Mathews' Euclid examination papers ... on Euc. i.-iv |
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Side 118
... proposition is directly inferred from the premisses naturally arising by a series of successive steps from the hypothesis , the theorem is said to be direct , e.g. , Bk . I. , Prop . 4 . When a proposition is proved to be true , by ...
... proposition is directly inferred from the premisses naturally arising by a series of successive steps from the hypothesis , the theorem is said to be direct , e.g. , Bk . I. , Prop . 4 . When a proposition is proved to be true , by ...
Side 120
... Proposition . These are stated by Proclus to be as follows : - - 1. The Proposition or general enunciation , which states in general terms the conditions of the problem or theorem . 2. The exposition or particular enunciation , which ...
... Proposition . These are stated by Proclus to be as follows : - - 1. The Proposition or general enunciation , which states in general terms the conditions of the problem or theorem . 2. The exposition or particular enunciation , which ...
Side 121
... Propositions of Euclid , their connection and mutual dependence one upon the other , before proceeding to work exercises bearing upon them . The following remarks given by RITCHIE will be found useful : - 1. A point is said to be given ...
... Propositions of Euclid , their connection and mutual dependence one upon the other , before proceeding to work exercises bearing upon them . The following remarks given by RITCHIE will be found useful : - 1. A point is said to be given ...
Side 128
... proposition for an obtuse- angled triangle . 4. Inscribe an equilateral and equiangular 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 ...
... proposition for an obtuse- angled triangle . 4. Inscribe an equilateral and equiangular 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 ...
Side 130
... fixed points on a circle from which tangents are drawn to any concentric circle ; the chords joining the points of contact which are not parallel to AB will pass through a fixed point . Fan . 1871 . 1. When is one proposition said 130.
... fixed points on a circle from which tangents are drawn to any concentric circle ; the chords joining the points of contact which are not parallel to AB will pass through a fixed point . Fan . 1871 . 1. When is one proposition said 130.
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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...
Side 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.
Side 156 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Side 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.
Side 153 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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.
Side 130 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 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.