The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 sider |
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Side 52
... rectangle , is said to be contained by any two of the straight lines which contain one of the right angles . 2. In every parallelogram , any of the parallelograms about a diameter , together with the two complements , is called a Gnomon ...
... rectangle , is said to be contained by any two of the straight lines which contain one of the right angles . 2. In every parallelogram , any of the parallelograms about a diameter , together with the two complements , is called a Gnomon ...
Side 53
... contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several ... rectangle contained by the straight lines A , BC , shall be equal to the rectangle contained by A , BD , together with ...
... contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several ... rectangle contained by the straight lines A , BC , shall be equal to the rectangle contained by A , BD , together with ...
Side 54
... rectangle contained by AB , BC , toge- ther with the rectangle ÃB , AC , shall be equal to the square on AB . [ Note . To avoid repeating the word contained too frequently , the rectangle contained by two straight lines AB , AC is ...
... rectangle contained by AB , BC , toge- ther with the rectangle ÃB , AC , shall be equal to the square on AB . [ Note . To avoid repeating the word contained too frequently , the rectangle contained by two straight lines AB , AC is ...
Side 55
... rectangle AE is equal to the rectangles AD , CE . But AE is the rectangle contained by AB , BC , for it is contained by AB , BE , of which BE is equal to BC ; ୯ F D [ I. 46 . B E and AD is contained by AC , CB , for CD is equal to CB ...
... rectangle AE is equal to the rectangles AD , CE . But AE is the rectangle contained by AB , BC , for it is contained by AB , BE , of which BE is equal to BC ; ୯ F D [ I. 46 . B E and AD is contained by AC , CB , for CD is equal to CB ...
Side 56
... rectangle contained by AC , CB , for CG is equal to CB ; therefore GE is also equal to the rectangle AC , CB . [ Ax . 1 . Therefore AG , GE are equal to twice the rectangle AC , CB . And HF , CK are the squares on AC , CB . Therefore ...
... rectangle contained by AC , CB , for CG is equal to CB ; therefore GE is also equal to the rectangle AC , CB . [ Ax . 1 . Therefore AG , GE are equal to twice the rectangle AC , CB . And HF , CK are the squares on AC , CB . Therefore ...
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Vanlige uttrykk og setninger
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore