Mathews' Euclid examination papers ... on Euc. i.-iv |
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Σελίδα 126
... respectively , and K , L , M are the feet of the perpendiculars on the same sides from the opposite angles . Prove that the greatest of the rectangles contained by BC and DK , CA and EL , AB and FM is equal to the sum of the other two ...
... respectively , and K , L , M are the feet of the perpendiculars on the same sides from the opposite angles . Prove that the greatest of the rectangles contained by BC and DK , CA and EL , AB and FM is equal to the sum of the other two ...
Σελίδα 129
... respectively , prove that the three straight lines , each of which bisects both straight lines of one of the pairs of BC1 , B1C ; CA1 , CA ; AB , A1B will meet in a point . Two chords AB , AC of a circle are drawn ; the perpen- dicular ...
... respectively , prove that the three straight lines , each of which bisects both straight lines of one of the pairs of BC1 , B1C ; CA1 , CA ; AB , A1B will meet in a point . Two chords AB , AC of a circle are drawn ; the perpen- dicular ...
Σελίδα 131
... 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 part of it produced , are ...
... 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 part of it produced , are ...
Σελίδα 134
... respectively in one case , and perpendicular to AC , BA , CB in the other case ; prove that these two triangles are in all respects equal . 1 3. If from an external point two straight lines be drawn , one of which cuts a circle and the ...
... respectively in one case , and perpendicular to AC , BA , CB in the other case ; prove that these two triangles are in all respects equal . 1 3. If from an external point two straight lines be drawn , one of which cuts a circle and the ...
Σελίδα 135
... respectively . Two equal circles touch at A ; a circle of twice the radius is described having internal contact with one of them at B , ana cutting the other in P , Q ; prove that the straight line AB will pass through either P or Q ...
... respectively . Two equal circles touch at A ; a circle of twice the radius is described having internal contact with one of them at B , ana cutting the other in P , Q ; prove that the straight line AB will pass through either P or Q ...
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.