . 2. The greater side in every triangle is opposite to the ...
... pentagon inscribe a circle in it . MATRICULATION , JANUARY 1875 . Afternoon , 3 to 6 . GEOMETRY . 1. Construct an isosceles triangle whose base and angle at the vertex are given . 2. The greater side in every triangle is opposite to the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 156 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Σελίδα 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.
Σελίδα 153 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 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.
Σελίδα 130 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 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.