The elements of plane geometry, Volum 1 |
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Side 56
... divided into as many triangles OAB , OBC , & c . , as the polygon has sides , and in each triangle the angles are together equal to two right angles , I. 25 . therefore all the angles of all the triangles are together equal to twice as ...
... divided into as many triangles OAB , OBC , & c . , as the polygon has sides , and in each triangle the angles are together equal to two right angles , I. 25 . therefore all the angles of all the triangles are together equal to twice as ...
Side 109
... equal to CG , and therefore to AB . Hence the rectangle contained by AB and CD is equal to the sum of the rectangles contained by AB and CE , AB and EF , AB and FD . Q.E.D. COR . 1. If a straight line is divided into EQUALITY OF AREAS .
... equal to CG , and therefore to AB . Hence the rectangle contained by AB and CD is equal to the sum of the rectangles contained by AB and CE , AB and EF , AB and FD . Q.E.D. COR . 1. If a straight line is divided into EQUALITY OF AREAS .
Side 110
... divided . COR . 2. If a straight line is divided into two parts , the square on the whole line is equal to the sum of the rectangles contained by the whole line and each of the parts . This follows from Theor . 5 by taking the two lines ...
... divided . COR . 2. If a straight line is divided into two parts , the square on the whole line is equal to the sum of the rectangles contained by the whole line and each of the parts . This follows from Theor . 5 by taking the two lines ...
Side 112
... divided internally into two 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 internally into two 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 ...
Side 113
... divided externally into two 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 ...
... divided externally into two 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 ...
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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.