The elements of plane geometry, Volum 1 |
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Side 112
... segments , is greater than the sum of the squares segments by twice the rectangle contained by them . on the Ex . 14. Give the algebraical formula corresponding to Theor . 6 . Ex . 15. If a straight line is divided into three parts ...
... segments , is greater than the sum of the squares segments by twice the rectangle contained by them . on the Ex . 14. Give the algebraical formula corresponding to Theor . 6 . Ex . 15. If a straight line is divided into three parts ...
Side 113
... segments , is less than the sum of the squares on the segments by twice the rectangle contained by them . Ex . 16. Give the algebraical formula corresponding to Theor . 7 . I THEOR . 8. The difference of the squares on two EQUALITY OF ...
... segments , is less than the sum of the squares on the segments by twice the rectangle contained by them . Ex . 16. Give the algebraical formula corresponding to Theor . 7 . I THEOR . 8. The difference of the squares on two EQUALITY OF ...
Side 115
... segments is equal to the difference of the squares on half the line and on the line between the point of division and the middle point of the line . Ex . 17. Give the algebraical formula corresponding to Theor . 8 . Ex . 18. Prove that ...
... segments is equal to the difference of the squares on half the line and on the line between the point of division and the middle point of the line . Ex . 17. Give the algebraical formula corresponding to Theor . 8 . Ex . 18. Prove that ...
Side 124
... segments is double the sum of the squares on half the line and on the line between the point of division and the middle point of the line . Let the straight line AB be bisected at C and divided internally or externally at D : E B B then ...
... segments is double the sum of the squares on half the line and on the line between the point of division and the middle point of the line . Let the straight line AB be bisected at C and divided internally or externally at D : E B B then ...
Side 132
... segments such that the rectangle contained by the given line and one of the segments may be equal to the square on the other segment . Let AB be the given straight line : it is required to divide it internally and externally so that the ...
... segments such that the rectangle contained by the given line and one of the segments may be equal to the square on the other segment . Let AB be the given straight line : it is required to divide it internally and externally so that the ...
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Vanlige uttrykk og setninger
AB is equal ABCD AC is equal adjacent angles adjoining sides alternate angle angle ABC angle ACB angle AFG angle BAC angle CAB angle DEF angle EDF angle FGD angles are equal angles equal BA and AC base BC bisector bisects centre circle cutting Constr construct a triangle contrapositive diagonal distance draw a circle equal angles equal to AC equal to CD exterior angle find the locus Geometry given angle given point given straight line greater Hence hypotenuse identically equal interior opposite angle isosceles triangle less Let ABC meet middle point obtuse angle opposite sides parallel straight lines parallelogram perpendicular point equidistant Prob produced quadrilateral rectangle contained rectangle whose base right angles right-angled triangle shew side AB side AC sides equal square on AC squares on AB straight line drawn Theorem trapezium triangle ABC triangles are identically twice the rectangle vertex
Populære avsnitt
Side 27 - 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. either the sides adjacent to the equal...
Side 98 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 35 - Any two sides of a triangle are together greater than the third side.
Side 26 - The straight lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal to one another.
Side 37 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Side 70 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 110 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 31 - Any two angles of a triangle are together less than two right angles.
Side 115 - In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6.