Mathews' Euclid examination papers ... on Euc. i.-iv |
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Página 126
... opposite side pro- duced , the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle , by twice the rectangle contained by the side on which , when produced , the ...
... opposite side pro- duced , the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle , by twice the rectangle contained by the side on which , when produced , the ...
Página 129
... side equal to one side , namely , either the sides adjacent to the equal angles , or sides which are opposite to equal angles in each , then shall the other sides be equal , each to each , also the third angle of the one equal to the ...
... side equal to one side , namely , either the sides adjacent to the equal angles , or sides which are opposite to equal angles in each , then shall the other sides be equal , each to each , also the third angle of the one equal to the ...
Página 130
... opposite sides of the pentagon and the perpendicular distances between these parallels are equal , prove that the pentagon is regular . A and B are two fixed points on a circle from which tangents are drawn to any concentric circle ...
... opposite sides of the pentagon and the perpendicular distances between these parallels are equal , prove that the pentagon is regular . A and B are two fixed points on a circle from which tangents are drawn to any concentric circle ...
Página 131
... opposite sides in A , B , C1 respectively ; prove that the triangles AB1C1 , BC11 , CA1B1 are all equal . 2. If a straight line be bisected , and produced to any point , the square on the whole line thus produced , and the square on the ...
... opposite sides in A , B , C1 respectively ; prove that the triangles AB1C1 , BC11 , CA1B1 are all equal . 2. If a straight line be bisected , and produced to any point , the square on the whole line thus produced , and the square on the ...
Página 132
... sides lie on a fixed circle . A quadrilateral is divided into four equal ... side subtending the right angle is equal to the sum of the squares described on the ... opposite angles of any quadrilateral figure in- scribed in a circle are ...
... sides lie on a fixed circle . A quadrilateral is divided into four equal ... side subtending the right angle is equal to the sum of the squares described on the ... opposite angles of any quadrilateral figure in- scribed in a circle are ...
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.