Mathews' Euclid examination papers ... on Euc. i.-iv |
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Σελίδα 118
... prove . Every theorem consists of a subject , or hypothesis , and a predicate , or conclusion , requiring ... proved to be true , by showing that any supposition to the contrary would lead to what logicians call a reductio ad absurdum ...
... prove . Every theorem consists of a subject , or hypothesis , and a predicate , or conclusion , requiring ... proved to be true , by showing that any supposition to the contrary would lead to what logicians call a reductio ad absurdum ...
Σελίδα 119
... PROVING THEOREMS . ( a ) A theorem is generally proved by assuming the truth of its predicate , and deducing therefrom , by the aid of accepted geometrical truths , the successive steps necessary to obtain the hypothesis first assumed ...
... PROVING THEOREMS . ( a ) A theorem is generally proved by assuming the truth of its predicate , and deducing therefrom , by the aid of accepted geometrical truths , the successive steps necessary to obtain the hypothesis first assumed ...
Σελίδα 120
... prove the truth or falsehood of the theorem , the possibility or impossibility of the problem in that particular case exhibited in the diagram . 6. The conclusion is merely the repetition of the general enunciation , wherein the ...
... prove the truth or falsehood of the theorem , the possibility or impossibility of the problem in that particular case exhibited in the diagram . 6. The conclusion is merely the repetition of the general enunciation , wherein the ...
Σελίδα 126
... prove that either the angles are equal , or the third angle is equal to the angle of an equilateral triangle . Fan . 1868 . 1. If a parallelogram and a triangle be on the same base and between the same parallels , the parallelogram ...
... prove that either the angles are equal , or the third angle is equal to the angle of an equilateral triangle . Fan . 1868 . 1. If a parallelogram and a triangle be on the same base and between the same parallels , the parallelogram ...
Σελίδα 127
... prove that their common tangents will touch A in points lying on a tangent to B. In a given quadrilateral a parallelogram is inscribed , whose sides are parallel to the diagonals of the quadrilateral ; prove that the diagonals of all ...
... prove that their common tangents will touch A in points lying on a tangent to B. In a given quadrilateral a parallelogram is inscribed , whose sides are parallel to the diagonals of the quadrilateral ; prove that the diagonals of all ...
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.